Deformable Beta Splatting

TL;DR

Deformable Beta Splatting (DBS) tackles the limitations of Gaussian-based geometry and low-order color encoding in real-time radiance-field rendering. By introducing a bounded, deformable Beta Kernel for geometry and a Spherical Beta color model for view-dependent lighting, along with Kernel-Agnostic MCMC optimization, DBS achieves higher fidelity with significantly fewer parameters and faster rendering than prior methods. The approach demonstrates state-of-the-art visual quality on diverse datasets, enabling efficient, interactive 3D scene reconstruction and rendering. The work also enables geometric and lighting decomposition post-training, offering practical tools for analysis and editing while maintaining real-time performance.

Abstract

3D Gaussian Splatting (3DGS) has advanced radiance field reconstruction by enabling real-time rendering. However, its reliance on Gaussian kernels for geometry and low-order Spherical Harmonics (SH) for color encoding limits its ability to capture complex geometries and diverse colors. We introduce Deformable Beta Splatting (DBS), a deformable and compact approach that enhances both geometry and color representation. DBS replaces Gaussian kernels with deformable Beta Kernels, which offer bounded support and adaptive frequency control to capture fine geometric details with higher fidelity while achieving better memory efficiency. In addition, we extended the Beta Kernel to color encoding, which facilitates improved representation of diffuse and specular components, yielding superior results compared to SH-based methods. Furthermore, Unlike prior densification techniques that depend on Gaussian properties, we mathematically prove that adjusting regularized opacity alone ensures distribution-preserved Markov chain Monte Carlo (MCMC), independent of the splatting kernel type. Experimental results demonstrate that DBS achieves state-of-the-art visual quality while utilizing only 45% of the parameters and rendering 1.5x faster than 3DGS-MCMC, highlighting the superior performance of DBS for real-time radiance field rendering. Interactive demonstrations and source code are available on our project website: https://rongliu-leo.github.io/beta-splatting/.

Figures (7)

• Figure 1: Unlike the fixed Gaussian Kernel, Deformable Beta Kernel adapts its shape to capture fine geometric and texture details. This figure shows how the kernel varies by different $b$ values as in \ref{['eq:beta']}. Negative $b$ generates flatter surface but sharper cutoffs for learning solid support and sharp geometry, while positive $b$ generates sharper peaks for learning high frequency details. When $b=0$, the beta kernel is almost identical to Gaussian (domain scaled by $3\sigma$)
• Figure 2: Learnable Spherical Beta can effectively capture specular highlights with varying sharpness. Smaller $b$ values result in broader reflections, while higher $b$ values correspond to sharper specular highlights.
• Figure 3: Geometry Decomposition: our designed Beta Kernel provides the capability to decompose scene geometry into fundamental structures and intricate details, such as high-frequency textures and fine surface variations.
• Figure 4: Qualitative Comparison: Leveraging our Deformable Beta Kernel, Spherical Beta color encoding, and Kernel-Agnostic MCMC optimization process, the Deformable Beta Splatting framework qualitatively outperforms the implicit SOTA method (Zip-NeRF) and the explicit SOTA method (3DGS-MCMC).
• Figure 5: Light Decomposition: our Spherical Beta color encoding can effectively decompose diffuse and specular components compared to 3DGS-based approaches using low-order Spherical Harmonics, as illustrated in this figure.