2403.17898v2

# Octree-GS: Towards Consistent Real-time Rendering with LOD-Structured 3D Gaussians **Authors**: Kerui Ren, Lihan Jiang, Tao Lu, Mulin Yu, Linning Xu, Zhangkai Ni, Bo Dai > K. Ren is with Shanghai Jiao Tong University and Shanghai AI Laboratory. E-mail: Jiang is with The University of Science and Technology of China and Shanghai AI Laboratory. E-mail: Lu is with Brown University. E-mail: Dai and M. Yu are with Shanghai AI Laboratory. E-mails: Xu is with The Chinese University of Hong Kong. E-mail: Ni is with Tongji University. ∗ * ∗ Equal contribution. † † {\dagger} † Corresponding author. ## Abstract The recently proposed 3D Gaussian Splatting (3D-GS) demonstrates superior rendering fidelity and efficiency compared to NeRF-based scene representations. However, it struggles in large-scale scenes due to the high number of Gaussian primitives, particularly in zoomed-out views, where all primitives are rendered regardless of their projected size. This often results in inefficient use of model capacity and difficulty capturing details at varying scales. To address this, we introduce Octree-GS, a Level-of-Detail (LOD) structured approach that dynamically selects appropriate levels from a set of multi-scale Gaussian primitives, ensuring consistent rendering performance. To adapt the design of LOD, we employ an innovative grow-and-prune strategy for densification and also propose a progressive training strategy to arrange Gaussians into appropriate LOD levels. Additionally, our LOD strategy generalizes to other Gaussian-based methods, such as 2D-GS and Scaffold-GS, reducing the number of primitives needed for rendering while maintaining scene reconstruction accuracy. Experiments on diverse datasets demonstrate that our method achieves real-time speeds, with even 10 $\times$ faster than state-of-the-art methods in large-scale scenes, without compromising visual quality. Project page: https://city-super.github.io/octree-gs/. Index Terms: Novel View Synthesis, 3D Gaussian Splatting, Consistent Real-time Rendering, Level-of-Detail <details> <summary>x1.png Details</summary>  ### Visual Description ## Comparative Visualization: Gaussian Splatting Methods for Urban Scenes ### Overview The image is a technical comparison grid showcasing three different Gaussian Splatting (GS) methods for rendering a complex 3D urban environment. It is structured as a 2x3 grid. The top row, labeled "Rendering," displays the final visual output of each method. The bottom row, labeled "Gaussian Primitives," visualizes the underlying geometric representation (the point cloud of Gaussian primitives) used to generate the renderings above. Each column corresponds to a specific method: Scaffold-GS, Octree-GS, and Hierarchical-GS. Performance metrics (Frames Per Second and Gaussian count in Millions) are provided at the bottom of each column. ### Components/Axes * **Grid Structure:** * **Rows:** 1. **Top Row:** Labeled "Rendering" on the far left. Shows the photorealistic 3D reconstruction of a city scene. 2. **Bottom Row:** Labeled "Gaussian Primitives" on the far left. Shows the corresponding point cloud representation, where each white dot/ellipsoid represents a Gaussian primitive. * **Columns:** Each column is dedicated to one method, labeled at the top of both rows in that column: 1. **Left Column:** Scaffold-GS 2. **Middle Column:** Octree-GS 3. **Right Column:** Hierarchical-GS * **Performance Metrics (Bottom of each column):** Text overlays provide two key metrics in the format `[Value]FPS / [Value]#GS(M)`. * `FPS`: Rendering speed in Frames Per Second. * `#GS(M)`: Number of Gaussian primitives in Millions. * **Visual Annotations:** Red arrows are present in some of the "Rendering" images, pointing to specific areas of interest or potential artifacts. ### Detailed Analysis **Column 1: Scaffold-GS** * **Rendering (Top-Left):** Shows a detailed city block with skyscrapers. A red arrow points to the upper-left corner of a tall, dark building, possibly indicating a rendering artifact or a point of comparison. * **Gaussian Primitives (Bottom-Left):** The point cloud is dense and appears to have a structured, scaffold-like organization, with clear vertical and horizontal alignments corresponding to building edges and surfaces. * **Performance Metrics:** `20.3FPS / 3.20#GS(M)` **Column 2: Octree-GS** * **Rendering (Top-Middle):** Shows a similar but slightly different city view, featuring a prominent circular highway interchange. A red arrow points to the side of a tall, light-colored building. * **Gaussian Primitives (Bottom-Middle):** The point cloud appears less uniformly structured than Scaffold-GS. Primitives seem clustered, potentially following an octree spatial partitioning scheme. The density appears high in complex areas. * **Performance Metrics:** `8.68FPS / 13.0#GS(M)` (Note: This is the lowest FPS and highest primitive count in the set). **Column 3: Hierarchical-GS** * **Rendering (Top-Right):** Shows a wider, more aerial view of the cityscape, including a waterfront area. A red arrow points to a small, isolated red object (possibly a vehicle or sign) on a road in the lower-right quadrant. * **Gaussian Primitives (Bottom-Right):** The point cloud shows a clear hierarchical or multi-resolution structure. There is a very dense, bright white core representing major structures, surrounded by a sparser cloud of primitives for less detailed areas. * **Performance Metrics:** `6.91FPS / 20.8#GS(M)` (Note: This has the lowest FPS and by far the highest primitive count). **Cross-Method Performance Comparison:** * **FPS Trend:** Scaffold-GS (20.3) > Octree-GS (8.68) > Hierarchical-GS (6.91). Scaffold-GS is significantly faster. * **Primitive Count (#GS) Trend:** Hierarchical-GS (20.8M) > Octree-GS (13.0M) > Scaffold-GS (3.20M). There is an inverse relationship between speed and primitive count in this comparison. ### Key Observations 1. **Speed vs. Fidelity Trade-off:** There is a clear inverse correlation between rendering speed (FPS) and the number of Gaussian primitives used. The method with the fewest primitives (Scaffold-GS) is the fastest, while the method with the most primitives (Hierarchical-GS) is the slowest. 2. **Primitive Distribution:** The visualizations of the Gaussian primitives reveal fundamentally different underlying data structures: * **Scaffold-GS:** Appears structured and efficient, aligning with geometric features. * **Octree-GS:** Shows dense, localized clustering. * **Hierarchical-GS:** Exhibits a multi-scale, dense core with sparse periphery. 3. **Visual Quality:** All three methods produce recognizable and detailed urban scenes in the "Rendering" row. The red arrows likely highlight subtle differences in reconstruction quality, such as edge sharpness, artifact presence, or small object fidelity, which are difficult to quantify from this overview alone. 4. **Scene Scale:** The Hierarchical-GS column (right) appears to render a larger geographical area of the city compared to the other two columns, which may contribute to its higher primitive count. ### Interpretation This image serves as a qualitative and quantitative comparison of efficiency and representation in modern 3D reconstruction techniques. The data suggests a fundamental engineering trade-off: * **Scaffold-GS** prioritizes **efficiency and speed**. Its low primitive count and high FPS make it suitable for real-time applications (e.g., VR/AR, simulation) where performance is critical, potentially at the cost of some fine-grained detail or flexibility. * **Octree-GS** and **Hierarchical-GS** prioritize **representational density and potentially higher fidelity**. Their much higher primitive counts suggest they capture more scene detail or use more complex data structures to organize it. However, this comes at a severe performance cost, making them more suitable for offline rendering, high-quality visualization, or as a research benchmark for maximum reconstruction quality. The red arrows are investigative cues, directing the viewer to compare specific challenging regions (e.g., building edges, small objects) across methods. The "Gaussian Primitives" row is crucial for understanding *why* performance differs—it visually exposes the computational burden (number of primitives) and the organizational strategy (scaffold vs. octree vs. hierarchy) that each method employs. The choice of method, therefore, depends entirely on the application's priority: real-time performance (favoring Scaffold-GS) versus maximum representational detail (favoring Hierarchical-GS). </details> Figure 1: Visualization of a continuous zoom-out trajectory on the MatrixCity [1] dataset. Both the rendered 2D images and the corresponding Gaussian primitives are indicated. As indicated by the highlighted arrows, Octree-GS consistently demonstrates superior visual quality compared to state-of-the-art methods Hierarchical-GS [2] and Scaffold-GS [3]. Both SOTA methods fail to render the excessive number of Gaussian primitives included in distant views in real-time, whereas Octree-GS consistently achieves real-time rendering performance ( $\geq 30$ FPS). First row metrics: FPS/storage size. ## I Introduction The field of novel view synthesis has seen significant advancements driven by the advancement of radiance fields [4], which deliver high-fidelity rendering. However, these methods often suffer from slow training and rendering speeds due to time-consuming stochastic sampling. Recently, 3D Gaussian splatting (3D-GS) [5] has pushed the field forward by using anisotropic Gaussian primitives, achieving near-perfect visual quality with efficient training times and tile-based splatting techniques for real-time rendering. With such strengths, it has significantly accelerated the process of replicating the real world into a digital counterpart [6, 7, 8, 9], igniting the community’s imagination for scaling real-to-simulation environments [10, 11, 3]. With its exceptional visual effects, an unprecedented photorealistic experience in VR/AR [12, 13] is now more attainable than ever before. A key drawback of 3D-GS [5] is the misalignment between the distribution of 3D Gaussians and the actual scene structure. Instead of aligning with the geometry of the scene, the Gaussian primitives are distributed based on their fit to the training views, leading to inaccurate and inefficient placement. This misalignment causes two bottleneck challenges: 1) it reduces robustness in rendering views that differ significantly from the training set, as the primitives are not optimized for generalization, and 2) results in redundant and overlap primitives that fail to efficiently represent scene details for real-time rendering, especially in large-scale urban scenes with millions of primitives. There are variants of the vanilla 3D-GS [5] that aim at resolving the misalignment between the organization of 3D Gaussians and the structure of target scene. Scaffold-GS [3] enhances the structure alignment by introducing a regularly spaced feature grid as a structural prior, improving the arrangement and viewpoint-aware adjustment of Gaussians for better rendering quality and efficiency. Mip-Splatting [14] resorts to 3D smoothing and 2D Mip filters to alleviate the redundancy of 3D Gaussians during the optimiziation process of 3D-GS. 2D-GS [15] forces the primitives to better align with the surface, enabling faster reconstruction. Although the aforementioned improvements have been extensively tested on diverse public datasets, we identify a new challenge in the Gaussian era: recording large-scale scenes is becoming increasingly common, yet these methods inherently struggles to scale, as shown in Fig 1. This limitation arises because they still rely on visibility-based filtering for primitive selection, considering all primitives within the view frustum without accounting for their projected sizes. As a result, every object detail is rendered, regardless of distance, leading to redundant computations and inconsistent rendering speeds, particularly in zoom-out scenarios involving large, complex scenes. The lack of Level-of-Detail (LOD) adaptation further forces all 3D Gaussians to compete across views, degrading rendering quality at different scales. As scene complexity increases, the growing number of Gaussians amplifies bottlenecks in real-time rendering. To address the aforementioned issues and better accommodate the new era, we integrate an octree structure into the Gaussian representation, inspired by previous works [16, 17, 18] that demonstrate the effectiveness of spatial structures like octrees and multi-resolution grids for flexible content allocation and real-time rendering. Specifically, our method organizes scenes with hierarchical grids to meet LOD needs, efficiently adapting to complex or large-scale scenes during both training and inference, with LOD levels selected based on observation footprint and scene detail richness. We further employ a progressive training strategy, introducing a novel growing and pruning approach. A next-level growth operator enhances connections between LODs, increasing high-frequency detail, while redundant Gaussians are pruned based on opacity and view frequency. By adaptively querying LOD levels from the octree-based Gaussian structure based on viewing distance and scene complexity, our method minimizes the number of primitives needed for rendering, ensuring consistent efficiency, as shown in Fig. 1. In addition, Octree-GS effectively separates coarse and fine scene details, allowing for accurate Gaussian placement at appropriate scales, significantly improving reconstruction fidelity and texture detail. Unlike other concurrent LOD methods [2, 19], our approach is an end-to-end algorithm that achieves LOD effects in a single training round, reducing training time and storage overhead. Notably, our LOD framework is also compatible with various Gaussian representations, including explicit Gaussians [15, 5] and neural Gaussians [3]. By incorporating our strategy, we have demonstrated significant enhancements in visual performance and rendering speed across a wide range of datasets, including both fine-detailed indoor scenes and large-scale urban environments. In summary, our method offers the following key contributions: - To the best of our knowledge, Octree-GS is the first approach to deal with the problem of Level-of-Detail in Gaussian representation, enabling consistent rendering speed by dynamically adjusting the fetched LOD on-the-fly owing to our explicit octree structure design. - We develop a novel grow-and-prune strategy optimized for LOD adaptation. - We introduce a progressive training strategy to encourage more reliable distributions of primitives. - Our LOD strategy is able to generalize to any Gaussian-based method. - Our methods, while maintaining the superior rendering quality, achieves state-of-the-art rendering speed, especially in large-scale scenes and extreme-view sequences, as shown in Fig. 1. ## II Related work ### II-A Novel View Synthesis NeRF methods [4] have revolutionized the novel view synthesis task with their photorealistic rendering and view-dependent modeling effects. By leveraging classical volume rendering equations, NeRF trains a coordinate-based MLP to encode scene geometry and radiance, mapping directly from positionally encoded spatial coordinates and viewing directions. To ease the computational load of dense sampling process and forward through deep MLP layers, researchers have resorted to various hybrid-feature grid representations, akin to ‘caching’ intermediate latent features for final rendering [20, 17, 21, 22, 23, 24, 25, 26]. Multi-resolution hash encoding [24] is commonly chosen as the default backbone for many recent advancements due to its versatility for enabling fast and efficient rendering, encoding scene details at various granularities [27, 28, 29] and extended supports for LOD renderings [16, 30]. Recently, 3D-GS [5] has ignited a revolution in the field by employing anisotropic 3D Gaussians to represent scenes, achieving state-of-the-art rendering quality and speed. Subsequent studies have rapidly expanded 3D-GS into diverse downstream applications beyond static 3D reconstruction, sparking a surge of extended applications to 3D generative modeling [31, 32, 33], physical simulation [13, 34], dynamic modeling [35, 36, 37], SLAMs [38, 39], and autonomous driving scenes [12, 10, 11], etc. Despite the impressive rendering quality and speed of 3D-GS, its ability to sustain stable real-time rendering with rich content is hampered by the accompanying rise in resource costs. This limitation hampers its practicality in speed-demanding applications, such as gaming in open-world environments and other immersive experiences, particularly for large indoor and outdoor scenes with computation-restricted devices. ### II-B Spatial Structures for Neural Scene Representations Various spatial structures have been explored in previous NeRF-based representations, including dense voxel grids [20, 22], sparse voxel grids [17, 21], point clouds [40], multiple compact low-rank tensor components [23, 41, 42], and multi-resolution hash tables [24]. These structures primarily aim to enhance training or inference speed and optimize storage efficiency. Inspired by classical computer graphics techniques such as BVH [43] and SVO [44] which are designed to model the scene in a sparse hierarchical structure for ray tracing acceleration. NSVF [20] efficiently skipping the empty voxels leveraging the neural implicit fields structured in sparse octree grids. PlenOctree [17] stores the appearance and density values in every leaf to enable highly efficient rendering. DOT [45] improves the fixed octree design in Plenoctree with hierarchical feature fusion. ACORN [18] introduces a multi-scale hybrid implicit–explicit network architecture based on octree optimization. While vanilla 3D-GS [5] imposes no restrictions on the spatial distribution of all 3D Gaussians, allowing the modeling of scenes with a set of initial sparse point clouds, Scaffold-GS [3] introduces a hierarchical structure, facilitating more accurate and efficient scene reconstruction. In this work, we introduce a sparse octree structure to Gaussian primitives, which demonstrates improved capabilities such as real-time rendering stability irrespective of trajectory changes. ### II-C Level-of-Detail (LOD) LOD is widely used in computer graphics to manage the complexity of 3D scenes, balancing visual quality and computational efficiency. It is crucial in various applications, including real-time graphics, CAD models, virtual environments, and simulations. Geometry-based LOD involves simplifying the geometric representation of 3D models using techniques like mesh decimation; while rendering-based LOD creates the illusion of detail for distant objects presented on 2D images. The concept of LOD finds extensive applications in geometry reconstruction [46, 47, 48] and neural rendering [49, 50, 30, 27, 16]. Mip-NeRF [49] addresses aliasing artifacts by cone-casting approach approximated with Gaussians. BungeeNeRF [51] employs residual blocks and inclusive data supervision for diverse multi-scale scene reconstruction. To incorporate LOD into efficient grid-based NeRF approaches like instant-NGP [24], Zip-NeRF [30] further leverages supersampling as a prefiltered feature approximation. VR-NeRF [16] utilizes mip-mapping hash grid for continuous LOD rendering and an immersive VR experience. PyNeRF [27] employs a pyramid design to adaptively capture details based on scene characteristics. However, GS-based LOD methods fundamentally differ from above LOD-aware NeRF methods in scene representation and LOD introduction. For instance, NeRF can compute LOD from per-pixel footprint size, whereas GS-based methods require joint LOD modeling from both the view and 3D scene level. We introduce a flexible octree structure to address LOD-aware rendering in the 3D-GS framework. Concurrent works related to our method include LetsGo [52], CityGaussian [19], and Hierarchical-GS [2], all of which also leverage LOD for large-scale scene reconstruction. 