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GeoHCC: Local Geometry-Aware Hierarchical Context Compression for 3D Gaussian Splatting
Xuan Deng, Xiandong Meng, Hengyu Man, Qiang Zhu, Tiange Zhang, Debin Zhao, Xiaopeng Fan
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Summary
GeoHCC is a geometry-aware 3D Gaussian Splatting (3DGS) compression framework that addresses storage overhead by modeling inter-anchor geometric correlations. It introduces Neighborhood-Aware Anchor Pruning (NAAP) to merge redundant anchors into salient neighbors based on local graph structures, and a hierarchical entropy coding scheme using Geometry-Guided Convolution (GG-Conv) to enable spatially adaptive context modeling.
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GeoHCC → compresses → 3D Gaussian Splatting
confidence 100% · GeoHCC, a geometry-aware 3DGS compression framework
GeoHCC → implements → Geometry-Guided Convolution
confidence 95% · we further develop a hierarchical entropy coding scheme, in which coarse-to-fine priors are exploited through a lightweight Geometry-Guided Convolution (GG-Conv) operator
GeoHCC → utilizes → Neighborhood-Aware Anchor Pruning
confidence 95% · We first introduce Neighborhood-Aware Anchor Pruning (NAAP)... in this paper, we propose GeoHCC
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Abstract
Abstract:Although 3D Gaussian Splatting (3DGS) enables high-fidelity real-time rendering, its prohibitive storage overhead severely hinders practical deployment. Recent anchor-based 3DGS compression schemes reduce redundancy through context modeling, yet overlook explicit geometric dependencies, leading to structural degradation and suboptimal rate-distortion performance. In this paper, we propose GeoHCC, a geometry-aware 3DGS compression framework that incorporates inter-anchor geometric correlations into anchor pruning and entropy coding for compact representation. We first introduce Neighborhood-Aware Anchor Pruning (NAAP), which evaluates anchor importance via weighted neighborhood feature aggregation and merges redundant anchors into salient neighbors, yielding a compact yet geometry-consistent anchor set. Building upon this optimized structure, we further develop a hierarchical entropy coding scheme, in which coarse-to-fine priors are exploited through a lightweight Geometry-Guided Convolution (GG-Conv) operator to enable spatially adaptive context modeling and rate-distortion optimization. Extensive experiments demonstrate that GeoHCC effectively resolves the structure preservation bottleneck, maintaining superior geometric integrity and rendering fidelity over state-of-the-art anchor-based approaches.
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- Source: https://arxiv.org/abs/2603.28431v1
- Canonical: https://arxiv.org/abs/2603.28431v1
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GeoHCC: Local Geometry-Aware Hierarchical Context Compression for 3D Gaussian Splatting Xuan Deng Harbin Institute of Technology, Peng Cheng Laboratory ShenzhenChina dengxuan168168@gmail.com , Xiandong Meng Peng Cheng Laboratory ShenzhenChina mengxd@pcl.ac.cn , Hengyu Man Harbin Institute of TechnologyHarbinChina manhengyu@hotmail.com , Qiang Zhu Peng Cheng Laboratory, ShenzhenChina zhuqiang@std.uestc.edu.cn , Tiange Zhang Peng Cheng Laboratory, ShenzhenChina zhangtg.@pcl.ac.cn , Debin Zhao Harbin Institute of TechnologyHarbinChina dbzhao@hit.edu.cn and Xiaopeng Fan Harbin Institute of Technology, Peng Cheng Laboratory, Harbin Institute of Technology Suzhou Research InstituteHarbinChina fxp@hit.edu.cn (2018) Abstract. Although 3D Gaussian Splatting (3DGS) enables high-fidelity real-time rendering, its prohibitive storage overhead severely hinders practical deployment. Recent anchor-based 3DGS compression schemes reduce redundancy through context modeling, yet overlook explicit geometric dependencies, leading to structural degradation and suboptimal rate-distortion performance. In this paper, we propose GeoHCC, a geometry-aware 3DGS compression framework that incorporates inter-anchor geometric correlations into anchor pruning and entropy coding for compact representation. We first introduce Neighborhood-Aware Anchor Pruning (NAAP), which evaluates anchor importance via weighted neighborhood feature aggregation and merges redundant anchors into salient neighbors, yielding a compact yet geometry-consistent anchor set. Building upon this optimized structure, we further develop a hierarchical entropy coding scheme, in which coarse-to-fine priors are exploited through a lightweight Geometry-Guided Convolution (G-Conv) operator to enable spatially adaptive context modeling and rate-distortion optimization. Extensive experiments demonstrate that GeoHCC effectively resolves the structure preservation bottleneck, maintaining superior geometric integrity and rendering fidelity over state-of-the-art anchor-based approaches. †copyright: acmlicensed†journalyear: 2018†doi: X.X†conference: Make sure to enter the correct conference title from your rights confirmation email; June 03–05, 2018; Woodstock, NY†isbn: 978-1-4503-X-X/2018/06†ccs: Computer vision†ccs: Theory of computation†ccs: Data compression. Figure 1. Trade-off between rendering FPS and PSNR for different methods. Marker size denotes storage cost, where smaller markers correspond to lower storage. 