EntropyGS: 3D Gaussian Compression

• EntropyGS is a factorized, statistically-parameterized coding system designed to compress 3D Gaussian Splatting models by leveraging detailed statistical characterizations of each attribute.
• It employs adaptive quantization and distribution parameter estimation (e.g., Laplace for SHAC, GMM for rotation/scaling) to achieve high compression ratios with minimal quality loss.
• The method achieves approximately 30× data rate reduction with fast encode/decode times, making it practical for real-time novel view synthesis in large-scale 3DGS pipelines.

EntropyGS is a factorized, statistically parameterized entropy coding system for compressing 3D Gaussian Splatting (3DGS) models used in real-time novel view synthesis. It is designed to reduce storage and transmission costs for large 3DGS representations by leveraging specific statistical insights into the distributions and correlations of the attributes constituting each Gaussian primitive. The method employs adaptive quantization tailored to the perceptual and statistical properties of each attribute, combines this with distribution parameter estimation, and applies entropy coding independently to each channel. EntropyGS achieves roughly 30-fold data rate reduction over original 3DGS models while maintaining nearly lossless rendering quality and fast (sub-20s on CPU, sub-4s on GPU) encode/decode performance (Huang et al., 13 Aug 2025).

1. Structure and Storage Challenges of 3D Gaussian Splatting

3DGS represents a scene as a collection of Gaussians, each parameterized by geometric position, rotation, scale, opacity, and spherical harmonics for view-dependent color. This results in millions of parameters for complex scenes. Because 3DGS separates the Gaussian creation (training) and view rendering stages—often running on different devices or at different times—storage and bandwidth quickly become bottlenecks. Addressing compression specifically for the attributes of 3DGS is critical due to their volume and weak locality properties.

2. Statistical Characterization of Gaussian Attribute Distributions

A comprehensive analysis of attribute statistics underpins the EntropyGS encoding pipeline:

• Partitioning of Attributes: Attributes are partitioned into geometry, rotation, scaling, opacity, spherical harmonics DC (SHDC), and spherical harmonics AC (SHAC).
• Correlation Analysis: Using Normalized Mutual Information (NMI), intra-group and inter-group correlations are quantified. SHAC channels are shown to be nearly uncorrelated both internally and with other groups, while most other groups show weak or moderate correlations.
• Distribution Fitting:
  • Rotation, scaling, opacity: Well-approximated by Gaussian Mixture Models (up to four components), or in some cases a single Gaussian.
  • SHDC: Exhibits multi-modal/peaked distributions not conforming to standard statistical models.
  • SHAC: Precisely follows a Laplace distribution, with negligible inter-attribute correlation apart from effects inherited from the color space.
• Distribution Verification: The computed empirical entropy from data histograms matches well with entropy calculated from Laplace or GMM fits, confirming the appropriateness of these parametric models.

3. Design and Implementation of the EntropyGS Encoding Pipeline

EntropyGS combines the following steps for optimal compression:

• Factorization: Each attribute channel is encoded independently, justified by the low degree of inter-channel correlation—particularly among SHAC channels.
• Parameter Estimation: For each channel group, probability distribution parameters are determined:
  • SHAC Laplace parameters are set as the channel median (location) and mean absolute deviation (scale):

  $$\mu = \mathrm{median}(x),\quad b = \frac{1}{N}\sum_{i=1}^{N} |x_i - \mu|$$ - GMM or single-Gaussian parameters for rotation, scaling, and opacity are estimated via MLE or EM.

• Adaptive Quantization:

  • Quantization granularity is adjusted based on attribute sensitivity. Geometry channels, being visually sensitive, are finely quantized; SHAC, consuming the largest memory but less perceptually sensitive, uses coarser steps.
  • For most channels (except SHAC), min–max uniform quantization is performed:

  $$q(x) = \mathrm{round} \left( \frac{(x - v_{min}) \cdot (L - 1)}{v_{max} - v_{min}} \right)$$

  where $L=2^Q$ is the number of quantization levels for $Q$ bits.

• Entropy Modeling and Coding:

  • The fitted distribution parameters are then used to calculate the probability mass function (PMF) for the quantized bins in each channel.
  • Lossless arithmetic coding is employed using these PMFs.
• Preparation Stage (Optional):
  • Gaussian pruning (importance-based and geometry-based) and post-pruning optimization remove non-essential primitives before encoding.
  • For geometry and SHDC attributes, standard point-cloud codecs (e.g., MPEG G-PCC) can be applied, further integrating with established pipelines.

4. Quantitative Compression and Quality Evaluation

EntropyGS achieves substantial compression without perceptible loss in render quality:

Model	Compression Ratio	PSNR Loss (Δ)	GPU Encode (s)	GPU Decode (s)
EntropyGS	≈30×	–0.04 dB	3.6	0.2

• Rate–Distortion: ΔPSNR is nearly negligible compared to the uncompressed 3DGS (sometimes even improved through pruning/post-optimization).
• Comparison to Other Methods: At equivalent quality, EntropyGS achieves higher compression ratios and similar or lower render-time memory footprints than recent state-of-the-art baselines (LightGaussian, C3DGS, MesonGS, CompactGS).
• Speed: Encoding and decoding times are fast, with GPU-based workflows suitable for real-time applications.

5. Mathematical Characterization of Factorized Coding

The effectiveness of EntropyGS is tied to the low normalized mutual information (NMI) among attribute channels, which enables channelwise factorization:

$$\text{NMI}(X, Y) = \frac{2 \cdot I(X; Y)}{H(X)+H(Y)} , \quad I(X; Y) = \sum_{x,y} p(x,y) \log \frac{p(x,y)}{p(x)p(y)}$$

The entropy $H(X)$ for any attribute $X$ is estimated from its fitted parametric PMF.

SHAC channels, following Laplace distributions, are encoded using their analytic PMF; Gaussian or GMM-based attributes use the respective standard PMFs. Adaptivity in quantization and encoding is crucial for high rate savings on high-variance SHAC channels.

6. Practical Implications and Future Directions

EntropyGS addresses a central bottleneck in scalable, distributed 3DGS pipelines where real-time rendering and data transmission requirements compete with memory and bandwidth constraints. The statistical-parameterized, factorized architecture is amenable to hardware acceleration and could further benefit from context-based entropy models should future research suggest non-negligible higher-order correlations in certain scene types. The method’s learning-free nature simplifies implementation and integration with existing 3DGS backends.

A plausible implication is that as 3DGS scales to larger, dynamic, or more diverse real-world scenes, channelwise parametric adaptation and pruning strategies as pioneered in EntropyGS will remain essential for maintaining both visual quality and storage efficiency.

7. Summary Table of Attribute Modeling

Attribute Group	Statistical Model	Quantization Strategy
Geometry	Data-driven	Fine (min–max)
Rotation, Scaling	Gaussian Mixture Model	Adaptive
Opacity	Gaussian Mixture Model	Adaptive
SHDC	Nonparametric/multimodal	Moderate
SHAC (AC)	Laplace	Coarse/Laplace-based

This table encapsulates the attribute-specific handling that enables EntropyGS's high compression ratios and coding efficiency.

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For detailed algorithmic parameters, PMF sampling, and integration points with external codecs, refer to the implementation specifics and supplementary experiments in (Huang et al., 13 Aug 2025).