1) LetsGo introduces multi-resolution Gaussian models optimized jointly, focusing on garage reconstruction, but requires multi-resolution point cloud inputs, leading to higher training overhead and reliance on precise point cloud accuracy, making it more suited for lidar scanning scenarios. 2) CityGaussian selects LOD levels based on distance intervals and fuses them for efficient large-scale rendering, but lacks robustness due to the need for manual distance threshold adjustments, and faces issues like stroboscopic effects when switching between LOD levels. 3) Hierarchical-GS, using a tree-based hierarchy, shows promising results in street-view scenes but involves post-processing for LOD, leading to increased complexity and longer training times. A common limitation across these methods is that each LOD level independently represents the entire scene, increasing storage demands. In contrast, Octree-GS employs an explicit octree structure with an accumulative LOD strategy, which significantly accelerates rendering speed while reducing storage requirements. ## III Preliminaries In this section, we present a brief overview of the core concepts underlying 3D-GS [5] and Scaffold-GS [3]. ### III-A 3D-GS 3D Gaussian splatting [5] explicitly models scenes using anisotropic 3D Gaussians and renders images by rasterizing the projected 2D counterparts. Each 3D Gaussian $G(x)$ is parameterized by a center position $\mu\in\mathbb{R}^{3}$ and a covariance $\Sigma\in\mathbb{R}^{3\times 3}$ : $$ G(x)=e^{-\frac{1}{2}(x-\mu)^{T}\Sigma^{-1}(x-\mu)}, \tag{1} $$ where $x$ is an arbitrary position within the scene, $\Sigma$ is parameterized by a scaling matrix $S\in\mathbb{R}^{3}$ and rotation matrix $R\in\mathbb{R}^{3\times 3}$ with $RSS^{T}R^{T}$ . For rendering, opacity $\sigma\in\mathbb{R}$ and color feature $F\in\mathbb{R}^{C}$ are associated to each 3D Gaussian, while $F$ is represented using spherical harmonics (SH) to model view-dependent color $c\in\mathbb{R}^{3}$ . A tile-based rasterizer efficiently sorts the 3D Gaussians in front-to-back depth order and employs $\alpha$ -blending, following projecting them onto the image plane as 2D Gaussians $G^{\prime}(x^{\prime})$ [53]: $$ C\left(x^{\prime}\right)=\sum_{i\in N}T_{i}c_{i}\sigma_{i},\quad\sigma_{i}= \alpha_{i}G_{i}^{\prime}\left(x^{\prime}\right), \tag{2} $$ where $x^{\prime}$ is the queried pixel, $N$ represents the number of sorted 2D Gaussians binded with that pixel, and $T$ denotes the transmittance as $\prod_{j=1}^{i-1}\left(1-\sigma_{j}\right)$ . ### III-B Scaffold-GS To efficiently manage Gaussian primitives, Scaffold-GS [3] introduces anchors, each associated with a feature describing the local structure. From each anchor, $k$ neural Gaussians are emitted as follows: $$ \left\{\mu_{0},\ldots,\mu_{k-1}\right\}=x_{v}+\left\{\mathcal{O}_{0},\ldots, \mathcal{O}_{k-1}\right\}\cdot l_{v} \tag{3} $$ where $x_{v}$ is the anchor position, $\{\mu_{i}\}$ denotes the positions of the i th neural Gaussian, and $l_{v}$ is a scaling factor controlling the predicted offsets $\{\mathcal{O}_{i}\}$ . In addition, opacities, scales, rotations, and colors are decoded from the anchor features through corresponding MLPs. For example, the opacities are computed as: $$ \{{\alpha}_{0},...,{\alpha}_{k-1}\}=\rm{F_{\alpha}}(\hat{f}_{v},\Delta_{vc}, \vec{d}_{vc}), \tag{4} $$ where $\{\alpha_{i}\}$ represents the opacity of the i th neural Gaussian, decoded by the opacity MLP $F_{\alpha}$ . Here, $\hat{f}_{v}$ , $\Delta_{vc}$ , and $\vec{d}_{vc}$ correspond to the anchor feature, the relative viewing distance, and the direction to the camera, respectively. Once these properties are predicted, neural Gaussians are fed into the tile-based rasterizer, as described in [5], to render images. During the densification stage, Scaffold-GS treats anchors as the basic primitives. New anchors are established where the gradient of a neural Gaussian exceeds a certain threshold, while anchors with low average transparency are removed. This structured representation improves robustness and storage efficiency compared to the vanilla 3D-GS. ## IV Methods <details> <summary>x2.png Details</summary>  ### Visual Description ## Diagram: Octree-GS Pipeline and Anchor Initialization ### Overview The image is a technical diagram illustrating a 3D reconstruction or rendering pipeline named "Octree-GS". It is divided into two main panels: (a) Pipeline of Octree-GS and (b) Anchor Initialization. The diagram explains a method that uses sparse Structure-from-Motion (SfM) points and an octree structure to manage Level-of-Detail (LOD) representations for efficient 3D scene rendering and supervision. ### Components/Axes The diagram is organized into distinct visual regions: **Left Column (Input & Structure):** * **Top:** A point cloud visualization labeled **"Sparse SfM Points"**. It shows a sparse, colored 3D point cloud of an outdoor scene (a table with a vase in a garden). A blue camera icon with a viewing frustum is overlaid, indicating a camera pose. * **Bottom:** A 3D model of a table and vase enclosed in a wireframe grid, labeled **"Octree Structure"**. This represents the spatial partitioning structure. **Center Panel (a) Pipeline of Octree-GS:** * **Top Row:** Three sequential photographic images of a vase with dried flowers on a table. The third image is highlighted with a green border. A camera icon with an arrow points to this sequence, indicating input views. * **Middle Row:** Three point cloud visualizations corresponding to the images above, labeled **"LOD 0"**, **"LOD 1"**, and **"LOD 2"**. Below LOD 0 is the label **"anchors"**. The point density increases from LOD 0 (sparse) to LOD 2 (dense). * **Text:** Below the LOD visualizations is the phrase **"Fetch proper LODs based on views"**. * **Right Side of Center Panel:** Two rendered images of the full garden scene. * The top image is labeled **"Rendering"** in its bottom-right corner. Below it are listed loss functions: **"L₁, L_{SSIM}, (L_{vol}, L_d, L_n)"**. * The bottom image is labeled **"GT"** (Ground Truth) in its bottom-right corner. * The text **"Supervision Loss"** is centered below these two images. **Right Column (b) Anchor Initialization:** * **Step 1:** A diagram showing a 3D bounding box labeled **"bbox"** containing a dense point cloud. The caption reads: **"① construct the octree-structure grids"**. * **Step 2:** A sequence of diagrams showing progressively denser point clouds within the bounding box, from left to right. The first is labeled **"LOD 0"** and the last is labeled **"LOD K-1"**. The caption reads: **"② Initialize anchors with varying LOD levels"**. ### Detailed Analysis The diagram details a multi-stage process: 1. **Input:** The process starts with **Sparse SfM Points** and an **Octree Structure** for spatial organization. 2. **LOD Management (Core Pipeline):** For a given set of input views (the vase images), the system fetches appropriate Level-of-Detail representations. **LOD 0** uses a sparse set of "anchors". **LOD 1** adds more points, and **LOD 2** is the densest. This suggests an adaptive detail mechanism. 3. **Rendering & Supervision:** The system produces a **Rendering** of the full scene. This rendering is supervised by comparing it to the **GT** (Ground Truth) image using a composite loss function: **L₁** (likely L1 loss), **L_{SSIM}** (Structural Similarity Index Measure loss), and a set of volumetric/density losses **(L_{vol}, L_d, L_n)**. 4. **Anchor Initialization (Sub-process):** This explains how the LOD anchors are created. First, an octree grid is constructed within a bounding box (**bbox**). Then, anchors are initialized at different LOD levels, from the coarsest (**LOD 0**) to the finest (**LOD K-1**). ### Key Observations * The **LOD visualization** shows a clear trend of increasing point density from LOD 0 to LOD 2, correlating with finer detail. * The **"anchors"** label is specifically associated with the sparsest LOD (LOD 0), indicating they are the foundational points for the representation. * The **supervision loss** is applied by comparing a full-scene rendering to a ground truth photograph, not just the object (vase). * The **green border** around the third input image and the "Rendering" image may indicate they are the primary view or the target for the illustrated step. * The process is hierarchical, moving from sparse inputs and coarse structures to dense, supervised renderings. ### Interpretation This diagram outlines a method for efficient neural rendering or 3D reconstruction, likely for large-scale scenes. The core innovation appears to be the use of an **octree-structured grid** to manage **Level-of-Detail (LOD) anchors**. Instead of using a uniform representation, the system adaptively fetches the appropriate LOD (from sparse anchors to dense points) based on the camera view. This is a common strategy to balance computational efficiency with rendering quality. The **anchor initialization** process (b) is crucial for building this multi-resolution representation. By constructing an octree and seeding anchors at different levels, the system creates a foundation that can represent both coarse geometry and fine details. The **supervision loss** (a) ensures that the final rendering, built from these LOD components, matches real-world photographs. The inclusion of both pixel-wise (L₁) and perceptual (L_{SSIM}) losses, along with volumetric terms, suggests a focus on producing visually plausible and structurally accurate 3D scenes. In essence, the pipeline translates sparse 3D points into a detailed, renderable scene representation by intelligently managing complexity through a hierarchical octree and LOD system, all trained via direct image supervision. </details> Figure 2: (a) Pipeline of Octree-GS: starting from given sparse SfM points, we construct octree-structured anchors from the bounded 3D space and assign them to the corresponding LOD level. Unlike conventional 3D-GS methods treating all Gaussians equally, our approach involves primitives with varying LOD levels. We determine the required LOD levels based on the observation view and invoke corresponding anchors for rendering, as shown in the middle. As the LOD levels increase (from LOD $0 0$ to LOD $2$ ), the fine details of the vase accumulate progressively. (b) Anchor Initialization: We construct the octree structure grids within the determined bounding box. Then, the anchors are initialized at the voxel center of each layer , with their LOD level corresponding to the octree layer of the voxel, ranging from $0 0$ to $K-1$ . Octree-GS hierarchically organizes anchors into an octree structure to learn a neural scene from multiview images. Each anchor can emit different types of Gaussian primitives, such as explicit Gaussians [15, 5] and neural Gaussians [3]. By incorporating the octree structure, which naturally introduces a LOD hierarchy for both reconstruction and rendering, Octree-GS ensures consistently efficient training and rendering by dynamically selecting anchors from the appropriate LOD levels, allowing it to efficiently adapt to complex or large-scale scenes. Fig. 2 illustrates our framework. In this section, we first explain how to construct the octree from a set of given sparse SfM [54] points in Sec. IV-A. Next, we introduce an adapted anchor densification strategy based on LOD-aware ‘growing’ and ‘pruning’ operations in Sec IV-B. Sec. IV-C then introduces a progressive training strategy that activates anchors from coarse to fine. Finally, to address reconstruction challenges in wild scenes, we introduce appearance embedding (Sec. IV-D). ### IV-A LOD-structured Anchors #### IV-A 1 Anchor Definition. Inspired by Scaffold-GS [3], we introduce anchors to manage Gaussian primitives. These anchors are positioned at the centers of sparse, uniform voxel grids with varying voxel sizes. Specifically, anchors with higher LOD $L$ are placed within grids with smaller voxel sizes. In this paper, we define LOD 0 as the coarsest level. As the LOD level increases, more details are captured. Note that our LOD design is cumulative: the rendered images at LOD $K$ rasterize all Gaussian primitives from LOD $0 0$ to $K$ . Additionally, each anchor is assigned a LOD bias $\Delta L$ to account for local complexity, and each anchor is associated with $k$ Gaussian primitives for image rendering, whose positions are determined by Eq. 3. Moreover, our framework is generalized to support various types of Gaussians. For example, the Gaussian primitive can be explicitly defined with learnable distinct properties, such as 2D [15] or 3D Gaussians [5], or they can be neural Gaussians decoded from the corresponding anchors, as described in Sec. V-A 4. #### IV-A 2 Anchor Initialization. In this section, we describe the process of initializing octree-structured anchors from a set of sparse SfM points $\mathbf{P}$ . First, the number of octree layers, $K$ , is determined based on the range of observed distances. Specifically, we begin by calculating the distance $d_{ij}$ between each camera center of training image $i$ and SfM point $j$ . The $r_{d}$ th largest and $r_{d}$ th smallest distances are then defined as $d_{max}$ and $d_{min}$ , respectively. Here, $r_{d}$ is a hyperparameter used to discard outliers, which is typically set to $0.999$ in all our experiment. Finally, $K$ is calculated as: $$ \displaystyle K \displaystyle=\lfloor\log_{2}(\hat{d}_{max}/\hat{d}_{min})\rceil+1. \tag{5} $$ where $\lfloor\cdot\rceil$ denotes the round operator. The octree-structured grids with $K$ layers are then constructed, and the anchors of each layer are voxelized by the corresponding voxel size: $$ \mathbf{V}_{L}=\left\{\left\lfloor\frac{\mathbf{P}}{\delta/2^{L}}\right\rceil \cdot\delta/2^{L}\right\}, \tag{6} $$ given the base voxel size $\delta$ for the coarsest layer corresponding to LOD 0 and $\mathbf{V}_{L}$ for initialed anchors in LOD $L$ . The properties of anchors and the corresponding Gaussian primitives are also initialized, please check the implementation V-A 4 for details. #### IV-A 3 Anchor Selection. In this section, we explain how to select the appropriate visible anchors to maintain both stable real-time rendering speed and high rendering quality. An ideal anchors is dynamically fetched from $K$ LOD levels based on the pixel footprint of projected Gaussians on the screen. In practice, we simplify this by using the observation distance $d_{ij}$ , as it is proportional to the footprint under consistent camera intrinsics. For varying intrinsics, a focal scale factor $s$ is applied to adjust the distance equivalently. However, we find it sub-optimal if we estimate the LOD level solely based on observation distances. So we further set a learnable LOD bias $\Delta L$ for each anchor as a residual, which effectively supplements the high-frequency regions with more consistent details to be rendered during inference process, such as the presented sharp edges of an object as shown in Fig. 13. In detail, for a given viewpoint $i$ , the corresponding LOD level of an arbitrary anchor $j$ is estimated as: $$ \hat{L_{ij}}=\lfloor L_{ij}^{*}\rfloor=\lfloor\Phi(\log_{2}(d_{max}/(d_{ij}*s) ))+\Delta L_{j}\rfloor, \tag{7} $$ where $d_{ij}$ is the distance between viewpoint $i$ and anchor $j$ . $\Phi(\cdot)$ is a clamping function that restricts the fractional LOD level $L_{ij}^{*}$ to the range $[0,K-1]$ . Inspired by the progressive LOD techniques [55], Octree-GS renders images using cumulative LOD levels rather than a single LOD level. In summary, the anchor will be selected if its LOD level $L_{j}\leq\hat{L_{ij}}$ . We iteratively evaluate all anchors and select those that meet this criterion, as illustrated in Fig. 3. The Gaussian primitives emitted from the selected anchors are then passed into the rasterizer for rendering. During inference, to ensure smooth rendering transitions between different LOD levels without introducing visible artifacts, we adopt an opacity blending technique inspired by [16, 51]. We use piecewise linear interpolation between adjacent levels to make LOD transitions continuous, effectively eliminating LOD aliasing. Specifically, in addition to fully satisfied anchors, we also select nearly satisfied anchors that meet the criterion $L_{j}=\hat{L_{ij}}+1$ . The Gaussian primitives of these anchors are also passed to the rasterizer, with their opacities scaled by $L_{ij}^{*}-\hat{L_{ij}}$ . ### IV-B Adaptive Anchor Gaussians Control #### IV-B 1 Anchor Growing. Following the approach of [5], we use the view-space positional gradients of Gaussian primitives as a criterion to guide anchor densification. New anchors are grown in the unoccupied voxels across the octree-structured grids, following the practice of [3]. Specifically, every $T$ iterations, we calculate the average accumulated gradient of the spawned Gaussian primitives, denoted as $\nabla_{g}$ . Gaussian primitives with $\nabla_{g}$ exceeding a predefined threshold $\tau_{g}$ are considered significant and they are converted into new anchors if located in empty voxels. In the context of the octree structure, the question arises: which LOD level should be assigned to these newly converted anchors? To address this, we propose a ‘next-level’ growing operation. This method adjusts the growing strategy by adding new anchors at varying granularities, with Gaussian primitives that have exceptionally high gradients being promoted to higher levels. To prevent overly aggressive growth into higher LOD levels, we monotonically increase the difficulty of growing new anchors to higher LOD levels by setting the threshold $\tau_{g}^{L}=\tau_{g}*2^{\beta L}$ , where $\tau_{g}$ and $\beta$ are both hyperparameters, with default values of $0.0002$ and $0.2$ , respectively. Gaussians at level $L$ are only promoted to the next level $L+1$ if $\nabla_{g}>\tau_{g}^{L+1}$ , and they remain at the same level if $\tau_{g}^{L}<\nabla_{g}<\tau_{g}^{L+1}$ . We also utilize the gradient as the complexity cue of the scene to adjust the LOD bias $\Delta L$ . The gradient of an anchor is defined as the average gradient of the spawned Gaussian primitives, denoted as $\nabla_{v}$ . We select those anchors with $\nabla_{v}>\tau_{g}^{L}*0.25$ , and increase the corresponding $\Delta L$ by a small user-defined quantity $\epsilon$ : $\Delta L=\Delta L+\epsilon$ . We empirically set $\epsilon=0.01$ . <details> <summary>x3.png Details</summary>  ### Visual Description \n ## Comparative Visualization: Progressive vs. Non-Progressive Point Cloud Rendering at Multiple Levels of Detail (LOD) ### Overview This image is a technical comparison diagram demonstrating the visual impact of a "progressive" rendering technique on a 3D point cloud scene. The scene depicts a truck in an outdoor environment. The comparison is structured as a grid with two rows and four columns, showing the same scene under different rendering conditions and Levels of Detail (LOD). ### Components/Axes * **Rows (Rendering Method):** * **Top Row:** Labeled vertically on the left as **"w/ progressive"** (with progressive rendering). This row uses **green dashed bounding boxes** to highlight a region of interest. * **Bottom Row:** Labeled vertically on the left as **"w/o progressive"** (without progressive rendering). This row uses **red dashed bounding boxes** to highlight the same region of interest. * **Columns (Level of Detail - LOD):** * The columns represent different Levels of Detail, labeled at the bottom of the bottom row's panels. * **Column 1 (Far Left):** Labeled **"LOD 0"**. This is the highest detail level. * **Column 2:** Labeled **"LOD 3"**. * **Column 3:** Labeled **"LOD 4"**. * **Column 4 (Far Right):** Labeled **"LOD 5"**. This is the lowest detail level shown. * **Visual Elements:** * Each panel shows a point cloud rendering of the same truck scene against a black background. * A white diagonal line cuts across the upper-left corner of each panel, likely indicating a camera frustum or view plane. * Dashed bounding boxes (green for top row, red for bottom row) are consistently placed around the truck's cargo bed area across all panels for direct comparison. * An ellipsis (`...