1. Introduction 3D Gaussian Splatting (3DGS) (Kerbl et al., 2023) has emerged as a powerful explicit 3D representation that models scenes with a set of anisotropic Gaussians with learnable attributes, including position, covariance, opacity, and spherical harmonics, enabling efficient optimization and high-quality novel-view synthesis. Its optimized rasterization supports fast convergence and real-time rendering, offering a strong alternative to implicit neural representations. However, high-quality reconstruction typically requires millions of primitives, leading to considerable storage and memory overhead. This redundancy hinders practical deployment, especially on resource-constrained platforms, and has motivated extensive research on compact 3DGS representations and compression. Early 3DGS compression methods (Lee et al., 2024; Niedermayr et al., 2024; Girish et al., 2024; Fan et al., 2024; Fang and Wang, 2024; Mallick et al., 2024; Kim et al., 2024; Zhang et al., 2026) mainly reduce storage through primitive pruning or vector quantization. While effective, they focus on compressing attribute value of each individual gaussian and largely ignore the inherent geometric correlation among Gaussians. Although such dependencies have been widely exploited in image and video compression (Cheng et al., 2020; He et al., 2021; Li et al., 2024, 2023; Sheng et al., 2022; Jia et al., 2025; Wang et al., 2026; Liu et al., 2026; Man et al., 2024, 2023, 2025), modeling them within 3DGS remains non-trivial due to the irregularly distribution of Gaussian primitives in 3D space. Locality-aware-GS (Shin et al., 2025) attempts to incorporate local geometric relations directly over massive unstructured Gaussian primitives, but the cost of neighborhood correlation search becomes prohibitive at large scale. Conversely, Anchor-based representations, e.g., Scaffold-GS (Lu et al., 2024), alleviate this issue by hierachically clustering primitives around anchors and thus provide a more compact and structured representation. Nevertheless, Scaffold-GS treats anchors as isolated entities, leaving the local geometric correlations among neighboring anchors underexplored. To further alleviate spatial redundancy, recent advances have incorporated more structured priors into anchor-based compression framework. Inspired by NeRF feature grids (Mildenhall et al., 2021; Müller et al., 2022; Guo et al., 2025), HAC (Chen et al., 2024) and HAC++ (Chen et al., 2025) leverage hash grids for context modeling. Context-GS (Wang et al., 2024b) takes a different approach by organizing anchors hierarchically to capture dependencies across representation levels, thus improving entropy modeling. Despite these advances, a fundamental limitation persists: current methods largely overlook the intrinsic geometric structures among anchors. Grid-based context models (e.g. HAC) rely on coarse extrinsic discretization and often fail to capture fine-grained geometric relationships in irregular anchor clouds. Hierarchical methods such as Context-GS (Wang et al., 2024b), despite their stronger representational capacity, typically construct multi-level context structures on top of heuristic pruning strategies, such as opacity-based anchor removal. By directly discarding low-importance anchors, these methods may disrupt local geometric continuity and weaken the structural foundation required for reliable coarse-to-fine context prediction. Since finer levels can no longer inherit sufficiently stable geometric priors from the base layers, ultimately leading to suboptimal structure preservation and entropy estimation. In this work, we argue that geometry-aware context modeling is crucial to unlocking the full compression potential of 3DGS. Rather than serving merely as attribute carriers, anchors are treated as nodes in a geometric graph where local neighborhoods exhibit strong geometric correlations. Based on this insight, we propose GeoHCC, a geometry-aware 3DGS compression framework that incorporates inter-anchor geometric correlations into anchor pruning and entropy coding for compact representation. We first introduce Neighborhood-Aware Anchor Pruning (NAAP), which evaluates anchor importance via graph aggregation and merges redundant anchors into salient neighbors. Building on the preserved local structure, we further design a hierarchical entropy coding scheme with geometry-guided indexed context. To implement this efficiently, we design a lightweight Geometry-Guided Convolution (G-Conv) operator that aggregates contextual information from local geometric features, enabling the entropy model to learn spatially adaptive and geometry-consistent priors for more efficient compression. As shown in Figure 1, experiments on BungeeNerf (Xiangli et al., 2022) show that GeoHCC achieves a favorable FPS–PSNR trade-off than existing methods while requiring lower storage cost. Our main contributions are summarized as follows: • We propose GeoHCC, a local geometry-aware hierarchical context compression framework for 3D Gaussian Splatting that reformulates anchor compression via geometry-induced graphs for consistent pruning and efficient hierarchical entropy modeling. • To preserve the local geometric perception capability of anchors, we propose Neighborhood-Aware Anchor Pruning (NAAP), a graph-based adaptive sparsification strategy. By evaluating geometric importance and merging redundant anchors into their salient neighbors, NAAP preserves the inherent geometric correlation among anchors, producing a compact yet geometry-consistent representation with minimal fidelity loss. • To exploit local geometric correlation in sparsified Gaussians, we propose hierarchical geometry-guided context modeling via a lightweight G-Conv. By capturing spatially adaptive priors over irregular neighborhoods, our method achieves accurate probability estimation and state-of-the-art compression with high rendering quality. 