Deformable Beta Splatting (2501.18630v2)

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/.

• The paper introduces DBS by replacing Gaussian kernels with adaptive Beta Kernels and Spherical Beta functions to boost rendering quality and efficiency.
• It employs a kernel-agnostic MCMC densification strategy that optimizes beta parameters and opacity for precise geometry and color representation.
• The method outperforms existing approaches by achieving a 1.5x speed increase and 45% fewer parameters while maintaining high visual fidelity.

A Review of "Deformable Beta Splatting"

This paper presents "Deformable Beta Splatting" (DBS), a new approach for enhancing real-time radiance field rendering, specifically focusing on both geometry and color representation. The authors argue that traditional 3D Gaussian Splatting (3DGS), while efficient, is hampered by its reliance on Gaussian kernels and low-order Spherical Harmonics (SH), which limit its ability to encapsulate complex geometries and diverse color details. To address these limitations, DBS introduces the use of deformable Beta Kernels and Spherical Beta functions, alongside a redefined densification strategy using Markov chain Monte Carlo (MCMC) methods.

The replacement of Gaussian kernels with Beta Kernels is a central innovation of this work. Beta Kernels are adaptable, possessing bounded support and capable of high-frequency geometric detail capture. They offer a contrast to the typically smooth and blurred outputs produced by Gaussian Kernels due to their long-tailed nature. The Beta Kernel’s ability to provide bounded support allows for precise control over the geometric representation, enabling it to more effectively delineate flat surfaces, sharp edges, and subtle transitions in texture.

The paper extends the Beta Kernel approach to the domain of color encoding through the Spherical Beta (SB) function. This function effectively models view-dependent color variations by disentangling specular and diffuse reflection components. With only 31% of the parameters required by traditional methods employing SH of degree 3, Spherical Beta functions are more computationally efficient and facilitate superior representation of specular lighting effects.

Experimentally, DBS demonstrates notable improvements compared to the existing state-of-the-art methods in radiance field rendering such as Zip-NeRF and 3DGS-MCMC. The authors report a 1.5x increase in rendering speed and the use of just 45% of the parameters required by previous methods, while still achieving high visual fidelity across various benchmarks. Notably, DBS is the first splatting-based method to surpass Neural Radiance Fields (NeRF) in terms of rendering quality and efficiency.

The methodology also incorporates a Kernel-Agnostic MCMC approach. By mathematically proving that regularizing opacity alone can maintain distribution-preserved densification, the authors simplify the optimization process, making it independent of specific kernel properties. This adaptation allows DBS to overcome challenges related to the deformable nature of Beta Kernels, optimizing both beta parameters and opacity to stabilize the learning process.

The implications of this research extend to several practical applications, including virtual reality, dynamic scene representation, and cinematic production. A key strength of DBS is its ability to efficiently manage computational resources, making it highly applicable for real-time scenarios where both speed and quality are crucial.

Future developments might explore enhancements in modeling mirror-like reflections and further reducing artifacts introduced by depth approximation errors during kernel splatting. Continued exploration should focus on refining the kernel parameters to manage scenes with highly complex or anisotropic specular highlights.

In conclusion, Deformable Beta Splatting (DBS) represents a significant advancement in the field of real-time radiance field rendering. Through the introduction of deformable Beta Kernels, Spherical Beta functions, and kernel-agnostic optimization strategies, this work pushes the boundaries of efficiency and quality in 3D scene representation, offering promising avenues for both theoretical exploration and practical application in fields reliant on high-quality visualization.