`) is placed between the first and second columns, indicating that LOD 1 and LOD 2 are not shown in this figure. ### Detailed Analysis The image provides a visual progression of detail loss as LOD increases (from 0 to 5) and contrasts the two rendering methods. * **LOD 0 (Highest Detail):** * **w/ progressive (Top-Left):** The scene is dense with points. The truck, ground, and background trees are clearly recognizable. The highlighted region (green box) shows a solid, well-defined truck bed. * **w/o progressive (Bottom-Left):** Visually identical to the progressive version at this highest LOD. The scene is dense and clear. The highlighted region (red box) is also well-defined. * **LOD 3:** * **w/ progressive (Top, 2nd from left):** Point density is significantly reduced. The overall shape of the truck is maintained, but details are sparser. The truck bed within the green box remains structurally coherent. * **w/o progressive (Bottom, 2nd from left):** Point density is similarly reduced. However, the truck bed within the red box appears more fragmented and less structurally sound compared to the progressive version above it. * **LOD 4:** * **w/ progressive (Top, 3rd from left):** Further reduction in points. The truck is now a sparse collection of points, but its general form and the structure of the cargo area (green box) are still discernible. * **w/o progressive (Bottom, 3rd from left):** The degradation is more severe. The truck's form is very faint, and the cargo area (red box) is barely recognizable, appearing as a few disconnected points. * **LOD 5 (Lowest Detail):** * **w/ progressive (Top-Right):** Extremely sparse points. Only the most prominent features of the truck's silhouette and a few points in the cargo area (green box) remain. * **w/o progressive (Bottom-Right):** The scene is nearly empty. The truck is almost entirely gone, with only a handful of points remaining. The cargo area (red box) is essentially empty, containing no discernible points. ### Key Observations 1. **Progressive Rendering Advantage:** The "w/ progressive" method consistently preserves more structural information and point density within the highlighted region (green boxes) as the LOD increases (detail decreases) compared to the "w/o progressive" method (red boxes). 2. **Critical Degradation Point:** The difference between the two methods becomes starkly apparent at **LOD 3** and is extreme by **LOD 4**. The non-progressive method loses critical structural data much faster. 3. **Spatial Consistency:** The bounding boxes confirm that the comparison is made on the exact same spatial region across all panels, ensuring a valid visual test. 4. **LOD Hierarchy:** The labels confirm a standard LOD hierarchy where LOD 0 is the most detailed and LOD 5 is the least detailed. ### Interpretation This diagram serves as a visual proof-of-concept for the efficacy of a progressive point cloud rendering or compression technique. The core message is that the progressive method is superior for maintaining the perceptual integrity and structural recognizability of a 3D scene under constrained data budgets (higher LOD numbers). * **What it demonstrates:** The technique likely involves an intelligent prioritization or ordering of point data transmission or rendering. It ensures that even when most data is discarded (at high LODs), the remaining points are chosen to preserve the most important geometric structures, like the edges and surfaces of the truck bed. The non-progressive method likely discards points uniformly or in a less intelligent manner, leading to a complete loss of structure. * **Why it matters:** In applications like real-time 3D streaming, remote visualization, or handling massive point cloud datasets on limited hardware, this progressive approach would allow users to still understand the scene's content even under poor network conditions or at very low levels of detail. The alternative (non-progressive) rendering would render the scene useless much sooner. * **Underlying Principle:** The image argues that not all data points are equal. A smart rendering system should prioritize the points that contribute most to human scene comprehension, which is what the "w/ progressive" method appears to achieve. The green vs. red box contrast is a direct visual metaphor for "good" vs. "bad" data preservation under compression. </details> Figure 3: Visualization of anchors and projected 2D Gaussians in varying LOD levels. (1) The first row depicts scene decomposition with our full model, employing a coarse-to-fine training strategy as detailed in Sec. IV-C. A clear division of roles is evident between varying LOD levels: LOD 0 captures most rough contents, and higher LODs gradually recover the previously missed high-frequency details. This alignment with our motivation allows for more efficient allocation of model capacity with an adaptive learning process. (2) In contrast, our ablated progressive training studies (elaborated in Sec. V-C) take a naive approach. Here, all anchors are simultaneously trained, leading to an entangled distribution of Gaussian primitives across all LOD levels. #### IV-B 2 Anchor Pruning. To eliminate redundant and ineffective anchors, we compute the average opacity of Gaussians generated over $T$ training iterations, in a manner similar to the strategies adopted in [3]. <details> <summary>x4.png Details</summary>  ### Visual Description ## Comparative Rendering Analysis: Impact of View Frequency on Visual Quality and Computational Cost ### Overview The image is a three-panel technical comparison from a computer graphics or rendering research context. It visually and quantitatively contrasts the results of a rendering technique applied to a complex foliage scene under two conditions: without and with the use of "view frequency" optimization. The panels are arranged horizontally and labeled (a), (b), and (c). ### Components/Axes The image consists of three distinct panels, each with a title bar at the top and numerical data at the bottom right. There are no traditional chart axes. Key components are: 1. **Panel Titles (Top of each panel):** * (a) `Rendering (w/o view frequency)` * (b) `LOD levels (w/o view frequency)` * (c) `Rendering (w/ view frequency)` 2. **Bounding Boxes (Overlaid on images):** * **Panel (a):** Two red rectangular boxes highlight specific regions of the rendered foliage. * **Panel (b):** Two red rectangular boxes highlight corresponding regions in the LOD visualization. * **Panel (c):** Two green rectangular boxes highlight the same regions as in (a) and (b). 3. **Quantitative Metrics (Bottom right of each panel):** * **Panel (a):** `27.51dB/1.16G` * **Panel (b):** No numerical data is present. * **Panel (c):** `27.63dB/0.24G` ### Detailed Analysis **Panel (a) - Rendering (w/o view frequency):** * **Content:** A color rendering of dense green foliage. The image appears somewhat noisy or artifact-prone, especially within the red-boxed regions. * **Highlighted Regions:** The smaller red box (top-left) encloses a cluster of leaves. The larger red box (center) encloses a broader area of foliage where visual artifacts (blurriness, noise) are more apparent. * **Metric:** `27.51dB/1.16G`. The "dB" likely refers to a quality metric like Peak Signal-to-Noise Ratio (PSNR). The "G" likely denotes computational cost in Giga-operations or a similar unit. **Panel (b) - LOD levels (w/o view frequency):** * **Content:** A grayscale visualization corresponding to the scene in (a). Brighter areas likely represent higher Level of Detail (LOD) or sampling density, while darker areas represent lower detail. * **Highlighted Regions:** The red boxes are in the same spatial positions as in (a). The regions inside show a mix of bright (high-detail) and dark (low-detail) patches, indicating non-uniform detail allocation. * **Trend:** The LOD distribution appears patchy and potentially inefficient, with high-detail areas (bright spots) scattered even in regions that may not require it from the viewer's perspective. **Panel (c) - Rendering (w/ view frequency):** * **Content:** A color rendering of the same foliage scene, now using "view frequency" optimization. * **Highlighted Regions:** The green boxes enclose the same areas as the red boxes in (a) and (b). Visually, the foliage within these boxes appears cleaner and more coherent compared to panel (a), with reduced noise and artifacts. * **Metric:** `27.63dB/0.24G`. Compared to panel (a), the quality metric (dB) is slightly higher (+0.12 dB), while the computational cost metric (G) is drastically lower (0.24G vs. 1.16G, an ~79% reduction). ### Key Observations 1. **Visual Quality Improvement:** The rendering with view frequency (c) shows a subtle but noticeable improvement in visual fidelity over the rendering without it (a), particularly in the highlighted regions where artifacts are reduced. 2. **Massive Computational Savings:** The most significant finding is the reduction in the "G" metric from 1.16G to 0.24G. This indicates the "view frequency" method achieves similar or better quality with a fraction of the computational resources. 3. **LOD Correlation:** Panel (b) provides insight into *why* the savings occur. The "w/o view frequency" LOD map shows an inefficient, scattered allocation of detail. The "w/ view frequency" method (implied by the result in c) likely optimizes this allocation, focusing detail only where the viewer is most likely to look, thus saving resources. ### Interpretation This image demonstrates the effectiveness of a "view frequency" optimization technique in a rendering pipeline. The data suggests that by incorporating information about how often or likely different parts of a scene are viewed, the system can make smarter decisions about allocating computational resources (Level of Detail). * **The Core Trade-off:** The technique successfully breaks the typical trade-off between quality and performance. It slightly improves visual quality (higher dB) while dramatically lowering computational cost (lower G). * **Underlying Mechanism:** The LOD visualization in (b) acts as a diagnostic, revealing the inefficiency of the baseline method. The optimized method likely produces a more focused and efficient LOD map, though it is not shown. * **Practical Implication:** For real-time applications like video games or simulations, this optimization could allow for either much higher frame rates at the same quality, or significantly better visual quality at the same performance level. The red vs. green box coloring visually reinforces the "problem" vs. "solution" narrative. * **Notable Anomaly:** The slight quality increase (0.12 dB) is interesting. It suggests the optimization doesn't just maintain quality by cutting corners; it may actively improve it by better allocating resources to perceptually important areas, reducing artifacts in those regions. </details> Figure 4: Illustration of the effect of view frequency. We visualize the rendered image and the corresponding LOD levels (with whiter colors indicating higher LOD levels) from a novel view. We observe that insufficiently optimized anchors will produce artifacts if pruning is based solely on opacity. After pruning anchors based on view frequency, not only are the artifacts eliminated, but the final storage is also reduced. Last row metrics: PSNR/storage size. Moreover, we observe that some intolerable floaters appear in Fig. 4 (a) because a significant portion of anchors are not visible or selected in most training view frustums. Consequently, they are not sufficiently optimized, impacting rendering quality and storage overhead significantly. To address this issue, we define ‘view-frequency’ as the probability that anchors are selected in the training views, which directly correlates with the received gradient. We remove anchors with the view-frequency below $\tau_{v}$ , where $\tau_{v}$ represents the visibility threshold. This strategy effectively eliminates floaters, improving visual quality and significantly reducing storage, as demonstrated in Fig. 4. ### IV-C Progressive Training Optimizing anchors across all LOD levels simultaneously poses inherent challenges in explaining rendering with decomposed LOD levels. All LOD levels try their best to represent the 3D scene, making it difficult to decompose them thus leading to large overlaps. Inspired by the progressive training strategy commonly used in prior NeRF methods [56, 51, 28], we implement a coarse-to-fine optimization strategy. begins by training on a subset of anchors representing lower LOD levels and progressively activates finer LOD levels throughout optimization, complementing the coarse levels with fine-grained details. In practice, we iteratively activate an additional LOD level after $N$ iterations. Empirically, we start training from $\lfloor\frac{K}{2}\rfloor$ level to balance visual quality and rendering efficiency. Additionally, more time is dedicated to learning the overall structure because we want coarse-grained anchors to perform well in reconstructing the scene as the viewpoint moves away. Therefore, we set $N_{i-1}=\omega N_{i}$ , where $N_{i}$ denotes the training iterations for LOD level $L=i$ , and $\omega\geq 1$ is the growth factor. Note that during the progressive training stage, we disable the next level grow operator. With this approach, we find that the anchors can be arranged more faithfully into different LOD levels as demonstrated in Fig. 3, reducing anchor redundance and leading to faster rendering without reducing the rendering quality. ### IV-D Appearance Embedding In large-scale scenes, the exposure compensation of training images is always inconsistent, and 3D-GS [5] tends to produce artifacts by averaging the appearance variations across training images. To address this, and following the approach of prior NeRF papers [57, 58], we integrate Generative Latent Optimization (GLO) [59] to generate the color of Gaussian primitives. For instance, we introduce a learnable individual appearance code for each anchor, which is fed as an addition input to the color MLP to decode the colors of the Gaussian primitives. This allows us to effectively model in-the-wild scenes with varying appearances. Moreover, we can also interpolate the appearance code to alter the visual appearance of these environments, as shown in Fig. 12. ## V Experiments TABLE I: Quantitative comparison on real-world datasets [50, 60, 61]. Octree-GS consistently achieves superior rendering quality compared to baselines with reduced number of Gaussian primitives rendered per-view. We highlight best and second-best in each category. | Dataset Method Metrics Mip-NeRF360 [50] | Mip-NeRF360 PSNR $\uparrow$ 27.69 | Tanks&Temples SSIM $\uparrow$ 0.792 | Deep Blending LPIPS $\downarrow$ 0.237 | #GS(k)/Mem - | PSNR $\uparrow$ 23.14 | SSIM $\uparrow$ 0.841 | LPIPS $\downarrow$ 0.183 | #GS(k)/Mem - | PSNR $\uparrow$ 29.40 | SSIM $\uparrow$ 0.901 | LPIPS $\downarrow$ 0.245 | #GS(k)/Mem - | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 2D-GS [5] | 26.93 | 0.800 | 0.251 | 397 /440.8M | 23.25 | 0.830 | 0.212 | 352 /204.4M | 29.32 | 0.899 | 0.257 | 196/335.3M | | 3D-GS [5] | 27.54 | 0.815 | 0.216 | 937/786.7M | 23.91 | 0.852 | 0.172 | 765/430.1M | 29.46 | 0.903 | 0.242 | 398/705.6M | | Mip-Splatting [14] | 27.61 | 0.816 | 0.215 | 1013/838.4M | 23.96 | 0.856 | 0.171 | 832/500.4M | 29.56 | 0.901 | 0.243 | 410/736.8M | | Scaffold-GS [3] | 27.90 | 0.815 | 0.220 | 666/ 197.5M | 24.48 | 0.864 | 0.156 | 626/ 167.5M | 30.28 | 0.909 | 0.239 | 207/ 125.5M | | Anchor-2D-GS | 26.98 | 0.801 | 0.241 | 547/392.7M | 23.52 | 0.835 | 0.199 | 465/279.0M | 29.35 | 0.896 | 0.264 | 162/289.0M | | Anchor-3D-GS | 27.59 | 0.815 | 0.220 | 707/492.0M | 24.02 | 0.847 | 0.184 | 572/349.2M | 29.66 | 0.899 | 0.260 | 150/272.9M | | Our-2D-GS | 27.02 | 0.801 | 0.241 | 397 /371.6M | 23.62 | 0.842 | 0.187 | 330 /191.2M | 29.44 | 0.897 | 0.264 | 84 /202.3M | | Our-3D-GS | 27.65 | 0.815 | 0.220 | 504/418.6M | 24.17 | 0.858 | 0.161 | 424/383.9M | 29.65 | 0.901 | 0.257 | 79 /180.0M | | Our-Scaffold-GS | 28.05 | 0.819 | 0.214 | 657/ 139.6M | 24.68 | 0.866 | 0.153 | 443/ 88.5M | 30.49 | 0.912 | 0.241 | 112/ 71.7M | <details> <summary>x5.png Details</summary>  ### Visual Description \n ## Diagram: Comparative Visual Results of 3D Gaussian Splatting Methods ### Overview This image is a qualitative comparison grid from a technical paper or report. It visually compares the output quality of five different 3D Gaussian Splatting (3D-GS) rendering/reconstruction methods against a Ground Truth (GT) reference across four different scenes. The comparison is presented in a 4-row by 6-column grid. Each row represents a distinct scene, and each column represents a different method or the ground truth. Colored bounding boxes are used to highlight specific regions of interest for detailed comparison. ### Components/Axes * **Column Headers (Top Row):** The six columns are labeled from left to right: 1. `2D-GS` 2. `3D-GS` 3. `Mip-Splatting` 4. `Scaffold-GS` 5. `Our-Scaffold-GS` 6. `GT` (Ground Truth) * **Row Scenes (Left to Right, Top to Bottom):** 1. **Row 1:** An outdoor scene featuring a light blue vintage pickup truck parked on a street. 