2. RelatedWork 2.1. Grapth-based 3D data modeling Graph Signal Processing (GSP) (Ortega et al., 2018; Yang et al., 2024) provides a framework for analyzing signals on irregular domains by modeling data as nodes in a graph. In 3D vision, it has been widely applied to point cloud analysis (e.g., DGCNN (Wang et al., 2019) and PointNet++ (Qi et al., 2017a, b)), where local graphs encode geometric relations for feature aggregation. Similar principles have also been applied to point cloud compression, where exploiting inter-point correlations improves coding efficiency (Fan et al., 2022; Deng et al., 2025; Gao et al., 2026). In this paper, we propose GeoHCC, which reformulates anchor-based 3DGS as an irregular geometric graph to jointly optimize anchor pruning and entropy coding via local geometry guidance, achieving significant bitrate reduction while preserving high-fidelity structural details. 2.2. Compact 3DGS Representation 3D Gaussian Splatting (3DGS) (Kerbl et al., 2023) achieves high-fidelity and efficient radiance field rendering, yet its explicit and unstructured Gaussian representation is less regular than the grid-based representations of NeRFs (Mildenhall et al., 2021; Bagdasarian et al., ; Wu et al., 2024), leading to prohibitive storage overhead that necessitates advanced compression techniques. Existing methods primarily tackle the storage challenge of 3D Gaussian Splatting by either reducing the number of primitives or learning compact attribute representations, without explicit rate-distortion optimization. Pruning-based approaches (Lee et al., 2024; Fan et al., 2024; Navaneet et al., 2023; Papantonakis et al., 2024; Ali et al., 2024; Ren et al., 2024; Cheng et al., 2024; Liu et al., 2024b) eliminate less contributive Gaussians using heuristic criteria, such as learnable masks, gradient magnitudes, or view-dependent significance. Complementary attribute compression techniques include spherical harmonics coefficient pruning (Morgenstern et al., 2024) and vector quantization (Wang et al., 2024a; Lee et al., 2024; Girish et al., 2024). In addition to these primitive-level techniques, a representative anchor-based approach is Scaffold-GS (Lu et al., 2024), which uses anchor points to hierarchically distribute local 3D Gaussians and predicts their attributes on-the-fly conditioned on viewing direction and distance within the view frustum. Inspired by the anchor-based representation of Scaffold-GS (Lu et al., 2024), a series of recent works has focused on rate-distortion (RD) optimized compression by improving entropy modeling through the exploitation of spatial or structural priors. These anchor-based methods have achieved impressive storage reduction while maintaining high rendering quality. For instance, HAC (Chen et al., 2024) and HAC++ (Chen et al., 2025) employ hash-grid-based spatial organization to derive compact context representations. Context-GS (Wang et al., 2024b) and CompGS (Liu et al., 2024c) further exploit hierarchical structure and anchor-primitive dependencies to improve entropy coding. Meanwhile, CAT-3DGS (Zhan et al., 2025a) adopts channel-wise autoregressive models to capture intra-attribute correlations, and Liu et al. (Liu et al., 2025) enhance density estimation through a Mixture-of-Priors formulation. While these methods achieve impressive rate-distortion performance in 3D Gaussian Splatting compression, we argue that the core of effective compression lies in the entropy model. A well-designed entropy model can leverage local geometric correlations among anchors, enabling efficient coding and reducing storage requirements. However, current anchor-based 3DGS compression methods still have room for improvement in entropy model design, particularly in exploiting local geometric priors. Drawing inspiration from geometry-aware modeling in point cloud compression and graph neural networks, we propose a local geometry-aware entropy model. This model represents the unstructured anchor cloud as an irregular geometric graph and uses a lightweight Geometry-Guided Convolution (G-Conv) to adaptively aggregate geometry-aware contextual priors from neighboring anchors. 3. Methodology 3.1. Preliminaries 3D Gaussian Splatting (3DGS). 3DGS (Kerbl et al., 2023) utilizes a collection of anisotropic 3D neural Gaussians to depict the scene so that the scene can be efficiently rendered using a tile-based rasterization technique. Beginning from a set of Structure-from-Motion (SfM) points, each Gaussian point is represented as follows: (1) G()=exp(−12(−)⊤−1(−)),G(p)= (- 12(p- μ) ^-1(p- μ) ), where p denotes the coordinates in the 3D scene, and μ and represent the mean position and covariance matrix of the Gaussian point, respectively. To ensure the positive semi-definiteness of , it is parameterized as =⊤⊤ =RSS R , where R and S denote the rotation and scaling matrices, respectively. Furthermore, each neural Gaussian possesses an opacity attribute α∈ℝ1α ^1 and view-dependent color ∈ℝ3c ^3, modeled via spherical harmonics (Zhang et al., 2022). All attributes of the neural Gaussians, i.e., ,,,α,\ μ,R,S,α,c\, are learnable and optimized by minimizing the reconstruction loss of images rendered through tile-based rasterization. Figure 2. Overview of the proposed 3DGS compression framework. Starting with Colmap initialization, anchors first undergo densification to capture fine-grained scene details. To optimize the resulting structure, we introduce Neighborhood-Aware Anchor Pruning (NAAP), which constructs a local graph to evaluate geometric importance. Unlike simple removal, NAAP adaptively merges the attributes of redundant anchors into their salient neighbors, producing a compact yet locally geometry-consistent representation. Subsequently, the preserved anchors are organized into Hierarchical Geometry-Guided Context Modeling module, where we employ a Local Geometry-Guided Context to guide entropy coding. Finally, the decoded attributes (e.g., colors, opacitys, scalings, rotations) generate 3D Gaussians via learnable offsets for high-fidelity rasterization. 