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CVT-GS: Learning to Simplify 3D Gaussian Splatting with Centroidal Voronoi Tessellation

Bingxian Li, Yilong Li, Jingliang Peng, Peng-Shuai Wang, Fei Zhu, Guozheng Li, Chi Harold Liu, Guoping Wang, Bo Pang

arXiv:2609.08730v1cs.CV

TL;DR

Large 3DGS scenes carry substantial storage and rendering overhead, while extreme primitive reduction can leave coverage holes. CVT-GS allocates spatial supports with geometry-aware CVT and predicts a representative Gaussian for each using MergeNet. Across benchmarks, it improves quality and simplification speed while retaining standard 3DGS compatibility.

  • Problem

    High-quality 3DGS scenes can require hundreds of thousands to millions of Gaussians, creating storage and rendering overhead, while extreme primitive deletion can leave coverage holes.

    Source: Introduction · p. 1

  • Method

    CVT-GS partitions pretrained Gaussian centers into coherent supports with geometry-aware CVT, then uses MergeNet to predict one standard Gaussian per support.

    Source: Introduction · pp. 1–2, Method · p. 2

  • Results

    +1.57/+1.30/+1.03 dB average PSNR gains over NanoGS at ρ=0.1/0.01/0.001 accompany the best rendering quality and shortest average simplification time at matched counts in every setting.

    Source: Experimental Results · p. 5

  • Takeaways & Limitations

    The simplified scenes retain the standard 3DGS format and remain plug-and-play with existing rasterizers.

    Source: Introduction · p. 2

Abstract

from arXiv · show

While 3D Gaussian Splatting (3DGS) has emerged as a powerful representation for real-time novel view synthesis, rendering high-fidelity scenes often relies on a massive number of Gaussian primitives, incurring substantial storage and computational overhead. Existing simplification techniques are largely intrusive, requiring training-time pruning, architectural modifications, or computationally expensive per-scene fine-tuning. These drawbacks limit their deployment on off-the-shelf pretrained models. In this paper, we propose CVT-GS, a novel optimization-free post-hoc simplification framework that directly compresses trained 3DGS scenes without sacrificing visual fidelity. Our approach first constructs spatially coherent cells over Gaussian centers via a geometry-aware Centroidal Voronoi Tessellation (CVT). Subsequently, a lightweight neural cell merger predicts the geometry and appearance of a single, highly representative Gaussian primitive for each cell under differentiable rendering supervision. By formulating simplification as a rendering-aware many-to-one merging process rather than naive primitive pruning, CVT-GS outputs a standard 3DGS scene that is seamlessly compatible with existing renderers. Experiments on various datasets demonstrate the superiority of our method. Notably, when achieving a 100-fold reduction in Gaussian points, our method operates 12 times faster than state-of-the-art methods while improving the PSNR by 1.3 dB.

Introduction

CVT-GS targets the storage and rendering burden of large 3DGS scenes with a post-hoc approach that merges spatial supports instead of simply deleting primitives. It preserves the standard 3DGS format while improving quality and simplification speed across benchmarks.

Introduction

  • High-quality 3DGS scenes can require hundreds of thousands to millions of Gaussians, creating substantial storage, transmission, sorting, and rendering overhead.Source: Introduction · p. 1
  • At extreme compression ratios, deleting primitives can leave coverage holes, so CVT-GS frames simplification as rendering-aware many-to-one merging.The merged output remains a standard 3DGS primitive compatible with existing renderers.Source: Introduction · p. 1
  • Geometry-aware CVT constructs density-adaptive, spatially coherent supports, and MergeNet predicts one representative Gaussian per support in a single feed-forward pass.The output retains the standard 3DGS format.Source: Introduction · pp. 1–2
  • Up to 12.3× faster simplification than prior state-of-the-art baselines accompanies higher PSNR across four datasets under the same immediate-output protocol.The comparison uses the immediate-output protocol.Source: Introduction · p. 2

Related Work

Prior work organizes or compresses 3DGS through altered representations, pruning, and coding, while recent post-training methods include merging and neural-field fitting. CVT-GS instead builds scene-level CVT supports and predicts a standard Gaussian for each support.

Structured 3DGS Representations

  • Structured representations use scaffolds, neural fields, many-in-one structures, or progressive bitstreams, but typically add auxiliary structures or alter decoding.CVT-GS starts from a pretrained standard scene and returns standard Gaussians without changing the renderer or original decoding pipeline.Source: Structured 3DGS Representations · p. 2

3DGS Simplification and Compression

  • Pruning and coding methods reduce redundancy through learned masks, heuristics, encodings, vector quantization, context models, or entropy coding.Post-training approaches include NanoGS pairwise merging, GHAP's optimal-transport view, and NeuralGS, which uses cluster-wise optimization and quality-restoring fine-tuning.Source: 3DGS Simplification and Compression · p. 2

CVT in Geometry Processing

  • CVT is a geometry-processing tool for spatial partitioning and distribution-preserving sampling, with representatives optimally modeling local regions in a least-squares sense.Here, CVT forms mergeable supports over trained 3DGS primitives, and a neural merger predicts one standard Gaussian per support.Source: CVT in Geometry Processing · p. 2

Method

CVT-GS simplifies a pretrained 3DGS scene by grouping Gaussian centers into support cells and predicting one standard Gaussian per cell. The shared predictor is trained with local rendering supervision, then applied without per-scene fine-tuning.