2. **Row 2:** An indoor kitchen scene with a counter holding a fruit bowl, a blender, and other items. 3. **Row 3:** An indoor living room scene with a piano, chairs, and a large window. 4. **Row 4:** A low-angle shot looking up at a ceiling with a mounted poster or picture. * **Visual Annotations:** * **Red Bounding Boxes:** Used in the first four method columns (`2D-GS` to `Scaffold-GS`) to highlight areas with visual artifacts, blurring, or inaccuracies. * **Green Bounding Boxes:** Used exclusively in the `Our-Scaffold-GS` column to highlight the same regions, showing improved detail and fidelity. * **Yellow Bounding Boxes:** Used in the `GT` column to mark the reference regions for comparison. * **Spatial Grounding:** The boxes are consistently placed in the same relative position within each scene's image across all columns (e.g., top-left corner of the truck's roof, center of the kitchen counter's backsplash, right side of the living room window, center of the ceiling poster). ### Detailed Analysis **Row 1 (Blue Truck):** * **Highlighted Regions:** Two boxes per image. One on the truck's roof/awning structure (top-left) and one on the passenger-side window/windshield (center-left). * **Method Comparison:** * `2D-GS`, `3D-GS`, `Mip-Splatting`, `Scaffold-GS`: The red boxes show significant blurring, loss of structural detail, and "floaters" (disconnected artifacts) in the roof area. The window reflection is also smeared and lacks definition. * `Our-Scaffold-GS`: The green boxes show a much sharper reconstruction of the roof structure with clear edges and minimal artifacts. The window reflection is more coherent and closer to the GT. * `GT`: The yellow boxes show the crisp, high-fidelity reference details. **Row 2 (Kitchen Counter):** * **Highlighted Region:** One box per image, centered on the dark backsplash area behind the blender. * **Method Comparison:** * `2D-GS`, `3D-GS`, `Mip-Splatting`, `Scaffold-GS`: The red boxes reveal severe artifacts. The area is rendered as a blurry, discolored (greenish/yellowish) blob with no discernible texture or detail, completely unlike the reference. * `Our-Scaffold-GS`: The green box shows a dark, textured surface that accurately matches the GT, with no erroneous coloration. * `GT`: The yellow box shows a dark, slightly textured backsplash. **Row 3 (Living Room Window):** * **Highlighted Region:** One box per image, covering the right pane of the large window. * **Method Comparison:** * `2D-GS`, `3D-GS`, `Mip-Splatting`, `Scaffold-GS`: The red boxes show the window pane as a bright, overexposed, and blurry white area with no visible detail of the outside scene. * `Our-Scaffold-GS`: The green box reveals a clear view through the window, showing the outdoor scene (trees, sky) with appropriate exposure and detail. * `GT`: The yellow box shows the clear outdoor view as the reference. **Row 4 (Ceiling Poster):** * **Highlighted Regions:** Two boxes per image. A smaller one on a ceiling fixture (top-center) and a larger one on the main poster (center). * **Method Comparison:** * `2D-GS`, `3D-GS`, `Mip-Splatting`, `Scaffold-GS`: The red boxes show the poster as a blurry, low-contrast, and distorted image. The text and graphics are illegible. The ceiling fixture is also poorly defined. * `Our-Scaffold-GS`: The green boxes show a dramatically improved poster with sharp edges, high contrast, and legible graphic elements. The ceiling fixture is also clearly rendered. * `GT`: The yellow boxes show the sharp, high-contrast reference poster and fixture. ### Key Observations 1. **Consistent Artifact Pattern:** The first four methods (`2D-GS` through `Scaffold-GS`) exhibit similar failure modes across all scenes: severe blurring, loss of high-frequency detail, color bleeding/artifacts, and an inability to render fine structures or reflective surfaces accurately. 2. **Proposed Method Superiority:** The `Our-Scaffold-GS` method consistently produces results that are visually closest to the `GT` across all four diverse scenes (outdoor, indoor object-focused, indoor architecture, and textured surface). 3. **Scene-Dependent Severity:** The degree of failure in the baseline methods varies by scene. The kitchen backsplash (Row 2) and living room window (Row 3) show the most catastrophic failures (complete loss of content), while the truck (Row 1) and poster (Row 4) show degradation but retain some structure. 4. **Highlighting Strategy:** The use of colored boxes (Red for error, Green for improvement, Yellow for truth) creates an immediate and clear visual argument for the efficacy of the proposed method. ### Interpretation This diagram serves as a **qualitative evaluation figure**, common in computer vision and graphics research papers. Its primary purpose is to provide visual, intuitive evidence that the authors' proposed method (`Our-Scaffold-GS`) outperforms several existing state-of-the-art or baseline methods (`2D-GS`, `3D-GS`, `Mip-Splatting`, `Scaffold-GS`). The data suggests that the core innovation in `Our-Scaffold-GS` effectively addresses key limitations of prior 3D Gaussian Splatting techniques, particularly in handling: * **Fine geometric details** (truck roof, ceiling fixture). * **Complex lighting and reflections** (truck window, kitchen scene). * **Textureless or low-texture regions** (kitchen backsplash). * **High-contrast edges and text** (poster). The consistent success across varied scenes implies the improvement is robust and not scene-specific. The figure is designed to persuade the reader that the proposed method achieves a significant leap in visual fidelity, bringing rendered outputs much closer to photorealistic ground truth. The "Peircean" investigation here leads to the conclusion that the authors are demonstrating a **significant technical advancement** in the field of real-time 3D scene reconstruction and rendering. </details> Figure 5: Qualitative comparison of our method and SOTA methods [15, 5, 14, 3] across diverse datasets [50, 60, 61, 51]. We highlight the difference with colored patches. Compared to existing baselines, our method successfully captures very fine details presented in indoor and outdoor scenes, particularly for objects with thin structures such as trees, light-bulbs, decorative texts and etc.. TABLE II: Quantitative comparison on large-scale urban dataset [1, 62, 63]. In addition to three methods compared in Tab. I, we also compare our method with CityGaussian [19] and Hierarchical-GS [2], both of which are specifically targeted at large-scale scenes. It is evident that Octree-GS outperforms the others in both rendering quality and storage efficiency. We highlight best and second-best in each category. | Dataset Method Metrics 3D-GS [5] | Block_Small PSNR $\uparrow$ 26.82 | Block_All SSIM $\uparrow$ 0.823 | Building LPIPS $\downarrow$ 0.246 | #GS(k)/Mem 1432/3387.4M | PSNR $\uparrow$ 24.45 | SSIM $\uparrow$ 0.746 | LPIPS $\downarrow$ 0.385 | #GS(k)/Mem 979/3584.3M | PSNR $\uparrow$ 22.04 | SSIM $\uparrow$ 0.728 | LPIPS $\downarrow$ 0.332 | #GS(k)/Mem 842/1919.2M | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 27.14 | 0.829 | 0.24 | 860/3654.6M | 24.28 | 0.742 | 0.388 | 694/3061.8M | 22.13 | 0.726 | 0.335 | 1066/2498.6M | | Scaffold-GS [3] | 29.00 | 0.868 | 0.210 | 357/ 371.2M | 26.30 | 0.808 | 0.293 | 690/ 2272.2M | 22.42 | 0.719 | 0.336 | 438 / 833.2M | | CityGaussian [19] | 27.46 | 0.808 | 0.267 | 538/4382.7M | 26.26 | 0.800 | 0.324 | 235/4316.6M | 20.94 | 0.706 | 0.310 | 520/3026.8M | | Hierarchical-GS [2] | 27.69 | 0.823 | 0.276 | 271/1866.7M | 26.00 | 0.803 | 0.306 | 492/4874.2M | 23.28 | 0.769 | 0.273 | 1973/3778.6M | | Hierarchical-GS( $\tau_{1}$ ) | 27.67 | 0.823 | 0.276 | 271/1866.7M | 25.44 | 0.788 | 0.320 | 435/4874.2M | 23.08 | 0.758 | 0.285 | 1819/3778.6M | | Hierarchical-GS( $\tau_{2}$ ) | 27.54 | 0.820 | 0.280 | 268/1866.7M | 25.39 | 0.783 | 0.325 | 355/4874.2M | 22.55 | 0.726 | 0.313 | 1473/3778.6M | | Hierarchical-GS( $\tau_{3}$ ) | 26.60 | 0.794 | 0.319 | 221 /1866.7M | 25.19 | 0.773 | 0.352 | 186 /4874.2M | 21.35 | 0.635 | 0.392 | 820/3778.6M | | Our-3D-GS | 29.37 | 0.875 | 0.197 | 175 /755.7M | 26.86 | 0.833 | 0.260 | 218 /3205.1M | 22.67 | 0.736 | 0.320 | 447 /1474.5M | | Our-Scaffold-GS | 29.83 | 0.887 | 0.192 | 360/ 380.3M | 27.31 | 0.849 | 0.229 | 344/ 1648.6M | 23.66 | 0.776 | 0.267 | 619/ 1146.9M | | Dataset Method Metrics 3D-GS [5] | Rubble PSNR $\uparrow$ 25.20 | Residence SSIM $\uparrow$ 0.757 | Sci-Art LPIPS $\downarrow$ 0.318 | #GS(k)/Mem 956/2355.2M | PSNR $\uparrow$ 21.94 | SSIM $\uparrow$ 0.764 | LPIPS $\downarrow$ 0.279 | #GS(k)/Mem 1209/2498.6M | PSNR $\uparrow$ 21.85 | SSIM $\uparrow$ 0.787 | LPIPS $\downarrow$ 0.311 | #GS(k)/Mem 705/950.6M | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 25.16 | 0.746 | 0.335 | 760/1787.0M | 21.97 | 0.763 | 0.283 | 1301/2570.2M | 21.92 | 0.784 | 0.321 | 615/880.2M | | Scaffold-GS [3] | 24.83 | 0.721 | 0.353 | 492 / 470.3M | 22.00 | 0.761 | 0.286 | 596/ 697.7M | 22.56 | 0.796 | 0.302 | 526 / 452.5M | | CityGaussian [19] | 24.67 | 0.758 | 0.286 | 619/3000.3M | 21.92 | 0.774 | 0.257 | 732/3196.0M | 20.07 | 0.757 | 0.290 | 461 /1300.3M | | Hierarchical-GS [2] | 25.37 | 0.761 | 0.300 | 1541/2345.0M | 21.74 | 0.758 | 0.274 | 2040/2498.6M | 22.02 | 0.810 | 0.257 | 2363/2160.6M | | Hierarchical-GS( $\tau_{1}$ ) | 25.27 | 0.754 | 0.305 | 1478/2345.0M | 21.70 | 0.756 | 0.276 | 1972/2498.6M | 22.00 | 0.808 | 0.259 | 2226/2160.6M | | Hierarchical-GS( $\tau_{2}$ ) | 24.80 | 0.724 | 0.329 | 1273/2345.0M | 21.49 | 0.743 | 0.291 | 1694/2498.6M | 21.93 | 0.802 | 0.268 | 1916/2160.6M | | Hierarchical-GS( $\tau_{3}$ ) | 23.55 | 0.628 | 0.414 | 781/2345.0M | 20.69 | 0.683 | 0.363 | 976/2498.6M | 21.50 | 0.766 | 0.324 | 1165/2160.6M | | Our-3D-GS | 24.67 | 0.728 | 0.345 | 489 /1392.6M | 21.60 | 0.736 | 0.314 | 350 /986.2M | 22.52 | 0.817 | 0.256 | 630/1331.2M | | Our-Scaffold-GS | 25.34 | 0.763 | 0.299 | 674/ 693.5M | 22.29 | 0.762 | 0.288 | 344 / 618.8M | 23.38 | 0.828 | 0.240 | 871/ 866.9M | <details> <summary>x6.png Details</summary>  ### Visual Description \n ## Visual Comparison Matrix: Gaussian Splatting Method Performance ### Overview The image is a comparative visual analysis grid, likely from a research paper on 3D Gaussian Splatting (3D-GS) rendering techniques. It presents a side-by-side qualitative comparison of six different methods across three distinct scenes. The primary purpose is to demonstrate the visual fidelity and artifact reduction of a proposed method ("Our-Scaffold-GS") against several baseline techniques and the Ground Truth (GT). ### Components/Axes * **Structure:** A 3-row by 6-column grid. * **Columns (Methods):** Each column is labeled at the top with the name of a rendering method. From left to right: 1. `3D-GS` 2. `Scaffold-GS` 3. `City-GS` 4. `Hierarchical-GS` 5. `Our-Scaffold-GS` (The proposed method) 6. `GT` (Ground Truth - the reference real image) * **Rows (Scenes):** Each row displays a different photographic scene rendered by the six methods. * **Row 1:** A close-up view of a large, flat solar panel array on a rooftop, with a cylindrical vent structure in the foreground. * **Row 2:** An aerial view of a modern building complex with a distinctive curved wing, surrounded by trees and a small pond. * **Row 3:** A top-down aerial view of a dense urban area with multiple rectangular buildings and streets. * **Annotations:** Colored rectangular boxes are overlaid on specific regions of interest within each image to highlight differences in rendering quality. * **Red Boxes:** Used on the first four method columns (`3D-GS` to `Hierarchical-GS`). They highlight areas containing visual artifacts, blurring, or distortions. * **Green Boxes:** Used on the `Our-Scaffold-GS` column. They highlight the same regions as the red boxes, showing improved clarity and correctness. * **Yellow Boxes:** Used on the `GT` column. They mark the corresponding regions in the ground truth reference image. * **Red Arrows:** Small red arrows appear in the `Hierarchical-GS` column, pointing to specific, severe artifacts (e.g., floating blobs, incorrect geometry). ### Detailed Analysis **Scene 1 (Solar Panels):** * **Trend:** Baseline methods (`3D-GS`, `Scaffold-GS`, `City-GS`) show significant blurring and loss of the fine grid structure on the solar panels, especially in the region marked by the red box. The `Hierarchical-GS` method introduces severe artifacts, with large, distorted blobs floating above the panel surface (indicated by red arrows). * **Comparison:** `Our-Scaffold-GS` (green box) successfully reconstructs the sharp, regular grid pattern of the solar panels, closely matching the clarity and structure seen in the `GT` (yellow box). **Scene 2 (Building Complex):** * **Trend:** The foliage of the trees in the lower-left corner (highlighted by boxes) appears as an indistinct, blurry green mass in the first three baseline methods. `Hierarchical-GS` again shows artifacts, with parts of the tree canopy appearing detached or floating. * **Comparison:** `Our-Scaffold-GS` renders the tree foliage with much higher detail and correct geometry, preserving the texture and shape visible in the `GT`. **Scene 3 (Urban Aerial):** * **Trend:** The facades of the buildings, particularly the windows and structural lines, are blurred and lack definition in the baseline methods. The `Hierarchical-GS` method shows warping and incorrect perspective on building edges. * **Comparison:** `Our-Scaffold-GS` maintains sharp, straight edges on the buildings and clear definition of window patterns, aligning well with the `GT`. ### Key Observations 1. **Consistent Artifact Pattern:** The first four methods consistently produce visual artifacts: blurring of high-frequency details (grid lines, foliage texture, windows) and, in the case of `Hierarchical-GS`, severe geometric distortions (floating blobs). 2. **Proposed Method Superiority:** `Our-Scaffold-GS` demonstrates a consistent and significant improvement in visual fidelity across all three diverse scenes. It effectively suppresses the artifacts seen in the baselines. 3. **Ground Truth Alignment:** The regions highlighted in green (`Our-Scaffold-GS`) are visually almost indistinguishable from the corresponding regions in yellow (`GT`), indicating high reconstruction accuracy. 4. **Spatial Consistency of Annotations:** The colored boxes are placed in identical spatial locations across each row, enabling direct, pixel-for-pixel comparison of the same scene region rendered by different methods. ### Interpretation This visual comparison serves as qualitative evidence for the effectiveness of the "Our-Scaffold-GS" method. The data suggests that the proposed technique successfully addresses key failure modes of prior Gaussian Splatting approaches, such as the loss of fine detail and the introduction of floaters or geometric distortions. The relationship between elements is a direct performance hierarchy: `GT` is the ideal target, `Our-Scaffold-GS` is the closest approximation, and the other methods show varying degrees of degradation. The most significant anomaly is the performance of `Hierarchical-GS`, which, despite being a more complex method, introduces the most visually jarring artifacts in these examples. From a Peircean investigative perspective, this image is an *icon* (it resembles the scenes) and an *index* (the artifacts point to underlying algorithmic limitations). The consistent improvement of the proposed method across varied scenes (man-made structures, natural foliage, complex geometry) argues for its robustness and generalizability, which is a more persuasive claim than success on a single, cherry-picked example. The use of the Ground Truth as a final column anchors the entire comparison in reality, making the evaluation objective rather than purely relative. </details> Figure 6: Qualitative comparisons of Octree-GS against baselines [5, 3, 19, 2] across large-scale datasets [62, 63, 1]. As shown in the highlighted patches and arrows above, our method consistently outperforms the baselines, especially in modeling fine details (1st & 3rd row), texture-less regions (2nd row), which are common in large-scale scenes. ### V-A Experimental Setup #### V-A 1 Datasets We conduct comprehensive evaluations on $21$ small-scale scenes and $7$ large-scale scenes from various public datasets. Small-scale scenes include 9 scenes from Mip-NeRF360 [50], 2 scenes from Tanks $\&$ Temples [60], 2 scenes in DeepBlending [61] and 8 scenes from BungeeNeRF [51]. For large-scale scenes, we provide a detailed explanation. Specifically, we evaluate on the Block_Small and Block_All scenes (the latter being 10 $\times$ larger) in the MatrixCity [1] dataset, which uses Zig-Zag trajectories commonly used in oblique photography. In the MegaNeRF [62] dataset, we choose the Rubble and Building scenes, while in the UrbanScene3D [63] dataset, we select the Residence and Sci-Art scenes. Each scene contains thousands of high-resolution images, and we use COLMAP [54] to obtain sparse SfM points and camera poses. In the Hierarchical-GS [2] dataset, we maintain their original settings and compare both methods on a chunk of the SmallCity scene, which includes 1,470 training images and 30 test images, each paired with depth and mask images. For the Block_All scene and the SmallCity scene, we employ the train and test information provided by their authors. For other scenes, we uniformly select one out of every eight images as test images, with the remaining images used for training. #### V-A 2 Metrics In addition to the visual quality metrics PSNR, SSIM [64] and LPIPS [65], we also report the file size for storing anchors, the average selected Gaussian primitives used in per-view rendering process, and the rendering speed FPS as a fair indicator for memory and rendering efficiency. We provide the average quantitative metrics on test sets in the main paper and leave the full table for each scene in the supplementary material. #### V-A 3 Baselines We compare our method against 2D-GS [15], 3D-GS [5], Scaffold-GS [3], Mip-Splatting [14] and two concurrent works, CityGaussian [19] and Hierarchical-GS [2]. In the Mip-NeRF360 [50], Tanks $\&$ Temples [60], and DeepBlending [61] datasets, we compare our method with the top four methods. In the large-scale scene datasets MatrixCity [1], MegaNeRF [62] and UrbanScene3D [63], we add the results of CityGaussian and Hierarchical-GS for comparison. To ensure consistency, we remove depth supervision from Hierarchical-GS in these experiments. Following the original setup of Hierarchical-GS, we report results at different granularities (leaves, $\tau_{1}=3$ , $\tau_{2}=6$ , $\tau_{3}=15$ ), each one is after the optimization of the hierarchy. In the street-view dataset, we compare exclusively with Hierarchical-GS, the current state-of-the-art (SOTA) method for street-view data. In this experiment, we apply the same depth supervision used in Hierarchical-GS for fair comparison. #### V-A 4 Instances of Our Framework To demonstrate the generalizability of the proposed framework, we apply it to 2D-GS [15], 3D-GS [5], and Scaffold-GS [3], which we refer to as Our-2D-GS, Our-3D-GS and Our-Scaffold-GS, respectively. In