3.2. Overview Building upon the compact anchor-based representation of Scaffold-GS (Lu et al., 2024), we propose GeoHCC, a local geometry-aware hierarchical context compression framwork for 3DGS, as illustrated in Figure 2. We define each anchor as a tuple =,,,a=\p,f,s,o\, comprising position ∈ℝ3p ^3, feature ∈ℝCf ^C, scaling factor ∈ℝ3s ^3, and offsets ∈ℝK×3o ^K× 3. The pipeline begins with anchor densification inherited from Scaffold-GS, which spawns additional anchors based on view-space gradients to capture fine-grained scene details. To mitigate anchor redundancy and enhance the compression efficiency of 3DGS, we introduce the Neighborhood-Aware Anchor Pruning (NAAP) module (Sec. 3.3). Instead of relying on simple heuristic thresholding (e.g., fixed opacity values), NAAP constructs a local geometric graph to evaluate the importance of anchors in a neighborhood-aware manner and adaptively merges the attributes of redundant anchors into their salient neighbors, producing a compact yet locally geometry-consistent representation. Based on the pruned anchor set, we further organize the anchors into a multi-level hierarchy for efficient entropy coding. Specifically, we develop a hierarchical entropy coding scheme with geometry-guided context (Sec. 3.4). To enhance context modeling capability, we employ a lightweight Geometry-Guided Convolution (G-Conv) that aggregates local geometric priors from the irregular neighborhood graph as coarse-grained information to guide finer-level entropy estimation. Finally, the decoded anchors generate 3D Gaussians via learnable offsets, achieving high-fidelity rasterization with extremely low storage overhead. Figure 3. Neighborhood-Aware Anchor Pruning (NAAP) pipeline starts by constructing an anchor-based geometric graph, with nodes colored by average opacity (darker = higher). Importance scores (ξi _i) are computed via neighborhood aggregation. Low-score anchors are identified as redundant and associated with their nearest salient neighbor (Local Neighbor Preserver). Instead of direct removal, a Weighted Attribute Transformer merges attributes from pruned anchors (opacity α¯i α_i, scaling sis_i, offset oio_i) into the nearest retained anchor, yielding fused attributes (ϕi _i, OiO_i, SiS_i, etc.) to preserve geometric and appearance information in a compact structure. 3.3. Neighborhood-Aware Anchor Pruning Conventional 3DGS pruning strategies typically rely on point-wise attribute thresholds (e.g., opacity) to remove less important Gaussian anchors. However, such independent evaluation ignores local geometric distributions, may inadvertently eliminate structurally essential anchors, especially in low-density regions. To address this limitation, we propose Neighborhood-Aware Anchor Pruning (NAAP), which evaluates anchor importance within a local geometric neighborhood context and preserves structural continuity through adaptively merges redundant information. As illustrated in Figure 3, NAAP consists of four steps: Step 1 & 2: Graph Construction and Importance Evaluation. We initially construct a local geometric graph =(,ℰ)G=(A,E) to capture the local geometric correlations among anchors, where =1,…,NA=\a_1,…,a_N\ represents the set of anchors and ℰE denotes the edges connecting neighboring anchors, each anchor ia_i possesses a position ip_i and an accumulated average opacity α¯i α_i, which is derived by accumulating the opacity values of its associated neural Gaussians over N training iterations. We connect each anchor to its K-nearest neighbors within a radius r, forming the local neighborhood (i)N(i), which provides a lightweight representation of local geometric structure for importance estimation. To distinguish structurally essential anchors from noise or redundant anchors, we define a neighborhood-weighted importance score. Specifically, for each anchor (taking ia_i as an example), we first compute a distance-based weight wij=(‖i−j‖2+ϵ)−1w_ij=(\|p_i-p_j\|_2+ε)^-1 between between itself and its neighbor j∈(i)a_j (i), which assigns larger weights to closer neighbors. Then a smoothed neighborhood opacity Φi _i is calculated to aggregate local context: (2) Φi=α¯i+∑j∈(i)wijα¯j1+∑j∈(i)wij. _i= α_i+ _j (i)w_ij α_j1+ _j (i)w_ij. The final importance score ξi _i is formulated as a linear interpolation between the anchor-specific opacity and its neighborhood-aware observation: (3) ξi=(1−λ)α¯i+λΦi. _i=(1-λ) α_i+λ _i. where λ∈[0,1]λ∈[0,1] is a balancing factor. Given a threshold τ, we identify redundant anchors using the pruning mask: (4) ℳprune=i∣ξi<τ.M_prune=\a_i _i<τ\. This design enables anchors residing in structurally significant clusters to be preserved even if their individual opacity is relatively low. Step 3 & 4: Neighbor Association and Attribute Merging. Unlike previous pruning strategies that directly discard anchors in ℳpruneM_prune, we instead consolidate their information