Method

  • CVT-GS constructs scene-level support cells and predicts one standard Gaussian for each in a feed-forward pass, rather than selecting a subset of input primitives.The output remains in the standard 3DGS format, and no per-scene fine-tuning is required.Source: Method · p. 2, MergeNet Prediction and Loss · p. 4

Centroidal Voronoi Support Construction

Cell Feature Construction

  • Each cell is normalized by a deterministic reference primitive that supplies a local coordinate system and initial parameter scale for residual prediction.The reference uses weighted position and appearance averages and a covariance derived from the cell's weighted second spatial moment.Source: Cell Feature Construction · p. 4
  • Reference-relative descriptors encode each member's local position, relative scale and rotation, opacity, and appearance residual for shared cross-cell prediction.Quaternion signs are aligned to the reference before relative rotations are formed.Source: Cell Feature Construction · p. 4

MergeNet Prediction and Loss

  • A permutation-invariant MergeNet pools cell-member features and predicts a residual update to the reference Gaussian, trained offline with local differentiable rendering supervision.The training compares rendered crops of each predicted Gaussian and its original cell; deployment exports standard 3DGS without per-scene optimization.Source: MergeNet Prediction and Loss · p. 4

Experiments

Across four standard 3DGS benchmarks, CVT-GS is reported to improve rendering quality and simplification efficiency over prior methods. Ablations show contributions from CVT support construction, MergeNet, and opacity filtering.

Experimental Settings

  • Evaluation covers NeRF-Synthetic, Mip-NeRF360, Tanks & Temples, and Deep Blending, with test-view PSNR, SSIM, LPIPS, and end-to-end simplification time.All methods use the same trained inputs, target counts, renderer/evaluator, and hardware, and are evaluated immediately after primitive-count reduction without recovery or fine-tuning.Source: Experimental Settings · pp. 4–5

Quantitative Results

  • Compared with NanoGS, average PSNR improves by +1.57/+1.30/+1.03 dB and SSIM by +0.055/+0.034/+0.025 at ρ = 0.1/0.01/0.001, respectively.At matched primitive counts, CVT-GS achieves the best rendering quality and shortest average simplification time in every setting.Source: Experimental Results · p. 5, Table 1 · p. 5
  • At ρ = 0.001, CVT-GS exceeds the strongest pruning, selection, or reduction baseline by +5.1 to +7.5 dB PSNR across datasets.On Mip-NeRF360 and Tanks & Temples, pruning and tree-based reduction degrade rapidly at low ratios, while CVT-based support construction maintains more stable fidelity.Source: Experimental Results · p. 5

Qualitative Results

  • On the garden scene, pruning, selection, and reduction baselines develop missing regions, speckles, and dark holes at ρ = 0.01 and 0.001, while NanoGS blurs details.CVT-GS better preserves the vase silhouette, plant details, tabletop contour, and background foliage.Source: Experimental Results · pp. 5–6, Figure 2 · p. 6

Simplification Time

  • CVT-GS is 12.3× faster than NanoGS and 3.1× faster than GHAP while achieving higher PSNR, using pooled end-to-end time across scenes and ratios.End-to-end timing runs from loading a trained scene through writing the simplified output.Source: Experimental Results · pp. 6–7, Figure 3 · p. 7

Ablation Studies

  • Replacing CVT with local k-NN grouping lowers average PSNR by 0.88, 1.65, and 2.53 dB at ρ = 0.1, 0.01, and 0.001, respectively.At ρ = 0.001, average LPIPS increases from 0.481 to 0.677; the reported trend favors scene-level density-adaptive supports over independent local groups.Source: Ablation Studies · p. 7, Table 2 · p. 7
  • Removing MergeNet drops average PSNR by 1.95, 3.01, and 4.23 dB across the three ratios; opacity filtering improves average PSNR by 0.76–0.86 dB and reduces LPIPS by 0.022–0.049.The authors attribute the largest degradation to MergeNet’s role in capturing residual geometry and appearance within each cell.Source: Ablation Studies · p. 7, Table 2 · p. 7

Conclusion

CVT-GS combines scene-level CVT support allocation with rendering-aware many-to-one merging to simplify pre-trained 3DGS scenes. Across four benchmarks, it improves the quality-speed trade-off under aggressive compression, with ablations supporting both components.

Conclusion

  • At 100× simplification, CVT-GS achieves an average PSNR of 21.32 dB, outperforming the sota post-hoc baseline by 1.30 dB.It operates more than one order of magnitude faster than existing baselines.Source: Conclusion · p. 7
  • Geometry-aware CVT allocates coherent, density-adaptive support cells that MergeNet condenses into representative Gaussians in one feed-forward pass.The resulting scenes retain strict compatibility with the standard 3DGS format.Source: Conclusion · p. 7
  • Ablations confirm the importance of both CVT spatial partitioning and neural cell merging; future work could explore richer MergeNet architectures and dynamic 4D representations.Source: Conclusion · p. 7
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