Flexible Compression Scheme for 3DGS

• The paper introduces the SALVQ framework, a scene-adaptive lattice vector quantization method that overcomes USQ limitations by exploiting inter-feature correlations.
• It employs an SVD-parametrized lattice basis that adapts per scene, enabling variable-rate encoding from a single model without retraining.
• The approach demonstrates significant BD-rate reductions across benchmarks, enhancing visual quality and compression efficiency in 3DGS applications.

A flexible compression scheme for 3D Gaussian Splatting (3DGS) addresses the critical challenge of compressing vast, high-dimensional data arising from photorealistic, real-time 3D scene representations. The Scene-Adaptive Lattice Vector Quantization (SALVQ) framework exemplifies a state-of-the-art solution that embeds rate–distortion (R–D) efficiency, adaptability, and seamless integration into existing neural 3DGS compression pipelines, advancing prior anchor-based single-rate codecs by orders of magnitude in both flexibility and coding efficacy (Xu et al., 16 Sep 2025).

1. Motivation and Limitations of Uniform Scalar Quantization

Historically, anchor-based 3DGS compressors such as HAC, HAC++, and ContextGS have relied on uniform scalar quantization (USQ) applied channel-wise to latent anchor features. USQ maps each latent component $f^{(i)}$ to discrete bins using a global step size $q_s$: $$Q_{\mathrm{USQ}}(f^{(i)}) = q_s \left\lfloor \frac{f^{(i)}}{q_s} \right\rceil$$ While straightforward, USQ corresponds to axis-aligned hypercube cells in feature space and neglects inter-component dependencies. This approach results in inefficient packing of high-dimensional anchor spaces and increased rate for a given distortion (Xu et al., 16 Sep 2025).

USQ’s inability to efficiently cover the latent space limits its rate–distortion trade-off, motivating the search for structured, correlation-exploiting quantization schemes with minimal system-side complexity.

2. Scene-Adaptive Lattice Vector Quantization: Algorithm and Mathematical Formulation

SALVQ replaces USQ with a learnable Lattice Vector Quantizer (LVQ) that operates on the full anchor latent vector $\mathbf{f}\in\mathbb{R}^n$. A lattice $\Lambda\subset\mathbb{R}^n$ is defined by a basis $\mathbf{B}\in\mathbb{R}^{n\times n}$: $$\Lambda = \{ \mathbf{z} = \mathbf{B} \mathbf{u} : \mathbf{u}\in\mathbb{Z}^n \}$$ Quantization centralizes features as $\mathbf{f}_c = \mathbf{f} - \boldsymbol\mu$ (where $\boldsymbol\mu$ is a learnable or spatially predicted mean), and projects to the lattice via: $$Q_{\mathrm{LVQ}}(\mathbf{f}_c) = \mathbf{B} \left\lfloor \mathbf{B}^{-1} \mathbf{f}_c \right\rceil$$ This quantization is efficiently implemented by Babai’s Rounding Technique for computational tractability and negligible additional encoding/decoding time.

The R–D-optimized training loss is: $$\mathcal{L} = \mathbb{E}[ \| \mathbf{f} - \widehat{\mathbf{f}} \|^2 ] + \lambda\mathbb{E}[ -\log p(\widehat{\mathbf{f}}_t) ] + \lambda_{\text{reg}} \mathcal{L}_{\text{reg}}$$ where $\widehat{\mathbf{f}}_t$ are quantized codes, $p$ denotes the entropy model, and $\lambda$ governs the rate–distortion trade-off.

3. Scene-Adaptivity via SVD-Parametrized Lattice Learning

Critical to SALVQ’s flexibility is the scene-specific optimization of the lattice basis. Rather than using a fixed lattice (e.g., $E_8$), the basis $\mathbf{B}$ is factorized per scene as: $$\mathbf{B} = \mathbf{U}\, \mathbf{\Sigma}\, \mathbf{V}^\top$$ Here, $\mathbf{U}, \mathbf{V}$ are orthogonal, and $\mathbf{\Sigma}$ is diagonal with positive entries, ensuring invertibility and allowing the lattice to adapt its shape—ranging from rotated hypercubes to arbitrary warps—optimally filling the support of anchor features for the current scene. All parameters $$(\mathbf{U},\mathbf{\Sigma},\mathbf{V}, \boldsymbol\mu)$$ are trained jointly with the entropy model in the end-to-end R–D loss.