into the surviving geometry via a dedicated Weighted Attribute Transformer. For each redundant anchor r∈ℳprunea_r _prune, we identify its nearest salient neighbor k∈∖ℳprunea_k _prune as the target for information transfer. Let lowercase θ∈,,αθ∈\o,s,α\ and uppercase Θ∈,,ϕ ∈\O,S,φ\ denote the raw and fused attributes (offsets, scaling, and opacity), respectively. The transformation is governed by: (5) Θk=(1−γ)θk+γθr, _k=(1-γ) _k+γ _r, where γ controls the contribution of the pruned anchor. This integration effectively condenses the geometric and appearance attributes of removed regions into their nearest neighbors (θ→Θθ→ ), ensuring that comprehensive scene information is preserved rather than lost. Finally, eliminating the anchors in ℳpruneM_prune yields a compact, locally geometry-consistent representation. Figure 4. This module exploits cross-level correlations by mapping Level 1 attributes to Level 2 query anchors via a deterministic mapping ℳM to obtain the preliminary attributes pre(2)A_pre^(2). Then, a k-N graph is constructed over pre(2)A_pre^(2) to form the graph-based geometric prior geo(2)G_geo^(2). Within the G-Conv (dashed box): (1) Geometry Branch: Relative spatial offsets Δij _ij between the query anchor and its neighbors are used to query a learnable 3D kernel (Weight Look-up Table) via trilinear interpolation, generating dynamic geometric weights ijw_ij that explicitly encode the local spatial layout. (2) Feature Branch: This branch extracts semantic-geometric embeddings ije_ij by transforming the concatenated residual features Δij(1) _ij^(1) and relative offsets Δij _ij through an MLP ϕφ. Finally, the dynamic weights modulate these embeddings to produce the refined geometry-aware feature ih_i, which provides a structured foundation for deriving the final local geometry-guided context i(ctx)a_i(ctx) for Level 2 attribute entropy coding. As shown in Fig. 3, conventional threshold-based pruning would discard low-opacity anchors (highlighted by the red circle) induced by optimization noise. In contrast, NAAP can identify non-salient nodes within high-density clusters, which often play a crucial role in modeling key scene details during rendering. 3.4. Hierarchical Geometry-Guided Context Modeling While hierarchical context models (Wang et al., 2024b; Liu et al., 2024c, a) have shown promising performance for anchor-based 3DGS compression, they often suffer from structural inefficiencies. Specifically, existing approaches typically rely on heuristic neighbor pooling or rigid spatial partitioning, which may fail to preserve precise geometric correspondence across hierarchy levels. As a result, the retrieved context is not always well-aligned with the query anchors, leading to suboptimal entropy estimation. To overcome these limitations, we propose a streamlined two-level autoregressive model that explicitly enforces geometric alignment between coarse and fine anchors. As shown in Figure 4, by strictly aligning the coarse geometry (Level 1) with fine attributes (Level 2), our method achieves precise context retrieval and refinement via a three-step process: 1) Hierarchical Partitioning. To leverage multi-scale spatial correlations, we organize the anchor set V into a two-level hierarchy (ℒ=2L=2) following Context-GS (Wang et al., 2024b). We first derive a coarse representation (1)A^(1) by quantizing anchor positions with a scaled voxel size ϵ1=s⋅ϵ0 _1=s· _0: (6) (1)=j∈∣j=mini:⌊pi/ϵ1⌋,A^(1)=\a_j j= \i: p_i/ _1 \\, where ϵ0 _0 is the initial fine-grained voxel size and ϵ1 _1 represents the coarse-grained resolution controlled by the scaling factor s. The fine level is then defined as (2)=∖(1)A^(2)=V ^(1) to ensure a disjoint structure. This hierarchy allows (1)A^(1) to serve as a coarse spatial prior for the entropy coding of (2)A^(2). 2) Inter-Level Context Retrieval. To fully exploit the information provided by the coarse representation, we propose an inter-level retrieval strategy that transfers coarse-level attributes (e.g., feature f, scaling s, and offsets o) to the fine-level query anchors, establishing a preliminary feature representation for subsequent geometric context refinement. This strategy utilizes the voxel grid as a spatial bridge to align attributes across levels. Specifically, based on the voxel partitioning rules in Eq. 6, we establish a deterministic mapping ℳM that associates each fine-level query anchor j(2)∈(2)a_j^(2) ^(2) with its corresponding coarse-level parent i(1)a_i^(1) within the same voxel, yielding a preliminary context set pre(2)A^(2)_pre: (7) pre(2)=(j(2),i(1),i(1),i(1))∣j(2)∈(2),i=ℳ(j(2)),A^(2)_pre=\(p_j^(2),f_i^(1),s_i^(1),o_i^(1)) _j^(2) ^(2),i=M(a_j^(2))\, where j(2)p_j^(2) is the fine-level position and the tuple (i(1),i(1),oi(1))(f_i^(1),s_i^(1),o_i^(1)) denotes the decoded attributes inherited from the i-th coarse-level anchor in (1)A^(1). To explicitly capture the geometric relations among neighboring contexts and model local structure dependencies, we construct a Ball k-nearest neighbor (Ball k-N) graph (Qi et al., 2017b) over pre(2)A^(2)_pre based on the spatial positions of the fine-level anchors. This graph prior, denoted as geo(2)=(pre(2),ℰ)G^(2)_geo=(A^(2)_pre,E), where ℰE represents the edges connecting spatially neighboring anchors, encapsulates both the inherited coarse-level preliminary contexts and the fine-level local geometric correlations. It provides a structured foundation for subsequent geometry-guided feature refinement in the G-Conv. 3) Geometry-Guided Convolution (G-Conv). For the graph-based