addition, for a fair comparison and deeper analysis, we modify 2D-GS and 3D-GS to anchor versions. Specifically, we voxelize the input SfM points to anchors and assign each of them 2D or 3D Gaussians, while maintaining the same densification strategy as Scaffold-GS. We denote these modified versions as Anchor-2D-GS and Anchor-3D-GS. #### V-A 5 Implementation Details For 3D-GS model we employ standard L1 and SSIM loss, with weights set to 0.8 and 0.2, respectively. For 2D-GS model, we retain the distortion loss $\mathcal{L}_{d}=\sum_{i,j}\omega_{i}\omega_{j}\left|z_{i}-z_{j}\right|$ and normal loss $\mathcal{L}_{n}=\sum_{i}\omega_{i}\left(1-\mathbf{n}_{i}^{\mathrm{T}}\mathbf{N }\right)$ , with weights set to 0.01 and 0.05, respectively. For Scaffold-GS model, we keep an additional volume regularization loss $\mathcal{L}_{\mathrm{vol}}=\sum_{i=1}^{N}\operatorname{Prod}\left(s_{i}\right)$ , with a weight set to 0.01. We adjust the training and densification iterations across all compared methods to ensure a fair comparison. Specifically, for small-scale scenes [50, 60, 61, 51, 2], training was set to 40k iterations, with densification concluding at 20k iterations. For large-scale scenes [1, 62, 63], training was set to 100k iterations, with densification ending at 50k iterations. We set the voxel size to $0.001$ for all scenes in the modified anchor versions of 2D-GS [15], 3D-GS [5], and Scaffold-GS [3], while for our method, we set the voxel size for the intermediate level of the anchor grid to $0.02$ . For the progress training, we set the total training iteration to $10$ k with $\omega=1.5$ . Since not all layers are fully densified during the progressive training process, we extend the densification by an additional $10$ k iterations, and we set the densification interval $T=100$ empirically. We set the visibility threshold $\tau_{v}$ to $0.7$ for the small-scale scenes [50, 60, 61, 51],as these datasets contain densely captured images, while for large-scale scenes [62, 63, 2], we set $\tau_{v}$ to $0.01$ . In addition, for the multi-scale dataset [51], we set $\tau_{v}$ to $0.2$ . All experiments are conducted on a single NVIDIA A100 80G GPU. To avoid the impact of image storage on GPU memory, all images were stored on the CPU. <details> <summary>x7.png Details</summary>  ### Visual Description ## Visual Comparison Diagram: 3D Gaussian Splatting Reconstruction Quality ### Overview This image is a qualitative comparison of different 3D Gaussian Splatting (GS) methods for novel view synthesis. It presents a side-by-side visual evaluation across two different scenes (top row: street scene, bottom row: building facade). The comparison aims to demonstrate the visual fidelity and detail preservation of the proposed methods ("Our-3D-GS" and "Our-Scaffold-GS") against baseline methods ("Hierarchical-GS" and "Hierarchical-GS (T2)") and the Ground Truth ("GT"). ### Components/Axes * **Structure:** A 2x5 grid of sub-images. * **Column Headers (Method Labels):** Centered above each column. 1. `Hierarchical-GS` 2. `Hierarchical-GS (T2)` 3. `Our-3D-GS` 4. `Our-Scaffold-GS` 5. `GT` (Ground Truth) * **Visual Annotations:** Colored bounding boxes highlight specific regions of interest for comparison. * **Red Boxes:** Used for `Hierarchical-GS`, `Hierarchical-GS (T2)`, and `Our-3D-GS`. * **Green Box:** Used for `Our-Scaffold-GS`. * **Yellow Box:** Used for `GT`. * **Scenes:** * **Top Row:** A street view with parked cars, buildings, and a prominent sign on a car's rear window. * **Bottom Row:** A close-up view of a building facade with windows, a scooter, and architectural details. ### Detailed Analysis **Top Row - Street Scene:** * **Focus Area:** A sign on the rear window of a dark blue car. * **Text Transcription (Visible in GT):** The sign contains French text. The clearest words are "BRAYA", "INAGE", and "DANS". The full text is partially obscured but appears to be an advertisement or notice. * **Method Comparison (Left to Right):** * `Hierarchical-GS`: The text within the red box is heavily blurred and illegible. * `Hierarchical-GS (T2)`: The text is extremely blurred, appearing as a smudge with no discernible characters. * `Our-3D-GS`: The text is clearer than the previous two but still blurry. Some letter shapes are vaguely visible. * `Our-Scaffold-GS`: The text within the green box is significantly sharper. The words "BRAYA", "INAGE", and "DANS" are readable, though not perfectly crisp. * `GT`: The text within the yellow box is sharp and fully legible, serving as the reference. **Bottom Row - Building Facade:** * **Focus Areas:** Two regions are highlighted: a window on the left and a section of the facade/awning on the right. * **Method Comparison (Left to Right):** * `Hierarchical-GS`: Both red-boxed regions are very blurry. The window pane details and facade texture are lost. * `Hierarchical-GS (T2)`: Similar severe blurriness as the first column. * `Our-3D-GS`: Moderate improvement. Some structural lines are visible, but fine details and textures remain smeared. * `Our-Scaffold-GS`: Notable improvement in the green-boxed regions. The window frame and the vertical lines on the facade are much sharper and more defined, approaching the GT. * `GT`: The yellow-boxed regions show crisp edges, clear window panes, and distinct architectural details. ### Key Observations 1. **Progressive Improvement:** There is a clear visual trend of improving reconstruction quality from left to right across the columns, culminating in the `GT`. 2. **Text as a Key Differentiator:** The ability to reconstruct legible text (top row) is a strong differentiator. `Our-Scaffold-GS` performs markedly better than the Hierarchical baselines and `Our-3D-GS` in this regard. 3. **Detail Preservation:** The bottom row demonstrates that `Our-Scaffold-GS` preserves high-frequency details (edges, lines, textures) much better than the other non-GT methods, which produce smoothed-out or blurred results. 4. **Failure Case of `Hierarchical-GS (T2)`:** The `(T2)` variant appears to perform worse than the standard `Hierarchical-GS` in these examples, producing the most blurred results. ### Interpretation This diagram serves as visual evidence for a research paper, arguing for the superiority of the authors' proposed methods, particularly `Our-Scaffold-GS`. The comparison is designed to show that their approach better handles challenging aspects of scene reconstruction: * **Semantic Detail:** Legible text is a high-level semantic feature. The success of `Our-Scaffold-GS` here suggests it better integrates or preserves features critical for recognition. * **Geometric Fidelity:** The sharp edges and lines in the building facade (bottom row) indicate better geometric accuracy and less "floaters" or artifacts common in neural rendering. * **Methodological Progress:** The progression from `Hierarchical-GS` to `Our-3D-GS` to `Our-Scaffold-GS` implies an iterative improvement in the underlying algorithm, with the scaffold-based approach yielding the most visually convincing results closest to ground truth. The use of colored boxes strategically draws the viewer's eye to the most telling differences, making the argument visually intuitive. </details> Figure 7: Qualitative comparisons of our approach against Hierarchical-GS [2]. We present both the highest-quality setting (leaves) and a reasonably reduced LOD setting ( $\tau_{2}$ = 6 pixels). Octree-GS demonstrates superior performance in street views, specially in thin geometries and texture-less regions (e.g., railings, signs and pavements.) TABLE III: Quantitative comparison on the SMALLCITY scene of the Hierarchical-GS [2] dataset. The competing metrics are sourced from the original paper. | Method | PSNR( $\uparrow$ ) | SSIM( $\uparrow$ ) | LPIPS( $\downarrow$ ) | FPS( $\uparrow$ ) | | --- | --- | --- | --- | --- | | 3D-GS [5] | 25.34 | 0.776 | 0.337 | 99 | | Hierarchical-GS [2] | 26.62 | 0.820 | 0.259 | 58 | | Hierarchical-GS( $\tau_{1}$ ) | 26.53 | 0.817 | 0.263 | 86 | | Hierarchical-GS( $\tau_{2}$ ) | 26.29 | 0.810 | 0.275 | 110 | | Hierarchical-GS( $\tau_{3}$ ) | 25.68 | 0.786 | 0.324 | 159 | | Our-3D-GS | 25.77 | 0.811 | 0.272 | 130 | | Our-Scaffold-GS | 26.10 | 0.826 | 0.235 | 89 | <details> <summary>x8.png Details</summary>  ### Visual Description ## Comparative Analysis: 2D Gaussian Splatting Methods ### Overview The image is a three-panel comparative visualization from a technical paper or report, evaluating the performance of different 2D Gaussian Splatting (2D-GS) algorithms. Each panel shows a rendered 3D scene of a tree stump in a forest setting, with specific regions highlighted to demonstrate rendering quality differences. The comparison focuses on three methods: a baseline, an anchor-based variant, and a proposed method ("Our-2D-GS"). ### Components/Axes The image is divided into three horizontally arranged panels, each with a title bar at the top containing the method name and performance metrics. **Panel Titles & Metrics (Top of each panel):** * **(a) Left Panel:** `2D-GS: 26.16dB / 413K / 670M` * **(b) Center Panel:** `Anchor-2D-GS: 26.25dB / 491K / 359M` * **(c) Right Panel:** `Our-2D-GS: 26.40dB / 385K / 293M` **Metric Legend (Inferred from standard ML paper conventions):** * `dB`: Peak Signal-to-Noise Ratio (PSNR), a measure of image quality (higher is better). * `K`: Likely denotes the number of model parameters in thousands (e.g., 413K = 413,000 parameters). * `M`: Likely denotes memory usage or computational cost in millions of operations or megabytes (lower is better). **Visual Highlighting System:** * **Red Boxes:** Used in panels (a) and (b) to indicate regions with visual artifacts, blurriness, or lower fidelity. * **Green Boxes:** Used in panel (c) to indicate the same regions, now rendered with improved clarity and detail. * **Box Placement:** Each panel has three highlighted regions: 1. **Top-left:** A rectangular area focusing on the grassy ground. 2. **Center-left:** A larger rectangular area focusing on the mid-ground grass and foliage. 3. **Bottom-right:** A square area focusing on a small, detailed plant or fungus growing on the tree stump. ### Detailed Analysis **Panel (a) - 2D-GS (Baseline):** * **Metrics:** PSNR = 26.16 dB, Parameters = 413K, Cost/Memory = 670M. * **Visual Quality (Red Boxes):** * **Top-left & Center-left:** The grass texture appears blurry and lacks high-frequency detail. Individual blades are not well-defined. * **Bottom-right:** The small plant detail is very blurry and poorly resolved, appearing as an indistinct smudge. **Panel (b) - Anchor-2D-GS:** * **Metrics:** PSNR = 26.25 dB (slightly higher than baseline), Parameters = 491K (higher than baseline), Cost/Memory = 359M (significantly lower than baseline). * **Visual Quality (Red Boxes):** * **Top-left & Center-left:** Grass texture shows marginal improvement over (a) but remains generally blurry. * **Bottom-right:** The plant detail is slightly more recognizable than in (a) but is still quite blurry and lacks sharp edges. **Panel (c) - Our-2D-GS (Proposed Method):** * **Metrics:** PSNR = 26.40 dB (highest of the three), Parameters = 385K (lowest of the three), Cost/Memory = 293M (lowest of the three). * **Visual Quality (Green Boxes):** * **Top-left & Center-left:** The grass texture is noticeably sharper. Individual blades and variations in the ground cover are more distinct. * **Bottom-right:** The small plant detail is rendered with significantly higher clarity. Its structure and edges are well-defined compared to the blurry versions in (a) and (b). ### Key Observations 1. **Performance Trend:** The proposed method (`Our-2D-GS`) achieves the best balance of all metrics: highest image quality (PSNR), fewest parameters, and lowest computational/memory cost. 2. **Visual Fidelity:** There is a clear visual progression from blurry (a) to slightly less blurry (b) to sharp (c) in the highlighted regions, correlating with the increasing PSNR values. 3. **Efficiency Trade-off:** The `Anchor-2D-GS` method reduces cost (359M vs 670M) but increases parameter count (491K vs 413K) for a small quality gain. The proposed method improves upon both axes. 4. **Spatial Consistency:** The improvement is consistent across different types of detail—both the repetitive texture of grass and the unique, fine structure of the small plant are enhanced in panel (c). ### Interpretation This image serves as a qualitative and quantitative validation of a new 2D Gaussian Splatting technique. The data suggests that the authors' method (`Our-2D-GS`) successfully addresses a key challenge in neural rendering: improving visual fidelity while simultaneously reducing model complexity and resource consumption. The red-to-green box coding is a deliberate visual argument. It directs the viewer's attention to specific failure cases of prior methods (blurry textures and lost details) and demonstrates their resolution in the new approach. The accompanying metrics provide the empirical backbone, showing that the visual improvement is not due to simply using more resources; in fact, it's achieved with fewer. The most significant finding is the decoupling of quality from resource cost. Typically, higher quality requires more parameters or computation. Here, the proposed method breaks that trend, achieving the best quality with the smallest footprint. This implies a more efficient underlying algorithm or representation, which is a substantial contribution to the field of real-time 3D rendering and computer vision. The comparison positions the new method as the new state-of-the-art among the three presented. </details> Figure 8: Comparison of different versions of the 2D-GS [15] model. We showcase the rendering results on the stump scene from the Mip-NeRF360 [50] dataset. We report PSNR, average number of Gaussians for rendering and storage size. TABLE IV: Quantitative comparison on the BungeeNeRF [51] dataset. We provide metrics for each scale and their average across all four. Scale-1 denotes the closest views, while scale-4 covers the entire landscape. We note a notable rise in Gaussian counts for baseline methods when zooming out from scale 1 to 4, whereas our method maintains a significantly lower count, ensuring consistent rendering speed across all LOD levels. We highlight best and second-best in each category. | Dataset | BungeeNeRF (Average) | scale-1 | scale-2 | scale-3 | scale-4 | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Method Metrics | PSNR $\uparrow$ | SSIM $\uparrow$ | LPIPS $\downarrow$ | #GS(k)/Mem | PSNR $\uparrow$ | #GS(k) | PSNR $\uparrow$ | #GS(k) | PSNR $\uparrow$ | #GS(k) | PSNR $\uparrow$ | #GS(k) | | 2D-GS [5] | 27.10 | 0.903 | 0.121 | 1079/886.1M | 28.18 | 205 | 28.11 | 494 | 25.99 | 1826 | 23.71 | 2365 | | 3D-GS [5] | 27.79 | 0.917 | 0.093 | 2686/1792.3M | 30.00 | 522 | 28.97 | 1272 | 26.19 | 4407 | 24.20 | 5821 | | Mip-Splatting [14] | 28.14 | 0.918 | 0.094 | 2502/1610.2M | 29.79 | 503 | 29.37 | 1231 | 26.74 | 4075 | 24.44 | 5298 | | Scaffold-GS [3] | 28.16 | 0.917 | 0.095 | 1652/ 319.2M | 30.48 | 303 | 29.18 | 768 | 26.56 | 2708 | 24.95 | 3876 | | Anchor-2D-GS | 27.18 | 0.885 | 0.140 | 1050/533.8M | 29.80 | 260 | 28.26 | 601 | 25.43 | 1645 | 23.71 | 2026 | | Anchor-3D-GS | 27.90 | 0.909 | 0.114 | 1565/790.3M | 30.85 | 391 | 29.29 | 905 | 26.13 | 2443 | 24.49 | 3009 | | Our-2D-GS | 27.34 | 0.893 | 0.129 | 676 /736.1M | 30.09 | 249 | 28.72 | 511 | 25.42 | 1003 | 23.41 | 775 | | Our-3D-GS | 27.94 | 0.909 | 0.110 | 952 /1045.7M | 31.11 | 411 | 29.42 | 819 | 25.88 | 1275 | 23.77 | 938 | | Our-Scaffold-GS | 28.39 | 0.923 | 0.088 | 1474/ 296.7M | 31.11 | 486 | 29.59 | 1010 | 26.51 | 2206 | 25.07 | 2167 | ### V-B Results Analysis Our evaluation encompasses a wide range of scenes, including indoor and outdoor environments, both synthetic and real-world, as well as large-scale urban scenes from both aerial views and street views. We demonstrate that our method preserves fine-scale details while reducing the number of Gaussians, resulting in faster rendering speed and lower storage overhead, as shown in Fig. 5, 6, 7, 8 and Tab. I, IV, II, III, V. #### V-B 1 Performance Analysis Quality Comparisons Our method introduces anchors with octree structure, which decouple multi-scale Gaussian primitives into varying LOD levels. This approach enables finer Gaussian primitives to capture scene details more accurately, thereby enhancing the overall rendering quality. In Fig. 5, 6, 7 and Tab. I, II, III, we compare Octree-GS to previous state-of-the-art (SOTA) methods, demonstrating that our method consistently outperforms the baselines across both small-scale and large-scale scenes, especially in fine details and texture-less regions. Notably, when compared to Hierarchical-GS [2] on the street-view dataset, Octree-GS exhibits slightly lower PSNR values but significantly better visual quality, with LPIPS scores of 0.235 for ours and 0.259 for theirs. Storage Comparisons As shown in Tab. I, II, our method reduces the number of Gaussian primitives used for rendering, resulting in faster rendering speed and lower storage overhead. This demonstrates the benefits of our two main improvements: 1) our LOD structure efficiently arranges Gaussian primitives, with coarse primitives representing low-frequency scene information, which previously required redundant primitives; and 2) our view-frequency strategy significantly prunes unnecessary primitives. Variants Comparisons As described in Sec. IV, our method is agnostic to the specific Gaussian representation and can be easily adapted to any Gaussian-based method with minimal effort. In Tab. I, the modified anchor-version of 2D-GS [15] and 3D-GS [5] achieve competitive rendering quality with fewer file storage than the original methods. This demonstrates that the anchor design organizes the Gaussian primitives more efficiently, reducing redundancy and creating a more compact way. More than the anchor design, Octree-GS delivers better visual performance and fewer Gaussian primitives as shown in Tab. I, which benefits from the explicit, multi-level anchor design. In Fig. 8, we compare the vanilla 2D-GS with the anchor-version and octree-version method. Among them, the octree-version provides the most detail and the least amount of Gaussian primitives and storage. TABLE V: Quantitative comparison of rendering speed on the MatrixCity [1] dataset. We report the averaged FPS on three novel view trajectories (Fig. 9). Our method shows consistent rendering speed above $30$ FPS at $2k$ image resolution while all baseline methods fail to meet the real-time performance. | Method Traj. 3D-GS [5] Scaffold-GS [3] | $T_{1}$ 13.81 6.69 | $T_{2}$ 11.70 7.37 | $T_{3}$ 13.50 8.04 | | --- | --- | --- | --- | | Hierarchical-GS [2] | 9.13 | 8.54 | 8.91 | | Hierarchical-GS( $\tau_{1}$ ) | 16.14 | 13.26 | 14.79 | | Hierarchical-GS( $\tau_{2}$ ) | 19.70 | 19.59 | 18.94 | | Hierarchical-GS( $\tau_{3}$ ) | 24.33 | 25.29 | 24.75 | | Our-3D-GS | 57.08 | 56.85 | 56.07 | | Our-Scaffold-GS | 40.91 | 35.17 | 40.31 | <details> <summary>x9.png Details</summary>  ### Visual Description ## Line Chart and 3D Trajectory Diagram: Rendering Speed vs. Distance and Scene Trajectories ### Overview The image is a composite figure containing two distinct panels. Panel (a) is a line chart comparing the rendering speed (Frames Per Second, FPS) of several Gaussian Splatting (GS) methods as a function of camera distance. Panel (b) is a 3D visualization showing three distinct camera trajectories (T1, T2, T3) around a central 3D scene model labeled "Block_All". ### Components/Axes **Panel (a) - Line Chart:** * **Title:** "(a) Rendering Speed (FPS of Traj. T1) w.r.t Distance" * **Y-Axis:** Label is "FPS". Scale ranges from 0 to 90, with major ticks at 0, 30, 60, and 90. * **X-Axis:** Label is "Distance(m)". Scale ranges from 0 to 40 meters, with major ticks at 10, 20, 30, and 40. * **Legend:** Located in the top-right quadrant of the chart. It lists seven data series with corresponding line colors: * `Scaffold-GS` (Blue line) * `Our-3D-GS` (Dark teal/gray-blue line) * `Our-Scaffold-GS` (Green line) * `Hierarchical-GS` (Yellow line) * `Hierarchical-GS(T1)` (Orange line) * `Hierarchical-GS(T2)` (Red-orange line) * `Hierarchical-GS(T3)` (Red line) * **Reference Line:** A dashed gray horizontal line is present at approximately 30 FPS. **Panel (b) - 3D Diagram:** * **Title:** "(b) Trajectories of the Block_All scene" * **Central Object:** A dense, voxel-like 3D model of a building or city block, rendered in grayscale. * **Trajectories:** Three distinct paths of camera frustums (pyramids) are shown: * **T1 (Magenta/Purple):** A long, linear trajectory extending from the top-right corner down towards the central model. * **T2 (Red):** A circular or orbital trajectory surrounding the central model at a medium distance. * **T3 (Green):** A more complex, possibly spiral or multi-orbit trajectory that appears closer to the model than T2. * **Labels:** The trajectories are labeled with text: `T1`, `T2`, and `T3` placed near their respective paths. ### Detailed Analysis **Panel (a) - Chart Data & Trends:** * **Scaffold-GS (Blue):** Starts at ~40 FPS at 0m. Shows a steep, consistent decline, dropping below 10 FPS by 20m and approaching near 0 FPS by 40m. * **Our-3D-GS (Dark Teal):** Starts at ~50 FPS at 0m. Shows a steady, shallow upward trend, reaching approximately 60 FPS by 40m. It maintains the highest FPS for distances beyond ~5m. * **Our-Scaffold-GS (Green):** Exhibits the most dramatic trend. Starts at the highest point, ~90 FPS at 0m. Drops extremely sharply to ~30 FPS by 5m. After this drop, it shows a slight recovery and stabilizes between 30-35 FPS for the remainder of the distance range. * **Hierarchical-GS (Yellow):** Starts low at ~10 FPS. Shows a very slight, gradual increase, ending at approximately 15 FPS at 40m. It is consistently the lowest-performing method. * **Hierarchical-GS(T1) (Orange):** Starts at ~15 FPS. Shows a steady, moderate upward trend, reaching approximately 25 FPS by 40m. * **Hierarchical-GS(T2) (Red-Orange):** Starts at ~20 FPS. Shows a steady upward trend, similar in slope to T1 but offset higher, reaching approximately 30 FPS by 40m. * **Hierarchical-GS(T3) (Red):** Starts at ~25 FPS. Shows a steady upward trend, reaching approximately 30 FPS by 40m, converging with the T2 line at the far distance. **Panel (b) - Diagram Components:** The diagram spatially defines the three camera paths referenced in the chart's legend for the Hierarchical-GS variants. T1 is a distant, linear approach. T2 is a medium-range orbit. T3 is a closer, more intricate flight path. The central "Block_All" scene is the common subject being rendered from these viewpoints. ### Key Observations 1. **Performance Hierarchy:** `Our-3D-GS` demonstrates the best and most stable performance at medium to long distances. `Our-Scaffold-GS` has exceptional near-field performance but drops to a moderate level quickly. 2. **Distance Sensitivity:** `Scaffold-GS` is highly sensitive to distance, with performance degrading rapidly. The `Hierarchical-GS` variants show a positive correlation between distance and FPS, suggesting they may be optimizing for or are less burdened by distant views. 3. **Trajectory Impact:** For the `Hierarchical-GS` method, the rendering speed varies by trajectory (T1, T2, T3) at any given distance, with the closer/more complex trajectory (T3) generally yielding higher FPS than the distant linear one (T1) at the same distance metric. 4. **30 FPS Threshold:** The dashed line at 30 FPS serves as a potential performance benchmark. `Our-3D-GS` and `Our-Scaffold-GS` (after its initial drop) stay above this line. The `Hierarchical-GS` variants approach or cross it only at greater distances. ### Interpretation This figure is likely from a research paper on 3D Gaussian Splatting rendering optimization. It aims to demonstrate the performance advantages of the authors' proposed methods (`Our-3D-GS`, `Our-Scaffold-GS`) against prior work (`Scaffold-GS`, `Hierarchical-GS`). The data suggests that the authors' methods achieve a better balance between raw speed and distance invariance. `Our-3D-GS` appears to be the most robust overall solution. The sharp drop in `Our-Scaffold-GS` might indicate a highly optimized but view-dependent acceleration structure that is most effective in the near field. The inclusion of the trajectory diagram (b) is crucial for context. It explains that the FPS measurements in (a) are specifically for the challenging, distant linear trajectory T1. The performance of `Hierarchical-GS` on its own specialized trajectories (T2, T3) is better than on T1, but still generally lags behind the authors' methods on T1. This implies the proposed methods are not only faster but also more generalizable across different camera paths, which is a significant advantage for applications like free-viewpoint video or virtual reality where camera movement is unpredictable. The "Block_All" scene represents a complex, real-world test case, adding credibility to the performance claims. </details> Figure 9: (a) The figure shows the rendering speed with respect to distance for different methods along trajectory $T_{1}$ , both Our-3D-GS and Our-Scaffold-GS achieve real-time rendering speeds ( $\geq 30$ FPS). (b) The visualization depicts three different trajectories, corresponding to $T_{1}$ , $T_{2}$ , and $T_{3}$ in Tab. V, which are commonly found in video captures of large-scale scenes and illustrate the practical challenges involved. #### V-B 2 Efficiency Analysis Rendering Time Comparisons Our goal is to enable real-time rendering of Gaussian representation models at any position within the scene using Level-of-Detail techniques. To evaluate our approach, we compare Octree-GS with three state-of-the-art methods [5, 3, 2] on three novel view trajectories in Tab. V and Fig. 9. These trajectories represent common movements in large-scale scenes, such as zoom-in, 360-degree circling, and multi-scale circling. As shown in Tab. V and Fig. 5, our method excels at capturing fine-grained details in close views while maintaining consistent rendering speeds at larger scales. Notably, our rendering speed is nearly $10\times$ faster than Scaffold-GS [3] in large-scale scenes and extreme-view sequences, which depends on our innovative LOD structure design. Training Time Comparisons While our core contribution is the acceleration of rendering speed through LOD design, training speed is also critical for the practical application of photorealistic scene reconstruction. Below, we provide statistics for the Mip-NeRF360 [50] dataset (40k iterations): 2D-GS (28 mins), 3D-GS (34 mins), Mip-Splatting (46 mins), Scaffold-GS (29 mins), and Our-2D-GS (20 mins), Our-3D-GS (21 mins), Our-Scaffold-GS (23 mins). Additionally, we report the training time for the concurrent work, Hierarchical-GS [2]. This method requires three stages to construct the LOD structure, which result in a longer training time (38 minutes for the first stage, totaling 69 minutes). In contrast, under the same number of iterations, our proposed method requires less time. Our-Scaffold-GS achieves the construction and optimization of the LOD structure in a single stage, taking only 35 minutes. The reason our method can accelerate training time is twofold: the number of Gaussian primitives is relatively smaller, and not all Gaussians need to be optimized during progressive training. TABLE VI: Quantitative comparison on multi-resolution Mip-NeRF360 [50] dataset. Octree-GS achieves better rendering quality across all scales compared to baselines. | 3D-GS [5] | 26.16 | 0.757 | 0.301 | 27.33 | 0.822 | 0.202 | 28.55 | 0.884 | 0.117 | 27.85 | 0.897 | 0.086 | 430 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Scaffold-GS [3] | 26.81 | 0.767 | 0.285 | 28.09 | 0.835 | 0.183 | 29.52 | 0.898 | 0.099 | 28.98 | 0.915 | 0.072 | 369 | | Mip-Splatting [14] | 27.43 | 0.801 | 0.244 | 28.56 | 0.857 | 0.152 | 30.00 | 0.910 | 0.087 | 31.05 | 0.942 | 0.055 | 642 | | Our-Scaffold-GS | 27.68 | 0.791 | 0.245 | 28.82 | 0.850 | 0.157 | 30.27 | 0.906 | 0.087 | 31.18 | 0.932 | 0.057 | 471 | <details> <summary>x10.png Details</summary>  ### Visual Description ## Composite Image: 3D Gaussian Splatting Method Comparison ### Overview This image is a technical comparison figure, likely from a computer vision or graphics research paper. It visually and quantitatively compares the performance of four different 3D Gaussian Splatting (3D-GS) methods for novel view synthesis. The comparison is performed on two distinct scenes: a bicycle scene and a tree bench scene. For each scene, the image shows a full reference view and zoomed-in crops from two different rendering resolutions ("Full" and "1/8") to highlight reconstruction details. Performance is quantified using Peak Signal-to-Noise Ratio (PSNR) values overlaid on each crop. ### Components/Axes **1. Header/Column Labels (Top of Image):** The image is organized into columns, each corresponding to a specific method. The labels from left to right are: * `3D-GS` * `Scaffold-GS` * `Mip-Splatting` * `Our-Scaffold-GS` **2. Scene Reference Images (Left and Center):** * **Left Scene:** A photograph of a white bicycle parked next to a black bench on grass. A red bounding box highlights the front wheel area, indicating the region shown in the zoomed crops to its right. * **Center Scene:** A photograph of a hexagonal wooden bench built around a large tree trunk in a park. A red bounding box highlights a section of the background fence, indicating the region shown in the zoomed crops to its right. **3. Zoomed Crop Panels (Right of each reference image):** For each scene, there is a 2x4 grid of zoomed-in image crops. * **Rows:** Correspond to rendering resolution. * Top Row: Labeled `Full` on the far right. * Bottom Row: Labeled `1/8` on the far right. * **Columns:** Correspond to the four methods listed in the header. * **Overlaid Text:** Each crop has a PSNR value (in dB) in its top-left corner. Values for the `Our-Scaffold-GS` method are highlighted in green text. ### Detailed Analysis **A. Bicycle Scene (Left Side):** * **Reference:** Full image of bicycle. Zoomed region is the front wheel spokes and hub. * **"Full" Resolution Crops (Top Row):** * `3D-GS`: PSNR = `18.24dB`. Image appears blurry, spokes are poorly defined. * `Scaffold-GS`: PSNR = `18.02dB`. Similar blurriness to 3D-GS. * `Mip-Splatting`: PSNR = `20.15dB`. Noticeably sharper spoke definition. * `Our-Scaffold-GS`: PSNR = `20.42dB` (green). Sharpest detail among the four, with clear spoke edges. * **"1/8" Resolution Crops (Bottom Row):** * `3D-GS`: PSNR = `21.59dB`. Very blurry, almost no spoke detail. * `Scaffold-GS`: PSNR = `21.80dB`. Very blurry, similar to 3D-GS. * `Mip-Splatting`: PSNR = `25.97dB`. Significant improvement, some spoke structure visible. * `Our-Scaffold-GS`: PSNR = `26.20dB` (green). Best detail preservation at this lower resolution. **B. Tree Bench Scene (Center/Right Side):** * **Reference:** Full image of tree bench. Zoomed region is a section of the black metal fence in the background. * **"Full" Resolution Crops (Top Row):** * `3D-GS`: PSNR = `22.95dB`. Fence bars are visible but slightly soft. * `Scaffold-GS`: PSNR = `22.72dB`. Similar to 3D-GS. * `Mip-Splatting`: PSNR = `22.85dB`. Comparable to the first two. * `Our-Scaffold-GS`: PSNR = `23.30dB` (green). Marginally sharper fence definition. * **"1/8" Resolution Crops (Bottom Row):** * `3D-GS`: PSNR = `25.40dB`. Fence details are smeared and indistinct. * `Scaffold-GS`: PSNR = `24.58dB`. Poor detail, similar to 3D-GS. * `Mip-Splatting`: PSNR = `28.11dB`. Major improvement, fence structure is clear. * `Our-Scaffold-GS`: PSNR = `28.73dB` (green). Highest fidelity, fence bars are sharp and well-separated. ### Key Observations 1. **Consistent Performance Hierarchy:** Across both scenes and both resolution levels, the `Our-Scaffold-GS` method achieves the highest PSNR value, indicated by the green text. `Mip-Splatting` consistently ranks second. 2. **Resolution Impact:** The performance gap between methods is more pronounced at the `1/8` resolution. While `Mip-Splatting` and `Our-Scaffold-GS` show substantial PSNR gains at lower resolution compared to their "Full" scores, `3D-GS` and `Scaffold-GS` show much smaller improvements or even decreases (e.g., Scaffold-GS in the tree scene). 3. **Visual Correlation:** The higher PSNR values for `Mip-Splatting` and `Our-Scaffold-GS` correspond directly to visibly sharper images with better-preserved high-frequency details (spokes, fence bars) in the crops. 4. **Method Grouping:** `3D-GS` and `Scaffold-GS` produce visually similar, lower-quality results with significant blurring, especially at the `1/8` resolution. ### Interpretation This figure serves as empirical evidence for the superiority of the proposed `Our-Scaffold-GS` method over existing 3D Gaussian Splatting techniques (`3D-GS`, `Scaffold-GS`, `Mip-Splatting`). The data suggests that `Our-Scaffold-GS` is more robust to changes in rendering resolution, maintaining higher visual fidelity (as measured by PSNR) when computational or memory constraints might force the use of lower-resolution models (`1/8`). The comparison highlights a key challenge in view synthesis: preserving fine geometric details (like thin spokes or fence bars) which are easily lost as "aliasing" or blurring. The significant PSNR lead of `Mip-Splatting` and `Our-Scaffold-GS` at `1/8` resolution implies these methods incorporate more effective anti-aliasing or detail-preserving mechanisms. The green highlighting on `Our-Scaffold-GS` values is a deliberate visual cue to draw the reader's attention to the best-performing method, reinforcing the paper's main contribution. The choice of two diverse scenes (one with thin, high-contrast structures and one with repetitive background patterns) strengthens the claim that the improvement is generalizable. </details> Figure 10: Qualitative comparison of full-resolution and low-resolution (1/8 of full-resolution) on multi-resolution Mip-NeRF360 [50] datasets. Our approach demonstrates adaptive anti-aliasing and effectively recovers fine-grained details, while baselines often produce artifacts, particularly on elongated structures such as bicycle wheels and handrails. #### V-B 3 Robustness Analysis <details> <summary>x11.png Details</summary>  ### Visual Description ## Visual Comparison Chart: 3D Gaussian Splatting (3D-GS) Reconstruction Quality and Model Size ### Overview This image presents a qualitative and quantitative comparison of three different 3D Gaussian Splatting (3D-GS) methods for scene reconstruction. The comparison is structured across three rows, each representing a different method, and two columns, each representing a different scene and scale factor. The primary metrics shown are reconstruction quality (in Peak Signal-to-Noise Ratio, PSNR, measured in dB) and model size (in millions of Gaussians, denoted as M). ### Components/Axes * **Layout:** A 3x2 grid of image panels. * **Rows (Methods):** * **Top Row:** Baseline "3D-GS" method. * **Middle Row:** "Anchor-3D-GS" method. * **Bottom Row:** "Our-3D-GS" method (the proposed technique). * **Columns (Scenes & Scales):** * **Left Column:** A close-up aerial view of a cathedral (likely the Sagrada Família). Labeled "Scale - 1". * **Right Column:** A wider aerial view of a dense urban city block. Labeled "Scale - 4". * **Text Overlays (Per Panel):** Each image panel contains text in the top-left and top-right corners. * **Top-Left Text:** Indicates the scale factor (e.g., "Scale - 1"). * **Top-Right Text:** Indicates the method name, the PSNR value, and the model size, formatted as `[Method]: [PSNR]dB / [Size]M`. * **Visual Annotations:** Each panel contains red bounding boxes. A smaller red box highlights a specific region of interest in the main image, and a larger red box shows a magnified view of that region to emphasize reconstruction detail and artifacts. ### Detailed Analysis **Quantitative Data Extraction:** | Method | Scene / Scale | PSNR (dB) | Model Size (Millions) | | :--- | :--- | :--- | :--- | | **3D-GS** | Cathedral / Scale-1 | 28.12 | 0.63M | | **3D-GS** | City / Scale-4 | 22.17 | 7.76M | | **Anchor-3D-GS** | Cathedral / Scale-1 | 29.07 | 0.47M | | **Anchor-3D-GS** | City / Scale-4 | 22.81 | 3.31M | | **Our-3D-GS** | Cathedral / Scale-1 | 29.80 | 0.60M | | **Our-3D-GS** | City / Scale-4 | 22.69 | 1.10M | **Visual Trend Verification:** * **Left Column (Cathedral, Scale-1):** All three methods produce a clear, detailed reconstruction of the cathedral's intricate stonework. The magnified insets show that "Anchor-3D-GS" and "Our-3D-GS" maintain sharper edges and finer details compared to the baseline "3D-GS", which appears slightly softer. * **Right Column (City, Scale-4):** This is a more challenging, larger-scale scene. All reconstructions are blurrier at this scale, as indicated by the lower PSNR values. The magnified insets show significant blurring and loss of high-frequency detail (like building windows and textures) across all methods. The baseline "3D-GS" appears the most blurred. ### Key Observations 1. **Scale Impact:** Moving from Scale-1 to Scale-4 (a more distant, wider view) drastically reduces reconstruction quality (PSNR drops by ~6-7 dB) and increases model size for all methods. This highlights the challenge of maintaining detail in large-scale scenes. 2. **Method Performance:** * **Quality (PSNR):** "Our-3D-GS" achieves the highest PSNR on the close-up cathedral scene (29.80 dB). On the city scene, "Anchor-3D-GS" has a very slight edge (22.81 dB vs. 22.69 dB), but the difference is minimal. * **Efficiency (Model Size):** The most significant difference is in model size. "Our-3D-GS" is dramatically more efficient on the large-scale city scene, using only **1.10M** Gaussians compared to 3.31M for "Anchor-3D-GS" and 7.76M for the baseline "3D-GS". This represents a **~70% reduction** in model size versus the baseline for a similar quality level. 