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From Scattered Gaussians to Structured Maps: Efficient Gaussian Splatting Coding via Dual-phase Morton Sorting

Bolin Chen, Shanzhi Yin, Ru-Ling Liao, Yibo Fan, Yan Ye

arXiv:2609.29041v1cs.MM

TL;DR

High-fidelity 3DGS scenes contain many Gaussian primitives with multiple attributes, creating substantial storage and transmission overhead and underscoring the need for efficient compression. The method combines Morton-based 1D indexing with a structured 2D Morton mapping table to arrange Gaussian attributes as block-wise feature maps. The approach achieves better rate-distortion performance and lower runtime than PLAS and conventional Morton-based sorting.

  • Problem

    High-fidelity 3DGS scenes contain many Gaussian primitives with multiple attributes, creating substantial storage and transmission overhead and underscoring the need for efficient compression.

    Source: §1 · p. 1

  • Method

    The method combines Morton-based 1D indexing with a structured 2D Morton mapping table to arrange Gaussian attributes as block-wise feature maps.

    Source: §1 · p. 3

  • Results

    The approach achieves better rate-distortion performance and lower runtime than PLAS and conventional Morton-based sorting.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The structured representation provides a standards-compatible solution for 3DGS compression using conventional block-based video codecs.

    Source: §4 · pp. 9–10

    Benefits vary by scene: gymnast and flowerdance show noticeable BD-rate losses, likely due to complex motion and highly non-uniform appearance distributions.

    Source: §3.2.2 · pp. 7–8

Abstract

from arXiv · show

3D Gaussian Splatting (3DGS) enables high fidelity novel view synthesis but suffers from excessive storage and bandwidth requirements due to its unstructured representation. To address this, a projection based video coding framework has emerged as a leading approach, supported by MPEG's ongoing standardization, where 3DGS attributes are converted into 2D maps to take advantage of efficient compression using established video codecs such as HEVC and VVC. However, the effectiveness of this approach depends heavily on the spatial coherence of the projected video, which current sorting strategies such as PLAS and Morton ordering fail to preserve adequately, either incurring high computational cost or achieving limited correlation retention. To overcome these limitations, we propose a dual phase Morton spatial sorting algorithm that improves both coding efficiency and processing speed. In the first phase, Morton based 1D indexing is applied to high dimensional attributes to enhance spatial locality. The second phase further refines layout continuity through a structured 2D Morton mapping table that enforces spatial adjacency. This hierarchical strategy generates highly regular, block wise feature maps with strong local correlation, making them well suited for compression via conventional block based coding tools. Experimental results show that our method significantly outperforms existing approaches in both compression performance and runtime efficiency, providing a practical and standard compatible solution for 3DGS data coding.

1 Introduction

Unstructured 3DGS primitives create substantial storage and transmission overhead, while existing sorting approaches trade layout coherence against computation. The paper proposes dual-phase Morton sorting to create coding-friendly 2D maps and reports better rate-distortion performance with lower runtime than existing sorting approaches.

  • Video-based coding converts Gaussian attributes into 2D maps for HEVC or VVC, making spatial coherence and block regularity important to coding efficiency.Source: §1 · p. 2
  • PLAS produces coherent layouts but is computationally costly, whereas Morton ordering is fast but can yield weak 2D neighborhood consistency after row-major reshaping.This leaves a trade-off between layout coherence and sorting efficiency for video coding.Source: §1 · p. 2
  • The proposed framework first orders splats spatially, then maps them into a 2D layout with stronger neighborhood continuity and applies the same ordering across attributes.The design targets improved spatial regularity, local correlation, block consistency, and cross-channel alignment.Source: §1 · p. 2
  • The dual-phase algorithm combines 1D indexing and 2D mapping to create block-wise feature maps while maintaining low computational complexity.Source: §1 · p. 3
  • A structured 2D Morton mapping table preserves pixel-domain adjacency for integration with block-based codecs and MPEG-oriented workflows.Source: §1 · p. 3
  • The method achieves better rate-distortion performance and lower runtime than PLAS and conventional Morton-based sorting.Source: §1 · p. 3

2 Method

The method reorganizes Gaussian splats into coding-friendly 2D feature maps by applying spatial locality in both a 1D ordering and a 2D layout. A shared permutation keeps attributes aligned for video coding.