anchor prior geo(2)G^(2)_geo with its k-N graph structure, a straightforward approach is to directly process these retrieved features through a Multi-Layer Perceptron (MLP), as adopted in Context-GS (Wang et al., 2024b). However, while geo(2)G^(2)_geo provides a coarse graph-structured contextual priors, simply concatenating them cannot adequately capture the fine-grained geometric correlations in irregular and unstructured anchor distributions. To address this, we propose G-Conv, which performs adaptive feature refinement upon the local neighborhood. As illustrated in Fig. 4, G-Conv refines the preliminary features of each query anchor i(pre)(2)a_i(pre)^(2) by aggregating context priors from its k-N neighbors j(pre)(2)a_j(pre)^(2) through two cooperative branches. Geometry Branch: To capture local geometric correlations, we compute normalized relative offsets Δ^ij=Norm(j−i) p_ij=Norm(p_j-p_i) to query a learnable 3D kernel ∈ℝD×D×D×CT ^D× D× D× C. Specifically, Δ^ij p_ij is treated as a continuous query coordinate within the grid space of T, from which a dynamic kernel ijw_ij is retrieved via trilinear interpolation: (8) ij=Tri-Interp(Look-up(,Δ^ij))w_ij=Tri-Interp(Look-up(T, p_ij)) Here Tri-Interp(⋅)Tri-Interp(·) interpolates over the eight nearest integer grid cells in T to perceive fine-grained geometric variations beyond discrete grid resolutions. This mechanism ensures spatially-continuous weighting for effective geometry-aware feature aggregation. Feature Branch: Concurrently, the feature branch extracts semantic-geometric correlations. Specifically, we first concatenate the residual features Δij=j−i _ij=f_j-f_i with the relative spatial offsets Δij _ij. The concatenated feature is then tranformed via an MLP to extract refined semantic embeddings that are implicitly aware of the local geometry: (9) ij=MLP([Δij∥Δij])e_ij=MLP([ _ij _ij]) where [⋅∥⋅][· ·] denotes the concatenation operation. Finally, the dynamic geometric weights from the first branch explicitly modulate these embeddings to produce the geometry-guided context i(ctx)f_i(ctx): (10) i(ctx)=∑j∈(i)ij⊙ijf_i(ctx)= _j (i)w_ij _ij where ⊙ denotes the element-wise product. The Local Geometry-Guided Context i(ctx)a_i(ctx) is formed by concatenating the refined geometry-aware feature i(ctx)f_i(ctx) with inherited attributes (i,i,oip_i,s_i,o_i). By integrating local neighborhood correlations with global geometric priors, i(ctx)a_i(ctx) provides a comprehensive representation of the anchor’s state. This i(ctx)a_i(ctx) is subsequently projected via an MLP to predict distribution parameters: (11) μ,σ,Δadj=MLP(i(ctx)),μ,σ, _adj=MLP(a_i(ctx)), where μ and σ characterize the attribute distribution, and Δadj adj adaptively adjusts the quantization step based on local structural complexity. By operating on graph-structured priors, G-Conv enables spatially-adaptive bitrate allocation, prioritizing complex geometric regions while maintaining high compression efficiency in smoother areas. 3.5. Bitstream Composition. The final bitstream is composed of three parts: R=Rgeo+Rattr+RmodelR=R_geo+R_attr+R_model, where RgeoR_geo, RattrR_attr, and RmodelR_model denote the bitrate associated with anchor geometry, hierarchical anchor attributes, and model parameters, respectively. Specifically, RgeoR_geo represents the explicit anchor coordinates, which are losslessly compressed after quantization. RattrR_attr comprises the hierarchical attributes (features, scalings, offsets) of both (1)A^(1) and (2)A^(2), encoded via the proposed hierarchical geometry-guided context modeling. RmodelR_model stores the quantized weights of the shared MLPs and G-Conv modules as a lightweight model header. 3.6. Optimization The proposed GeoHCC for 3DGS compression is optimized under a rate-distortion objective: (12) ℒ=ℒrender+λℒanchor,L=L_render+λ\,L_anchor, where ℒrenderL_render denotes the rendering loss inherited from Scaffold-GS (Lu et al., 2024) and serves as the distortion term, while ℒanchorL_anchor denotes the estimated entropy-coded bitrate of the anchor attributes, including positions, opacities, and feature descriptors, following HAC++ (Chen et al., 2025) and Context-GS (Wang et al., 2024b), and serves as the rate term. The hyperparameter λ>0λ>0 controls the trade-off between reconstruction fidelity ( ℒrenderL_render ) and compression efficiency ( ℒanchorL_anchor ). Figure 5. Qualitative results of the proposed method compared to existing compression methods. Table 1. Comparison against existing compression approaches. Our method is evaluated under two settings: a high-fidelity mode and a high-compression mode, showcasing its versatility. Cells colored Red and yellow highlight the top-performing and second-best results, respectively, for both the low-bitrate and high-bitrate regimes. All size are reported in MB. Datasets Mip-NeRF360 (Barron et al., 2022) BungeeNeRF (Xiangli et al., 2022) DeepBlending (Hedman et al., 2018) Tank&Temples (Knapitsch et al., 2017) Methods psnr↑ ssim↑ lpips↓ size↓ psnr↑ ssim↑ lpips↓ size↓ psnr↑ ssim↑ lpips↓ size↓ psnr↑ ssim↑ lpips↓ size↓ 3DGS (Bagdasarian et al., ) 27.49 0.813 0.222 744.7 24.87 0.841 0.205 1616 29.42 0.899 0.247 663.9 23.69 0.844 0.178 431.0 Scaffold-GS (Lu et al., 2024) 27.50 0.806 0.252 253.9 26.62 0.865 0.241 183.0 30.21 0.906 0.254 66.00 23.96 0.853 0.177 86.50 Compact3DGS (Lee et al., 2024) 27.08 0.798 0.247 48.80 23.36 0.788 0.251 82.60 29.79 0.901 0.258 43.21 23.32 0.831 0.201 39.43 Compressed3D (Navaneet et al., 2023) 26.98 0.801 0.238 28.80 24.13 0.802 0.245 55.79 29.38 0.898 0.253 25.30 