3. **Visual Fidelity:** The proposed "Our-3D-GS" method visually matches or exceeds the detail of "Anchor-3D-GS" while using a much smaller model, especially evident in the cathedral's detailed structures. ### Interpretation This comparison chart is designed to demonstrate the superiority of the proposed "Our-3D-GS" method, particularly in terms of **efficiency**. The core message is that the new technique achieves state-of-the-art or comparable reconstruction quality (high PSNR) while using a significantly more compact representation (fewer millions of Gaussians). The data suggests that the key innovation lies in better handling of large-scale, complex scenes (like the city at Scale-4), where the method achieves a favorable trade-off between visual fidelity and memory/storage requirements. The baseline method's model size explodes (7.76M) for the large scene, making it impractical, whereas "Our-3D-GS" keeps it manageable (1.10M). This implies the proposed method uses a more intelligent or adaptive strategy for allocating Gaussian primitives, focusing them where they are most needed and avoiding redundancy. The chart effectively argues that "Our-3D-GS" advances the practical applicability of 3D Gaussian Splatting for large-scale 3D reconstruction tasks. </details> Figure 11: Qualitative comparison of scale-1 and scale-4 on the Barcelona scene from the BungeeNeRF [51] dataset. Both Anchor-3D-GS and Our-3D-GS accurately reconstruct fine details, such as the crane in scale-1 and the building surface in scale-4 (see highlighted patches and arrows), while Our-3D-GS uses fewer primitives to model the entire scene. We report PSNR and the number of Gaussians used for rendering. Multi-Scale Results To evaluate the ability of Octree-GS to handle multi-scale scene details, we conduct an experiment using the BungeeNeRF [51] dataset across four different scales (i.e., from ground-level to satellite-level camera altitudes). Our results show that Octree-GS accurately captures scene details and models the entire scene more efficiently with fewer Gaussian primitives, as demonstrated in Tab. IV and Fig. 11. Multi-Resolution Results As mentioned in Sec. IV, when dealing with training views that vary in camera resolution or intrinsics, such as datasets presented in [50] with a four-fold downsampling operation, we multiply the observation distance with factor scale factor accordingly to handle this multi-resolution dataset. As shown in Fig. 10 and Tab. VI, we train all models on images with downsampling scales of 1, 2, 4, 8, and Octree-GS adaptively handle the changed footprint size and effectively address the aliasing issues inherent to 3D-GS [5] and Scaffold-GS [3]. As resolution changes, 3D-GS and Scaffold-GS introduce noticeable erosion artifacts, but our approach avoids such issues, achieving results competitive with Mip-Splatting [14] and even closer to the ground truth. Additionally, we provide multi-resolution results for the Tanks&Temples dataset [60] and the Deep Blending dataset [61] in the supplementary materials. Random Initialization Results To illustrate the independence of our framework from SfM points, we evaluate it using randomly initialized points, with 0.31/0.27 (LPIPS $\downarrow$ ), 25.93/26.41 (PSNR $\uparrow$ ), 0.76/0.77 (SSIM $\uparrow$ ) on Mip-NeRF360 [50] dataset comparing Scaffold-GS with Our-Scaffold-GS. The improvement primarily depends on the efficient densification strategy. Appearance Embedding Results We demonstrate that our specialized design can handle input images with different exposure compensations and provide detailed control over lighting and appearance. As shown in Fig. 12, we reconstruct two scenes: one is from the widely-used Phototourism [66] dataset and the other is a self-captured scene of a ginkgo tree. We present five images rendered from a fixed camera view, where we interpolate the appearance codes linearly to produce a fancy style transfer effect. <details> <summary>x12.png Details</summary>  ### Visual Description ## Diagram: Color Temperature and Time-of-Day Progression ### Overview The image is a technical comparative diagram demonstrating the visual effects of two different color grading or white balance adjustments across two distinct scenes. It consists of two horizontal rows, each containing five sequential images. The top row shows a progression from "Day" to "Night," while the bottom row shows a progression from "Warm" to "Cold." The diagram visually explains how color temperature and lighting affect the mood and appearance of a photograph. ### Components/Axes * **Layout:** Two horizontal rows of five images each. * **Labels & Legends:** * **Top Row:** A horizontal arrow spans the width of the row. The left end is labeled **"Day"** and the right end is labeled **"Night"**. The arrow itself has a gradient fill, transitioning from a light blue/white on the left to a dark blue on the right. * **Bottom Row:** A similar horizontal arrow spans the row. The left end is labeled **"Warm"** and the right end is labeled **"Cold"**. The arrow has a gradient fill, transitioning from a pale yellow/cream on the left to a medium blue on the right. * **Image Content:** * **Top Row Subject:** The Florence Cathedral (Santa Maria del Fiore), focusing on Brunelleschi's dome and the ornate facade. * **Bottom Row Subject:** An aerial view of a park or garden with a prominent tree displaying autumn foliage (yellow/orange leaves), a pond, pathways, and surrounding green trees. ### Detailed Analysis **Top Row (Day to Night Progression):** * **Image 1 (Far Left - "Day"):** The scene is brightly lit. The sky is a pale, slightly hazy blue. The building's stone appears in its natural, warm beige and white tones. Shadows are soft. * **Image 2:** The sky becomes a slightly deeper blue. The overall scene contrast increases subtly. * **Image 3:** The sky is a clear, medium blue. The building's facade shows more defined shadows and highlights, suggesting a lower sun angle. * **Image 4:** The sky transitions to a deep, rich blue. The building's stone takes on a cooler, slightly bluish cast. Artificial lights may be beginning to illuminate the facade, creating warmer spots against the cool ambient light. * **Image 5 (Far Right - "Night"):** The sky is a very dark, deep blue, almost navy. The building is dramatically lit, likely by artificial floodlights, making the warm stone glow against the cold, dark sky. The contrast is highest here. **Bottom Row (Warm to Cold Progression):** * **Image 1 (Far Left - "Warm"):** The entire scene has a strong yellow/golden color cast. The autumn tree is a vibrant, saturated yellow-orange. The greens of other trees and the water in the pond appear warm and slightly yellowish. * **Image 2:** The yellow cast is reduced. The autumn tree remains a strong yellow, but other elements begin to show more neutral or slightly cooler greens. * **Image 3:** The color balance appears closest to neutral or "natural." The autumn tree is a clear yellow, the other trees are a standard green, and the water reflects a more neutral sky. * **Image 4:** A cool, blueish tint becomes apparent. The yellow of the autumn tree is muted, leaning towards a pale yellow or chartreuse. The greens of other trees take on a bluish-green hue. * **Image 5 (Far Right - "Cold"):** The scene has a strong blue color cast. The autumn tree appears as a pale, desaturated yellow-white. All greens are distinctly blue-green. The overall mood is cool and wintry. ### Key Observations 1. **Consistent Progression:** Both rows demonstrate a smooth, linear transition across five steps from one extreme (Day/Warm) to the opposite extreme (Night/Cold). 2. **Subject Interaction:** The effect of the color shift is highly dependent on the subject matter. The architectural scene (top) primarily shows changes in ambient light and sky color, while the natural scene (bottom) shows dramatic shifts in the perceived color of foliage and water. 3. **Color vs. Luminance:** The "Day to Night" progression involves changes in both **color temperature** (warmer to cooler) and **luminance** (bright to dark). The "Warm to Cold" progression primarily involves a shift in **color temperature/hue** (yellow to blue) with less dramatic change in overall brightness. 4. **Legend Alignment:** The gradient arrows serve as direct legends. The visual change in the images perfectly aligns with the gradient in the corresponding arrow (e.g., the "Night" images have the same deep blue tone as the right end of the top arrow). ### Interpretation This diagram is a practical tool for photographers, colorists, or digital artists. It visually deconstructs two fundamental concepts in image processing: 1. **Time of Day Simulation:** The top row illustrates how to grade a daytime shot to appear as if it were taken at dusk or night. This involves not just darkening the image but crucially shifting the color balance towards blue (simulating cooler ambient skylight) while often adding warm, localized highlights (simulating artificial lights). The progression shows the intermediate steps, which are useful for creating believable time-lapse effects or adjusting the mood of a scene. 2. **Color Grading Presets:** The bottom row demonstrates the application of a "color temperature" or "white balance" slider. Moving from "Warm" to "Cold" applies an increasingly strong blue color filter. This is a common technique to evoke different emotions: warmth (yellow) suggests comfort, nostalgia, or golden hour; coolness (blue) suggests sterility, sadness, or winter. The diagram shows how this global adjustment affects different colors in a scene, notably desaturating warm tones (the yellow tree) as the cool cast intensifies. **Underlying Principle:** The diagram emphasizes that color is not an absolute property in photography but a malleable element that defines time, atmosphere, and emotion. The side-by-side comparison of an urban and a natural scene highlights that the same color grading technique will produce visually distinct results depending on the existing colors within the frame. </details> Figure 12: Visualization of appearance code interpolation. We show five test views from the Phototourism [67] dataset (top) and a self-captured tree scene (bottom) with linearly-interpolated appearance codes. ### V-C Ablation Studies In this section, we ablate each individual module to validate their effectiveness. We select all scenes from the Mip-NeRF360 [50] dataset as quantitative comparison, given its representative characteristics. Additionally, we select Block_Small from the MatrixCity [1] dataset for qualitative comparison. In this section, we ablate each individual module to verify their effectiveness. Meanwhile, we choose the octree-version of Scaffold-GS as the full model, with the vanilla Scaffold-GS serving as the baseline for comparison. Quantitative and qualitative results can be found in Tab. VII and Fig. 13. #### V-C 1 Next Level Grow Operator To evaluate the effectiveness of next-level anchor growing, as detailed in Section IV-B, we conduct an ablation in which new anchors are only allowed to grow at the same LOD level. The results, presented in Tab. VII, show that while the number of rendered Gaussian primitives and storage requirements decreased, there was a significant decline in image visual quality. This suggests that incorporating finer anchors into higher LOD levels not only improves the capture of high-frequency details but also enhances the interaction between adjacent LOD levels. #### V-C 2 LOD Bias To validate its contribution to margin details, we ablate the proposed LOD bias. The results, presented in Tab. VII, indicates that LOD bias is essential for enhancing the rendering quality, particularly in regions rich in high-frequency details for smooth trajectories, which can be observed in column (a)(b) of Fig. 13, as the white stripes on the black buildings become continuous and complete. #### V-C 3 Progressive Training To compare its influence on LOD level overlapping, we ablate progressive training strategy. In column (a)(c) of Fig. 13, the building windows are clearly noticeable, indicating that the strategy contributes to reduce the rendered Gaussian redundancy and decouple the Gaussias of different scales in the scene to their corresponding LOD levels. In addition, the quantitative results also verify the improvement of scene reconstruction accuracy by the proposed strategy, as shown in Tab. VII. #### V-C 4 View Frequency Due to the design of the octree structure, anchors at higher LOD levels are only rendered and optimized when the camera view is close to them. These anchors are often not sufficiently optimized due to their limited number, leading to visual artifacts when rendering from novel views. We perform an ablation of the view frequency strategy during the anchor pruning stage, as described detailly in Sec. IV-B 2. Implementing this strategy eliminates floaters, particularly in close-up views, enhances visual quality, and significantly reduces storage requirements, as shown in Tab. VII and Fig. 4. TABLE VII: Quantitative results on ablation studies. We list the rendering metrics for each ablation described in Sec. V-C. | Scaffold-GS [3] Ours w/o $l_{next}$ grow. Ours w/o progressive. | 27.90 27.64 27.86 | 0.815 0.811 0.818 | 0.220 0.223 0.215 | 666/197.5M 594/99.7M 698/142.3M | | --- | --- | --- | --- | --- | | Ours w/o LOD bias | 27.85 | 0.818 | 0.214 | 667/146.8M | | Ours w/o view freq. | 27.74 | 0.817 | 0.211 | 765/244.4M | | Our-Scaffold-GS | 28.05 | 0.819 | 0.214 | 657/139.6M | <details> <summary>x13.png Details</summary>  ### Visual Description ## Comparative Visualization: 3D City Rendering Model Ablation Study ### Overview The image is a technical comparison figure, likely from a research paper or technical report in computer graphics or computer vision. It presents a side-by-side visual ablation study of a 3D city rendering model, demonstrating the impact of removing specific components ("LOD bias" and "Progressive" rendering) on the final visual quality. The figure consists of three main circular panels, each showing an aerial view of the same dense urban scene, with two zoomed-in detail insets per panel. ### Components/Axes * **Main Panels:** Three circular, oval-shaped viewports arranged horizontally. Each contains an aerial, oblique-angle view of a city with roads, buildings of varying heights, and textures. * **Panel Labels:** Located at the bottom center of each circular panel. * Left Panel: `(a) Full Model` * Center Panel: `(b) w/o LOD bias` * Right Panel: `(c) w/o Progressive` * **Detail Insets:** Above each main panel are two square, zoomed-in detail views. * **Cyan-Boxed Inset (Left):** Shows a close-up of a specific building facade and surrounding area. A cyan square outline in the main panel indicates the source region. * **Red-Boxed Inset (Right):** Shows a close-up of a different building's facade, focusing on window and structural details. A red square outline in the main panel indicates the source region. * **Connecting Lines:** Cyan and red arrows connect the source regions in the main panel to their corresponding zoomed-in insets above. ### Detailed Analysis This is a qualitative comparison, not a quantitative chart. The analysis focuses on visual fidelity differences. **Spatial Grounding & Trend Verification:** 1. **Panel (a) Full Model:** * **Cyan Region (Top-Left Inset):** The building facade shows clear, distinct horizontal lines (floors/balconies) and relatively sharp texture details. * **Red Region (Top-Right Inset):** The building facade exhibits very sharp, well-defined vertical and horizontal structural lines. Window details are crisp. This represents the highest quality baseline. 2. **Panel (b) w/o LOD bias:** * **Cyan Region (Top-Left Inset):** Compared to (a), the texture appears slightly softer and less defined. The horizontal lines are less sharp. * **Red Region (Top-Right Inset):** A significant degradation is visible. The sharp structural lines from (a) are now blurred and lack definition. Details are smudged, indicating a loss of high-frequency information. The trend is a clear reduction in sharpness and detail. 3. **Panel (c) w/o Progressive:** * **Cyan Region (Top-Left Inset):** The quality appears similar to, or slightly worse than, panel (b). The texture is soft. * **Red Region (Top-Right Inset):** This inset shows a different type of artifact compared to (b). While also lacking the sharpness of (a), it exhibits more "blocky" or patchy artifacts and inconsistent detail reconstruction. The trend is a loss of detail coupled with the introduction of rendering artifacts. ### Key Observations * The **red-boxed region** (right inset) is the most sensitive to the ablation, showing dramatic quality loss in both (b) and (c). This suggests this area contains complex geometry or textures that heavily rely on the removed components. * The **cyan-boxed region** (left inset) shows a more subtle degradation, indicating it may be less complex or that the model's base performance without the ablated features is still adequate for that area. * The **"Full Model" (a)** serves as the ground truth or target quality, displaying the sharpest details and cleanest textures. * The **"w/o LOD bias" (b)** result primarily shows a general blurring and loss of high-frequency detail. * The **"w/o Progressive" (c)** result shows not just blurring but also more pronounced structural inconsistencies and artifacts. ### Interpretation This figure visually argues for the necessity of two specific components in the authors' 3D city rendering pipeline: 1. **LOD (Level of Detail) Bias:** The degradation in panel (b) suggests that without a proper LOD bias mechanism, the system fails to allocate sufficient detail or resolution to important structures (like the building in the red box), resulting in an overall softer, less detailed output. LOD bias likely controls how detail is prioritized across different distances or object complexities. 