4. Variable-Rate Compression with Basis Scaling

A principal feature of SALVQ is variable-rate encoding from a single trained model. Given $M$ target bit-rates, for each target $i$, a gain $g_i$ scales the lattice density: the quantization step becomes $g_i q_s$, i.e.,

$$Q_{i}(\mathbf{f}_c) = \mathbf{B} \left\lfloor \frac{1}{g_i q_s} \mathbf{B}^{-1} \mathbf{f}_c \right\rceil \times g_i q_s$$

Each gain has a corresponding Lagrange multiplier $\lambda_i$ in the R–D loss. At inference, selecting any $g_i$ produces the corresponding bit-rate—eliminating the need to retrain separate models for each operating point and reducing both computational and memory overhead.

The practical rate range per gain vector is moderate ($\sim$1.5$\times$), and for finer granularity, scale tables or entropy-model interpolation can be combined.

5. System Integration, Overhead, and Implementation

SALVQ is designed as a drop-in USQ replacement for the anchor latent features in nearly all recent 3DGS neural codecs (including HAC, HAC++, ContextGS):

• No changes are required in the context model, rendering MLPs, or the rasterization pipeline.
• Memory cost is negligible: for $n=50$, the learned basis and mean require $\sim$0.02 MB.
• Encoding/decoding runtime is effectively unchanged relative to USQ; a measured $\sim$10% increase in training time is subsumed by the overall training duration.
• All compression/entropy coding steps for quantized values remain identical to previous practice (Gaussian+uniform noise model).

Implementation proceeds by predicting or loading the mean $\boldsymbol\mu$, centering features, applying the lattice transform, rounding, and entropy coding the resulting integer coordinates.

6. Quantitative Performance and Visual Effects

SALVQ achieves significant improvements on standard 3DGS benchmarks:

• Average BD-rate reduction (vs. USQ, at fixed reconstruction quality) is $-13.48\%$ (HAC), $-4.55\%$ (HAC++), and $-5.71\%$ (ContextGS); fixed-lattice $E_8$ LVQ achieves only $-2\%$ to $-8\%$ (Xu et al., 16 Sep 2025).
• Maximal compression ratios: up to $131\times$ over uncompressed 3DGS and $23.7\times$ over Scaffold-GS at $\text{PSNR} \geq 27.6$ dB with HAC++.
• Visual improvements: reduced blur/flicker, improved preservation of high-frequency detail, and elimination of floater artifacts.
• Variable-bit-rate operation: SALVQ-VBR models often match or outperform retrained single-rate USQ models, while USQ-VBR models incur $1$–$15\%$ BD-rate loss across datasets. For example, in variable-rate mode, BD-rate improvements over USQ-VBR are $-6.44\%$ (Mip-NeRF360), $-13.83\%$ (Tanks), $-16.89\%$ (DeepBlending).
• Progressive coding (e.g., in PCGS context): $-3.47\%$, $-20.57\%$, $-7.01\%$ BD-rate improvement across three representative datasets.

7. Practical Recommendations, Limitations, and Future Extensions

SALVQ is optimal in contexts where anchor latent features are high-dimensional and available context models are of limited capacity—i.e., where inter-component correlation is substantial and cannot be exploited by context alone. The computational overhead is insignificant; the added training time is small compared to overall scene training. For broader variable-rate adaptation, lightweight auxiliary scaling or interpolation can be employed, and the fundamental approach is applicable to other attribute groups (e.g., offsets, scales) or in multi-dimensional entropy contexts.

Future directions include extending scene-adaptive LVQ to compress additional attribute groups beyond the anchor features, exploring broader families of learnable lattice structures, and integrating SALVQ with advanced entropy coding models to further push the limit of R–D efficiency for real-time, cost-effective 3DGS applications (Xu et al., 16 Sep 2025).

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Key Reference:

"Improving 3D Gaussian Splatting Compression by Scene-Adaptive Lattice Vector Quantization" (Xu et al., 16 Sep 2025)