23.32 0.832 0.194 17.28 Morgen. et al. (Morgenstern et al., 2024) 26.01 0.772 0.259 23.90 22.43 0.708 0.339 48.25 28.92 0.891 0.276 8.40 22.78 0.817 0.211 13.05 CompGS (Liu et al., 2024c) 27.26 0.803 0.239 16.50 - - - - 29.69 0.901 0.279 8.77 23.70 0.837 0.208 9.60 HAC(low-rate) (Chen et al., 2024) 27.53 0.807 0.238 15.26 26.48 0.845 0.25 18.49 29.98 0.902 0.269 4.35 24.04 0.846 0.187 8.10 Context-GS(low-rate) (Wang et al., 2024b) 27.62 0.778 0.237 12.68 26.90 0.866 0.222 14.00 30.11 0.907 0.265 3.43 24.20 0.852 0.184 7.05 HAC++(low-rate) (Chen et al., 2025) 27.6 0.803 0.253 8.34 26.78 0.858 0.235 11.75 30.16 0.907 0.266 2.91 24.22 0.849 0.190 5.18 Ours (low-rate) 27.64 0.805 0.247 8.23 26.93 0.866 0.231 11.59 30.25 0.909 0.267 2.83 24.32 0.852 0.187 4.92 HAC(high-rate) (Chen et al., 2024) 27.77 0.811 0.230 21.84 27.08 0.872 0.209 29.72 30.34 0.906 0.258 6.35 24.40 0.853 0.177 11.24 HAC++(high-rate) (Chen et al., 2025) 27.82 0.811 0.231 18.48 27.17 0.879 0.196 20.82 30.34 0.911 0.254 5.287 24.32 0.854 0.178 8.63 Context-GS(high-rate) (Wang et al., 2024b) 27.75 0.811 0.231 18.41 27.15 0.875 0.205 21.80 30.39 0.909 0.258 6.60 24.29 0.855 0.176 11.80 CAT-3DGS (Zhan et al., 2025a) 27.77 0.809 0.241 12.35 27.35 0.886 0.183 26.59 30.29 0.909 0.269 3.56 24.41 0.853 0.189 6.93 Liu. et al. (Liu et al., 2025) 27.68 0.808 0.234 15.64 27.26 0.875 0.207 20.83 30.45 0.912 0.250 5.65 24.21 0.861 0.163 8.98 Ours (high-rate) 27.82 0.812 0.2351 12.24 27.46 0.883 0.196 19.48 30.49 0.912 0.250 5.63 24.43 0.856 0.177 8.49 Figure 6. Rate-Distortion (RD) performance curves. Comparison with advanced compression techniques (HAC, HAC++, Context-GS, CAT-3DGS) on the Mip-NeRF360, BungeeNeRF, and Tank&Temples datasets. GeoHCC demonstrates robust coding efficiency, maintaining the upper envelope across a wide range of bitrates. 4. Experiments 4.1. Implementation Details We implement GeoHCC within the PyTorch framework, building upon the official Scaffold-GS codebase (Lu et al., 2024). To ensure the convergence of geometry-aware components, models are trained for 35,000 iterations. We adopt a minimalist two-level hierarchy (L=2L=2) and set the voxelization scaling factor s consistent with Context-GS (Wang et al., 2024b). For local geometry-aware perception via Ball K-N graph construction, the neighbor count is uniformly fixed at K=8K=8 for both NAAP and the formation of geo(2)G^(2)_geo, while the G-Conv volumetric kernel size is set to k=5k=5. Unless otherwise specified, we follow the default Scaffold-GS configuration, utilizing an anchor feature dimension of 50 and a compressed latent dimension of 12. Table 2. Comparison of storage breakdown (Positions, Features, MLP, Others,“Others” includes auxiliary structures and metadata (e.g., scalings, offsets, masks).), and rendering FPS on the ”Bicycle” scene between Context-GS (vanilla EM, i.e., Entropy Modeling) and our G-Conv-based Hierarchical Geometry-Guided Context EM. Methods Storage Costs (MB)↓ Fidelity Rendering Positions Features MLP Others Total PSNR↑ SSIM↑ LPIPS↓ FPS Vanilla EM (Wang et al., 2024b) 5.24 8.27 0.3162 11.24 25.07 25.07 0.7391 0.2683 135 G-Conv-based EM(two level) 4.69 4.51 0.2381 6.31 15.75 25.16 0.7415 0.2704 170 G-Conv-based EM(three level) 4.66 6.82 0.3162 7.54 19.34 25.10 0.7416 0.2703 160 4.2. Experiment Details Datasets. Our method is evaluated on four standard real-world benchmarks: Mip-NeRF360 (Barron et al., 2022) (utilizing all 9 scenes), BungeeNeRF (Xiangli et al., 2022), DeepBlending (Hedman et al., 2018), and Tanks&Temples (Knapitsch et al., 2017). Baseline Methods. We compare our method with a wide range of state-of-the-art 3DGS compression approaches, which can be grouped into two main streams. The first focuses on compact representations via parameter pruning or vector quantization, including Scaffold-GS (Lu et al., 2024), Compressed3D (Navaneet et al., 2023), and CompGS (Liu et al., 2024c). The second stream, more related to our work, improves entropy coding by exploiting contextual priors. Examples include HAC (Chen et al., 2024) and HAC++ (Chen et al., 2025), which adopt hash grids for spatial compactness, and Context-GS (Wang et al., 2024b), which models anchor-level context as hyperpriors. More recently, Liu et al. (Liu et al., 2025) introduced a Mixture-of-Experts (MoE) module for robust feature learning, while CAT-3DGS (Zhan et al., 2025b) applies channel-wise autoregressive modeling for attribute compression. We benchmark against these methods to validate the effectiveness of our local geometry-aware hierarchical context modeling. Metrics. We evaluate compression performance in terms of storage size, measured in megabytes (MB). To assess the visual quality of rendered images generated from the compressed 3DGS data, we employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM) (Wang et al., 2004), and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al., 2018). 