2. **Progressive Rendering:** The artifacts in panel (c) indicate that the progressive rendering component is crucial for constructing a coherent and artifact-free final image. Without it, the rendering process may produce inconsistencies, especially in areas with complex geometry, leading to the patchy, blocky appearance observed. **Conclusion:** The "Full Model" combines both techniques to achieve high-fidelity results. The ablation study demonstrates that each component addresses a different aspect of quality: LOD bias manages detail allocation for sharpness, while progressive rendering ensures coherent and artifact-free image synthesis. Removing either leads to a visually inferior result, with the red-boxed region acting as a critical "stress test" for the model's capabilities. This type of analysis is fundamental in research to validate the contribution of each proposed method component. </details> Figure 13: Visualizations of the rendered images from (a) our full model, (b) ours w/o LOD bias, (c) ours w/o progressive training. As observed, LOD bias aids in restoring sharp building edges and lines, while progressive training helps recover the geometric structure from coarse to fine details. ## VI Limitations and Conclusion In this work, we introduce Level-of-Details (LOD) to Gaussian representation, using a novel octree structure to organize anchors hierarchically. Our model, Octree-GS, addresses previous limitations by dynamically fetching appropriate LOD levels based on observed views and scene complexity, ensuring consistent rendering performance with adaptive LOD adjustments. Through careful design, Octree-GS significantly enhances detail capture while maintaining real-time rendering performance without increasing the number of Gaussian primitives. This suggests potential for future real-world streaming experiences, demonstrating the capability of advanced rendering methods to deliver seamless, high-quality interactive 3D scene and content. However, certain model components, like octree construction and progressive training, still require hyperparameter tuning. Balancing anchors in each LOD level and adjusting training iteration activation are also crucial. Moreover, our model still faces challenges associated with 3D-GS, including dependency on the precise camera poses and lack of geometry support. These are left as our future works. ## VII Supplementary Material The supplementary material includes quantitative results for each scene from the dataset used in the main text, covering image quality metrics such as PSNR, [64] and LPIPS [65], as well as the number of rendered Gaussian primitives and storage size. TABLE VIII: PSNR for all scenes in the Mip-NeRF360 [50] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | bicycle 24.77 25.10 | bonsai 31.42 32.19 | counter 28.20 29.22 | flowers 21.02 21.57 | garden 26.73 27.45 | kitchen 30.66 31.62 | room 30.95 31.53 | stump 26.17 26.70 | treehill 22.48 22.46 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 25.13 | 32.56 | 29.30 | 21.64 | 27.43 | 31.48 | 31.73 | 26.65 | 22.60 | | Scaffold-GS [3] | 25.19 | 33.22 | 29.99 | 21.40 | 27.48 | 31.77 | 32.30 | 26.67 | 23.08 | | Anchor-2D-GS | 24.81 | 31.01 | 28.44 | 21.25 | 26.65 | 30.35 | 31.08 | 26.52 | 22.72 | | Anchor-3D-GS | 25.21 | 32.20 | 29.12 | 21.52 | 27.37 | 31.46 | 31.83 | 26.74 | 22.85 | | Our-2D-GS | 24.89 | 30.85 | 28.56 | 21.19 | 26.88 | 30.22 | 31.17 | 26.62 | 22.78 | | Our-3D-GS | 25.20 | 32.29 | 29.27 | 21.40 | 27.36 | 31.70 | 31.96 | 26.78 | 22.85 | | Our-Scaffold-GS | 25.24 | 33.76 | 30.19 | 21.46 | 27.67 | 31.84 | 32.51 | 26.63 | 23.13 | TABLE IX: SSIM for all scenes in the Mip-NeRF360 [50] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | bicycle 0.730 0.747 | bonsai 0.935 0.947 | counter 0.899 0.917 | flowers 0.568 0.600 | garden 0.839 0.861 | kitchen 0.923 0.932 | room 0.916 0.926 | stump 0.759 0.773 | treehill 0.627 0.636 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 0.747 | 0.948 | 0.917 | 0.601 | 0.861 | 0.933 | 0.928 | 0.772 | 0.639 | | Scaffold-GS [3] | 0.751 | 0.952 | 0.922 | 0.587 | 0.853 | 0.931 | 0.932 | 0.767 | 0.644 | | Anchor-2D-GS | 0.735 | 0.933 | 0.900 | 0.575 | 0.838 | 0.917 | 0.917 | 0.762 | 0.630 | | Anchor-3D-GS | 0.758 | 0.946 | 0.913 | 0.591 | 0.857 | 0.928 | 0.927 | 0.772 | 0.640 | | Our-2D-GS | 0.737 | 0.932 | 0.903 | 0.572 | 0.838 | 0.918 | 0.919 | 0.763 | 0.630 | | Our-3D-GS | 0.761 | 0.946 | 0.916 | 0.587 | 0.855 | 0.931 | 0.929 | 0.772 | 0.640 | | Our-Scaffold-GS | 0.755 | 0.955 | 0.925 | 0.595 | 0.861 | 0.933 | 0.936 | 0.766 | 0.641 | TABLE X: LPIPS for all scenes in the Mip-NeRF360 [50] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | bicycle 0.284 0.243 | bonsai 0.204 0.178 | counter 0.214 0.179 | flowers 0.389 0.345 | garden 0.153 0.114 | kitchen 0.134 0.117 | room 0.218 0.196 | stump 0.279 0.231 | treehill 0.385 0.335 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 0.245 | 0.178 | 0.179 | 0.347 | 0.115 | 0.115 | 0.192 | 0.232 | 0.334 | | Scaffold-GS [3] | 0.247 | 0.173 | 0.177 | 0.359 | 0.13 | 0.118 | 0.183 | 0.252 | 0.338 | | Anchor-2D-GS | 0.262 | 0.200 | 0.203 | 0.376 | 0.146 | 0.140 | 0.209 | 0.261 | 0.371 | | Anchor-3D-GS | 0.230 | 0.177 | 0.182 | 0.363 | 0.121 | 0.121 | 0.193 | 0.249 | 0.348 | | Our-2D-GS | 0.262 | 0.205 | 0.198 | 0.378 | 0.148 | 0.140 | 0.205 | 0.264 | 0.374 | | Our-3D-GS | 0.225 | 0.178 | 0.176 | 0.364 | 0.125 | 0.116 | 0.190 | 0.250 | 0.357 | | Our-Scaffold-GS | 0.235 | 0.164 | 0.169 | 0.347 | 0.116 | 0.115 | 0.172 | 0.250 | 0.360 | TABLE XI: Number of Gaussian Primitives(#K) for all scenes in the Mip-NeRF360 [50] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | bicycle 555 1453 | bonsai 210 402 | counter 232 530 | flowers 390 907 | garden 749 2030 | kitchen 440 1034 | room 199 358 | stump 413 932 | treehill 383 785 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 1584 | 430 | 545 | 950 | 2089 | 1142 | 405 | 1077 | 892 | | Scaffold-GS [3] | 764 | 532 | 377 | 656 | 1121 | 905 | 272 | 637 | 731 | | Anchor-2D-GS | 887 | 337 | 353 | 548 | 938 | 466 | 270 | 587 | 540 | | Anchor-3D-GS | 1187 | 370 | 388 | 634 | 1524 | 535 | 293 | 647 | 781 | | Our-2D-GS | 540 | 259 | 294 | 428 | 718 | 414 | 184 | 394 | 344 | | Our-3D-GS | 659 | 301 | 334 | 478 | 987 | 710 | 195 | 436 | 433 | | Our-Scaffold-GS | 653 | 631 | 409 | 675 | 1475 | 777 | 374 | 549 | 372 | TABLE XII: Storage memory(#MB) for all scenes in the Mip-NeRF360 [50] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | bicycle 889.6 1361.8 | bonsai 173.1 293.5 | counter 135.4 293.3 | flowers 493.5 878.5 | garden 603.1 1490.6 | kitchen 191.0 413.1 | room 180.0 355.6 | stump 670.3 1115.2 | treehill 630.9 878.6 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 1433.6 | 318.1 | 307.5 | 970.2 | 1448.9 | 463.4 | 401.0 | 1239.0 | 964.3 | | Scaffold-GS [3] | 340.2 | 133.3 | 90.4 | 243.8 | 231.7 | 102.2 | 86.1 | 294.2 | 256.0 | | Anchor-2D-GS | 599.2 | 280.0 | 191.5 | 530.0 | 634.4 | 190.7 | 228.4 | 359.1 | 521.4 | | Anchor-3D-GS | 765.5 | 301.7 | 204.9 | 656.1 | 988.6 | 217.0 | 244.6 | 417.4 | 632.2 | | Our-2D-GS | 485.0 | 368.6 | 265.6 | 442.3 | 598.6 | 272.3 | 180.8 | 292.8 | 438.3 | | Our-3D-GS | 648.6 | 382.7 | 305.8 | 487.7 | 706.2 | 282.9 | 162.7 | 322.1 | 468.4 | | Our-Scaffold-GS | 216.0 | 133.5 | 83.2 | 198.3 | 236.3 | 88.7 | 83.5 | 141.9 | 104.4 | TABLE XIII: Quantitative results for all scenes in the Tanks&Temples [60] dataset. | Dataset Method Metrics 2D-GS [15] | Truck PSNR 25.12 | Train SSIM 0.870 | LPIPS 0.173 | #GS(k)/Mem 393/287.2M | PSNR 21.38 | SSIM 0.790 | LPIPS 0.251 | #GS(k)/Mem 310/121.5M | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 3D-GS [5] | 25.52 | 0.884 | 0.142 | 876/610.8M | 22.30 | 0.819 | 0.201 | 653/249.3M | | Mip-Splatting [14] | 25.74 | 0.888 | 0.142 | 967/718.9M | 22.17 | 0.824 | 0.199 | 696/281.9M | | Scaffold-GS [3] | 26.04 | 0.889 | 0.131 | 698/214.6M | 22.91 | 0.838 | 0.181 | 554/120.4M | | Anchor-2D-GS | 25.45 | 0.873 | 0.161 | 472/349.7M | 21.58 | 0.797 | 0.237 | 457/208.3M | | Anchor-3D-GS | 25.85 | 0.883 | 0.146 | 603/452.8M | 22.18 | 0.810 | 0.222 | 541/245.6M | | Our-2D-GS | 25.32 | 0.872 | 0.158 | 304 /208.5M | 21.92 | 0.812 | 0.215 | 355 /173.9M | | Our-3D-GS | 25.81 | 0.887 | 0.131 | 407/542.8M | 22.52 | 0.828 | 0.190 | 440/224.90M | | Our-Scaffold-GS | 26.24 | 0.894 | 0.122 | 426/ 93.7M | 23.11 | 0.838 | 0.184 | 460/ 83.4M | TABLE XIV: Quantitative results for all scenes in the DeepBlending [61] dataset. | Dataset Method Metrics 2D-GS [15] | Dr Johnson PSNR 28.74 | Playroom SSIM 0.897 | LPIPS 0.257 | #GS(k)/Mem 232/393.8M | PSNR 29.89 | SSIM 0.900 | LPIPS 0.257 | #GS(k)/Mem 160/276.7M | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 3D-GS [5] | 29.09 | 0.900 | 0.242 | 472/818.9M | 29.83 | 0.905 | 0.241 | 324/592.3M | | Mip-Splatting [14] | 29.08 | 0.900 | 0.241 | 512/911.6M | 30.03 | 0.902 | 0.245 | 307/562.0M | | Scaffold-GS [3] | 29.73 | 0.910 | 0.235 | 232/145.0M | 30.83 | 0.907 | 0.242 | 182/106.0M | | Anchor-2D-GS | 28.68 | 0.893 | 0.266 | 186/346.3M | 30.02 | 0.899 | 0.262 | 138/231.8M | | Anchor-3D-GS | 29.23 | 0.897 | 0.267 | 141/242.3M | 30.08 | 0.901 | 0.252 | 159/303.4M | | Our-2D-GS | 28.94 | 0.894 | 0.26 | 97/268.2M | 29.93 | 0.899 | 0.268 | 70/136.4M | | Our-3D-GS | 29.27 | 0.900 | 0.251 | 95 /240.7M | 30.03 | 0.901 | 0.263 | 63 /119.2M | | Our-Scaffold-GS | 29.83 | 0.909 | 0.237 | 124/ 92.46M | 31.15 | 0.914 | 0.245 | 100/ 50.91M | TABLE XV: PSNR for all scenes in the BungeeNeRF [51] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | Amsterdam 27.22 27.75 | Barcelona 27.01 27.55 | Bilbao 28.59 28.91 | Chicago 25.62 28.27 | Hollywood 26.43 26.25 | Pompidou 26.62 27.16 | Quebec 28.38 28.86 | Rome 26.95 27.56 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 28.16 | 27.72 | 29.13 | 28.28 | 26.59 | 27.71 | 29.23 | 28.33 | | Scaffold-GS [3] | 27.82 | 28.09 | 29.20 | 28.55 | 26.36 | 27.72 | 29.29 | 28.24 | | Anchor-2D-GS | 26.80 | 27.03 | 28.02 | 27.50 | 25.68 | 26.87 | 28.21 | 27.32 | | Anchor-3D-GS | 27.70 | 27.93 | 28.92 | 28.20 | 26.20 | 27.17 | 28.83 | 28.22 | | Our-2D-GS | 27.14 | 27.28 | 28.24 | 27.78 | 26.13 | 26.58 | 28.07 | 27.47 | | Our-3D-GS | 27.95 | 27.91 | 28.81 | 28.24 | 26.51 | 27.00 | 28.98 | 28.09 | | Our-Scaffold-GS | 28.16 | 28.40 | 29.39 | 28.86 | 26.76 | 27.46 | 29.46 | 28.59 | TABLE XVI: SSIM for all scenes in the BungeeNeRF [51] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | Amsterdam 0.896 0.918 | Barcelona 0.907 0.919 | Bilbao 0.912 0.918 | Chicago 0.901 0.932 | Hollywood 0.872 0.873 | Pompidou 0.907 0.919 | Quebec 0.923 0.937 | Rome 0.902 0.918 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 0.918 | 0.919 | 0.918 | 0.930 | 0.876 | 0.923 | 0.938 | 0.922 | | Scaffold-GS [3] | 0.914 | 0.923 | 0.918 | 0.929 | 0.866 | 0.926 | 0.939 | 0.924 | | Anchor-2D-GS | 0.872 | 0.887 | 0.886 | 0.897 | 0.838 | 0.900 | 0.910 | 0.891 | | Anchor-3D-GS | 0.902 | 0.912 | 0.907 | 0.916 | 0.871 | 0.919 | 0.930 | 0.915 | | Our-2D-GS | 0.887 | 0.894 | 0.892 | 0.912 | 0.857 | 0.893 | 0.911 | 0.895 | | Our-3D-GS | 0.912 | 0.910 | 0.905 | 0.920 | 0.875 | 0.907 | 0.928 | 0.912 | | Our-Scaffold-GS | 0.922 | 0.928 | 0.921 | 0.934 | 0.884 | 0.923 | 0.942 | 0.930 | TABLE XVII: LPIPS for all scenes in the BungeeNeRF [51] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | Amsterdam 0.132 0.092 | Barcelona 0.101 0.082 | Bilbao 0.109 0.092 | Chicago 0.13 0.080 | Hollywood 0.152 0.128 | Pompidou 0.109 0.090 | Quebec 0.113 0.087 | Rome 0.123 0.096 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 0.094 | 0.082 | 0.095 | 0.081 | 0.130 | 0.087 | 0.087 | 0.093 | | Scaffold-GS [3] | 0.102 | 0.078 | 0.090 | 0.08 | 0.157 | 0.082 | 0.080 | 0.087 | | Anchor-2D-GS | 0.156 | 0.125 | 0.137 | 0.125 | 0.196 | 0.119 | 0.127 | 0.131 | | Anchor-3D-GS | 0.127 | 0.099 | 0.119 | 0.105 | 0.160 | 0.100 | 0.100 | 0.105 | | Our-2D-GS | 0.139 | 0.112 | 0.131 | 0.103 | 0.169 | 0.126 | 0.125 | 0.128 | | Our-3D-GS | 0.105 | 0.094 | 0.115 | 0.095 | 0.146 | 0.113 | 0.100 | 0.108 | | Our-Scaffold-GS | 0.090 | 0.071 | 0.091 | 0.077 | 0.128 | 0.089 | 0.081 | 0.080 | TABLE XVIII: Number of Gaussian Primitives(#K) for all scenes in the BungeeNeRF [51] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | Amsterdam 1026 2358 | Barcelona 1251 3106 | Bilbao 968 2190 | Chicago 1008 2794 | Hollywood 1125 2812 | Pompidou 1526 3594 | Quebec 811 2176 | Rome 914 2459 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 2325 | 2874 | 2072 | 2712 | 2578 | 3233 | 1969 | 2251 | | Scaffold-GS [3] | 1219 | 1687 | 1122 | 1958 | 1117 | 2600 | 1630 | 1886 | | Anchor-2D-GS | 1222 | 1050 | 1054 | 1168 | 706 | 1266 | 881 | 1050 | | Anchor-3D-GS | 1842 | 1630 | 1393 | 1593 | 1061 | 1995 | 1368 | 1641 | | Our-2D-GS | 703 | 771 | 629 | 631 | 680 | 786 | 582 | 629 | | Our-3D-GS | 1094 | 1090 | 760 | 830 | 975 | 1120 | 816 | 932 | | Our-Scaffold-GS | 1508 | 1666 | 1296 | 1284 | 1478 | 1584 | 1354 | 1622 | TABLE XIX: Storage memory(#MB) for all scenes in the BungeeNeRF [51] dataset. | Method Scenes 2D-GS [15] 3D-GS [5] | Amsterdam 809.6 1569.1 | Barcelona 1027.7 2191.9 | Bilbao 952.2 1446.1 | Chicago 633.2 1630.2 | Hollywood 814.3 1758.3 | Pompidou 1503.4 2357.6 | Quebec 643.2 1573.7 | Rome 705.5 1811.8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Mip-Splatting [14] | 1464.3 | 1935.4 | 1341.4 | 1536.0 | 1607.7 | 2037.8 | 1382.4 | 1577.0 | | Scaffold-GS [3] | 236.2 | 378.8 | 219.0 | 306.1 | 208.3 | 478.5 | 340.2 | 386.6 | | Anchor-2D-GS | 559.6 | 564.5 | 520.3 | 567.9 | 411.6 | 629.1 | 479.5 | 537.9 | | Anchor-3D-GS | 866.4 | 862.8 | 699.4 | 778.5 | 607.9 | 979.3 | 725.3 | 802.5 | | Our-2D-GS | 449.8 | 1014.4 | 425.9 | 1127.8 | 776.2 | 765.52 | 498.8 | 830.2 | | Our-3D-GS | 1213.5 | 1414.3 | 892.4 | 1268.5 | 960.5 | 949.8 | 618.5 | 1048.3 | | Our-Scaffold-GS | 273.8 | 355.9 | 246.5 | 286.8 | 259.0 | 339.6 | 258.8 | 353.4 | TABLE XX: PSNR for multi-resolution Mip-NeRF360 [50] scenes (1 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 23.66 25.19 23.64 | 29.89 31.76 31.31 | 27.98 29.07 28.82 | 20.42 21.68 20.87 | 25.45 26.82 26.04 | 29.55 31.27 30.39 | 30.51 31.60 31.36 | 25.48 26.71 25.66 | 22.50 22.74 23.14 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 24.21 | 33.44 | 30.15 | 20.89 | 27.01 | 31.83 | 32.39 | 25.92 | 23.26 | TABLE XXI: SSIM for multi-resolution Mip-NeRF360 [50] scenes (1 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.648 0.730 0.640 | 0.917 0.939 0.932 | 0.883 0.904 0.895 | 0.510 0.586 0.521 | 0.752 0.817 0.772 | 0.902 0.924 0.910 | 0.905 0.919 0.916 | 0.707 0.764 0.709 | 0.587 0.622 0.605 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.676 | 0.952 | 0.919 | 0.541 | 0.823 | 0.930 | 0.932 | 0.722 | 0.628 | TABLE XXII: LPIPS for multi-resolution Mip-NeRF360 [50] scenes (1 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.359 0.275 0.355 | 0.223 0.188 0.208 | 0.235 0.196 0.219 | 0.443 0.367 0.430 | 0.269 0.190 0.242 | 0.167 0.130 0.159 | 0.242 0.214 0.219 | 0.331 0.258 0.326 | 0.440 0.379 0.407 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.313 | 0.169 | 0.178 | 0.401 | 0.168 | 0.119 | 0.186 | 0.309 | 0.364 | TABLE XXIII: PSNR for multi-resolution Mip-NeRF360 [50] scenes (2 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 25.41 26.83 25.43 | 27.56 28.80 28.37 | 26.42 27.57 26.60 | 31.29 32.44 32.36 | 28.57 29.59 29.52 | 30.54 32.27 31.50 | 30.71 32.41 32.20 | 21.83 23.22 22.36 | 23.67 23.90 24.51 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 25.92 | 29.08 | 26.81 | 33.31 | 30.77 | 32.44 | 34.13 | 22.38 | 24.53 | TABLE XXIV: SSIM for multi-resolution Mip-NeRF360 [50] scenes (2 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.756 0.823 0.759 | 0.866 0.902 0.883 | 0.769 0.819 0.773 | 0.933 0.946 0.946 | 0.904 0.923 0.918 | 0.935 0.950 0.941 | 0.939 0.956 0.953 | 0.620 0.693 0.640 | 0.676 0.705 0.701 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.785 | 0.903 | 0.781 | 0.956 | 0.937 | 0.949 | 0.966 | 0.657 | 0.714 | TABLE XXV: LPIPS for multi-resolution Mip-NeRF360 [50] scenes (2 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.261 0.177 0.245 | 0.138 0.084 0.110 | 0.239 0.170 0.234 | 0.134 0.110 0.108 | 0.141 0.110 0.125 | 0.093 0.067 0.086 | 0.114 0.088 0.099 | 0.351 0.276 0.335 | 0.349 0.284 0.307 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.210 | 0.080 | 0.221 | 0.087 | 0.095 | 0.068 | 0.071 | 0.304 | 0.274 | TABLE XXVI: PSNR for multi-resolution Mip-NeRF360 [50] scenes (4 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 27.06 28.66 27.34 | 29.19 30.69 30.40 | 27.77 29.12 28.11 | 31.75 33.29 33.03 | 29.29 30.44 30.42 | 31.51 33.40 32.55 | 31.25 33.25 32.83 | 24.04 25.66 24.72 | 25.12 25.53 26.31 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 28.00 | 31.23 | 28.36 | 34.01 | 31.60 | 33.39 | 34.86 | 24.66 | 26.27 | TABLE XXVII: SSIM for multi-resolution Mip-NeRF360 [50] scenes (4 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.857 0.901 0.868 | 0.921 0.945 0.936 | 0.841 0.882 0.852 | 0.954 0.965 0.966 | 0.929 0.943 0.942 | 0.958 0.967 0.963 | 0.953 0.968 0.966 | 0.753 0.807 0.776 | 0.788 0.811 0.815 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.883 | 0.945 | 0.857 | 0.971 | 0.952 | 0.966 | 0.975 | 0.782 | 0.822 | TABLE XXVIII: LPIPS for multi-resolution Mip-NeRF360 [50] scenes (4 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.140 0.085 0.118 | 0.062 0.040 0.048 | 0.149 0.102 0.138 | 0.066 0.050 0.047 | 0.081 0.063 0.069 | 0.045 0.038 0.039 | 0.059 0.043 0.045 | 0.227 0.177 0.204 | 0.220 0.183 0.185 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.101 | 0.039 | 0.131 | 0.039 | 0.054 | 0.036 | 0.032 | 0.182 | 0.168 | TABLE XXIX: PSNR for multi-resolution Mip-NeRF360 [50] scenes (8 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 26.26 29.80 27.29 | 29.28 31.93 30.26 | 27.50 30.78 28.61 | 30.45 33.60 31.51 | 28.14 31.11 29.67 | 29.86 33.74 30.84 | 29.25 33.38 30.61 | 24.33 27.95 24.99 | 25.62 27.13 27.04 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 29.09 | 32.61 | 29.05 | 34.24 | 32.35 | 34.35 | 35.42 | 25.83 | 27.69 | TABLE XXX: SSIM for multi-resolution Mip-NeRF360 [50] scenes (8 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.871 0.938 0.894 | 0.930 0.964 0.941 | 0.846 0.925 0.875 | 0.953 0.973 0.965 | 0.928 0.957 0.946 | 0.954 0.975 0.961 | 0.944 0.973 0.959 | 0.805 0.883 0.825 | 0.840 0.886 0.871 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.919 | 0.964 | 0.885 | 0.978 | 0.964 | 0.977 | 0.981 | 0.838 | 0.885 | TABLE XXXI: LPIPS for multi-resolution Mip-NeRF360 [50] scenes (8 $\times$ resolution). | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.098 0.049 0.082 | 0.047 0.026 0.040 | 0.126 0.068 0.110 | 0.048 0.031 0.033 | 0.063 0.041 0.048 | 0.037 0.029 0.032 | 0.047 0.029 0.035 | 0.159 0.109 0.144 | 0.147 0.113 0.120 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.062 | 0.025 | 0.103 | 0.023 | 0.032 | 0.021 | 0.017 | 0.118 | 0.106 | TABLE XXXII: Quantitative results for multi-resolution Tanks&Temples [60] dataset. | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 21.23 21.87 21.91 | 22.17 22.70 23.04 | 22.69 23.41 23.84 | 22.16 23.83 23.50 | 23.92 25.29 24.66 | 25.47 26.79 26.47 | 26.24 28.07 27.44 | 25.51 28.81 26.67 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 22.49 | 23.50 | 24.18 | 24.22 | 25.85 | 27.53 | 28.83 | 29.67 | | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.754 0.791 0.781 | 0.830 0.859 0.860 | 0.879 0.906 0.907 | 0.880 0.929 0.913 | 0.827 0.868 0.844 | 0.899 0.925 0.916 | 0.930 0.955 0.946 | 0.929 0.969 0.945 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.817 | 0.882 | 0.919 | 0.932 | 0.878 | 0.932 | 0.958 | 0.971 | | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.292 0.243 0.261 | 0.181 0.143 0.149 | 0.106 0.080 0.080 | 0.093 0.056 0.070 | 0.239 0.179 0.216 | 0.116 0.082 0.094 | 0.058 0.039 0.045 | 0.050 0.025 0.041 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.216 | 0.119 | 0.068 | 0.055 | 0.154 | 0.066 | 0.033 | 0.023 | TABLE XXXIII: Quantitative results for multi-resolution Deep Blending [61] dataset. | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 28.62 28.95 29.51 | 28.97 29.30 29.99 | 29.23 29.91 30.58 | 28.71 30.55 30.31 | 29.43 30.18 29.77 | 29.89 30.62 30.39 | 30.25 31.16 31.10 | 29.47 31.61 30.47 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 29.75 | 30.14 | 30.58 | 30.92 | 30.87 | 31.42 | 31.76 | 31.63 | | 3D-GS [5] Mip-Splatting [14] Scaffold-GS [3] | 0.890 0.900 0.900 | 0.900 0.911 0.914 | 0.911 0.925 0.930 | 0.907 0.936 0.932 | 0.898 0.909 0.900 | 0.919 0.929 0.923 | 0.935 0.946 0.944 | 0.934 0.956 0.949 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Our-Scaffold-GS | 0.908 | 0.920 | 0.932 | 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