2.1 Problem Formulation

  • The objective is to place spatially related Gaussian primitives near one another in structured 2D maps, while applying the same permutation across attributes.The design requirements call for a spatially meaningful unified permutation, locality in both 1D and 2D, and lightweight processing for large-scale primitives.Source: §2.1 · pp. 3–4

2.2 Overview of the Proposed Dual-Phase Morton Sorting

  • Two consecutive stages sort splats by their 3D mean positions, then map the ordered sequence onto a 2D grid before applying the same permutation to other attributes.The resulting feature maps are used for subsequent video coding.Source: §2.2 · p. 4

2.3 Phase I: Morton-Based 1D Spatial Sorting

  • Morton sorting by Gaussian mean position yields a permutation driven by each primitive’s spatial center, producing a 1D ordering where neighboring indices tend to correspond to nearby 3D locations.The permutation is consistently applied to all remaining Gaussian attributes, preserving their cross-attribute correspondence under the same geometry-aware order.Source: §2.3 · p. 5

2.4 Phase II: Structured 2D Morton Mapping

  • A 2D Morton mapping assigns consecutive indices to neighboring pixels, avoiding row-boundary discontinuities that can arise with row-major reshaping.The mapping table is constructed once and reused across frames; the combined layout has more regular block structure suited to conventional block-based codecs.Source: §2.4 · pp. 5–6

3 Experimental Results

Experiments on MPEG 1F and NF sequences compare coding quality and sorting efficiency against PLAS and Morton. The proposed method improves rate-distortion performance on average and sorts much faster than PLAS, while its benefits vary by scene.

3.1 Experimental Settings

  • Experiments use MPEG common-testing-condition 1F static single-frame and NF dynamic multi-frame sequences on GSCodec Studio, evaluating PSNR, SSIM, bitrate, and sorting time.The platform uses an NVIDIA Tesla V100 SXM2 32GB GPU and an Intel Xeon Platinum 8163 CPU with 12 cores.Source: §3.1 · p. 7

3.2.1 Rate-Distortion Performance

  • Across test sequences in GSCodec Studio, the proposed sorting method generally achieves better rate-distortion performance than PLAS and Morton.The comparison is reported across different test sequences; the result is not uniform for every sequence.Source: §3.2.1 · p. 7

3.2.2 BD-Rate Savings

  • The method averages BD-rate gains of 1.29%, 1.69%, and 3.19% over Morton and 1.15%, 0.88%, and 0.45% over PLAS for RGB-PSNR, YUV-PSNR, and YUV-SSIM, respectively.Some sequences, including gymnast and flowerdance, nevertheless show noticeable BD-rate losses, likely because complex motion and non-uniform appearance reduce alignment with the underlying compressibility structure.Source: §3.2.2 · pp. 7–8, Table 1 · p. 8

3.2.3 Sorting Efficiency Comparisons

  • Average sorting time is 144.63 ms for the proposed method, versus 18,698.91 ms for PLAS and 24.51 ms for Morton.The increase over Morton reflects performing Morton sorting twice to trade some speed for sorting quality.Source: §3.2.3 · p. 8, Table 2 · p. 9

3.2.4 Subjective Comparisons for Different Reorganized Attribute Videos

  • The proposed sorting produces more compact, locally clustered attribute videos than PLAS and Morton, with layouts better aligned to block-based video coding.The comparison is presented as a subjective evaluation of reorganized attribute videos.Source: §3.2.4 · p. 9

4 Conclusion

The paper presents dual-phase Morton sorting to organize Gaussian attributes into block-wise feature maps with improved spatial coherence and local correlation. It reports improved rate-distortion performance and reduced runtime versus existing sorting strategies, positioning the method as a practical, scalable, standards-compliant approach to 3DGS coding.

4 Conclusion

  • Dual-phase Morton sorting combines 1D indexing and a structured 2D mapping table to produce block-wise feature maps with improved spatial coherence and local correlation.The resulting representation is suited to conventional block-based video codecs.Source: §4 · p. 9
  • The method achieves improved rate-distortion performance and reduced runtime compared with existing sorting strategies.The paper describes this as a favorable trade-off between coding performance and computational complexity.Source: §4 · p. 9
  • The authors present dual-phase Morton sorting as a practical, scalable solution for standards-compliant representation and coding of Gaussian-based scene data.The conclusion describes it as a promising direction for 3DGS compression.Source: §4 · pp. 9–10
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