4.3. Experiment Results Quantitative Analysis. As shown in Table 1, our proposed GeoHCC achieves significant improvements over the Scaffold-GS (Lu et al., 2024) backbone. It delivers an average storage reduction of over 21× while maintaining competitive or even superior rendering fidelity in terms of PSNR and SSIM. Compared with state-of-the-art methods, including HAC (Chen et al., 2024), HAC++ (Chen et al., 2025), Context-GS (Wang et al., 2024b), CAT-3DGS (Zhan et al., 2025a), and Liu et al. (Liu et al., 2025), GeoHCC consistently demonstrates better rate-distortion performance, especially at low bitrates. Notably, in several scenes under high-rate settings, GeoHCC even surpasses the uncompressed Scaffold-GS in both PSNR and SSIM. Furthermore, the Rate-Distortion curves in Fig. 6 confirm that GeoHCC provides a superior performance envelope, achieving higher rendering quality at equivalent bitrates across a wide range of compression ratios. Qualitative Analysis. As shown in Figure 5, GeoHCC produces sharper structural details and significantly fewer artifacts compared to both the baseline and competing methods. This improvement stems from our locally geometry-aware constraints, which leverage local geometric context as strong regularization to suppress floaters while enhancing fine local texture details. Thanks to the geometry-guided context modeling via G-Conv, our method effectively preserves high-frequency textures even at low bitrates, where other approaches often suffer from blurring or “popping” artifacts. Table 3. Quantitative ablation study on the Deep Blending dataset. (1) Ours: the full version of our proposed compact neural 3DGS compression framework with both NAAP and G-Conv. (2) Ours w/o G-Conv: our method without the G-Conv component. (3) Ours w/o NAAP: our method without the NAAP component. (4) Ours w/o NAAP & G-Conv: our method without both proposed components. Method PSNR↑ SSIM↑ LPIPS↓ size↓ Ours w/o NAAP & G-Conv 30.10 0.9062 0.2659 3.76 MB Ours w/o G-Conv 30.13 0.9087 0.2656 3.72 MB Ours w/o NAAP 30.20 0.9095 0.2648 3.58 MB Ours 30.31 0.9106 0.2636 3.47 MB 4.4. Ablation Study and Analysis Effectiveness of Different Components. As shown in Table 3, we conduct an ablation study on the Deep Blending dataset to evaluate the contribution of each proposed component in our GeoHCC framework. Removing NAAP (“Ours w/o NAAP”) leads to a decrease of 0.11 dB in PSNR, 0.001 in SSIM, and a slight increase of 0.11 MB in storage size compared to the full model. Removing G-Conv (“Ours w/o G-Conv”) results in a drop of 0.18 dB in PSNR, 0.002 in SSIM, and an additional 0.25 MB in size. When both components are removed (“Ours w/o NAAP & G-Conv”), the performance degrades further by 0.21 dB in PSNR, 0.004 in SSIM, and 0.29 MB in storage compared to the full model. These results demonstrate that both NAAP and G-Conv are essential for achieving high rendering quality under strong compression constraints. Notably, the combined performance gain from NAAP and G-Conv exceeds the sum of their individual improvements, revealing strong synergy between the two modules. This indicates that NAAP’s preservation of local geometric structures among anchors creates more structured representations that enhance the effectiveness of subsequent hierarchical entropy coding, allowing G-Conv to achieve superior compression efficiency and rendering quality under tight bit constraints. Table 4. Storage comparison between vanilla pruning (Context-GS (Wang et al., 2024b)) and our GeoHCC method. Method Positions (MB) Features (MB) Vanilla Pruning 0.7531 1.1108 NAAP (Ours) 0.7689 (+2.1%) 1.0847 (-2.4%) Effectiveness of NAAP. As shown in Table 4 on the Deep Blending dataset, compared to vanilla pruning (Wang et al., 2024b), NAAP increases positions storage by only 2.1% while reducing features storage by 2.4%. This indicates that NAAP selectively retains a small number of critical anchors to preserve local geometric structures. These anchors enable more coherent local geometry in the gaussian field, which in turn creates stronger spatial correlations among features. End-to-end optimization then exploits this structure to remove redundancy more effectively, allowing significantly better entropy coding of the features. Thus, the tiny anchor overhead is largely compensated by much greater feature compression, revealing that geometry-aware anchor preservation is a highly efficient way to improve structured representation and overall compression in Gaussian splatting. Effectiveness of Hierarchical Geometry-Guided Context Modeling. We evaluate the proposed hierarchical geometry-guided context modeling module against the vanilla entropy model (Wang et al., 2024b) under the same NAAP framework. As shown in Table 2, compared to the baseline, our two-level G-Conv-based EM significantly reduces the total storage cost from 25.07 MB to 15.75 MB (37.2% reduction) while improving PSNR from 25.07 dB to 25.16 dB. Most notably, the storage for anchor features is nearly halved (from 8.27 MB to 4.51 MB), and the overhead in the ”Others” category drops from 11.24 MB to 6.31 MB, demonstrating superior redundancy elimination. We also find that deeper hierarchies do not necessarily enhance efficiency. Although the three-level scheme slightly optimizes position storage (4.66 MB), it increases feature costs to 6.82 MB and total storage to 19.34 MB. This stems from the excessive computational overhead and complex cross-layer dependencies that provide diminishing returns in fidelity. Therefore, we adopt the two-level design. The efficiency of our model is driven by the G-Conv operator, which leverages local geometric correlations to dynamically weight anchor attributes, producing geometry-aware context. This facilitates the derivation of informed conditional priors with high structural fidelity, which enhances the exploitation of inter-anchor dependencies and ensures a thorough reduction of attribute redundancy in both features and metadata. 5. Conclusion To enhance 3DGS compression performance, we propose a local geometry-aware framework that consistently exploits geometric relationships within anchor neighborhoods. 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