DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions

2025-01-21

AI Summary

The reliance on exponential-family kernels (e.g., Gaussian) in 3D Gaussian Splatting imposes computational inefficiency and high memory overhead. Method: We propose the Decay-type Anisotropic Radial Basis Function (DARBF)—a differentiable, anisotropic, analytically integrable, non-exponential-family reconstruction kernel. Constructed via Mahalanobis distance, DARBF is non-negative and admits closed-form projection integrals—the first such non-exponential-family kernel systematically integrated into Splatting. It seamlessly embeds into optimization-driven 3D Gaussian Splatting and enables end-to-end training via differentiable rasterization. Results: Experiments show a 34% faster training speed and 15% reduced GPU memory consumption, while preserving PSNR, SSIM, and LPIPS—matching Gaussian-kernel rendering quality across diverse scenes. DARBF achieves faster convergence and lower memory footprint without sacrificing visual fidelity. Code will be open-sourced.

Technology Category

• Machine Learning: Kernel Methods
• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integrability in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function's closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 15% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

Problem

• 3D Reconstruction
• Image Processing
• DARBFs Optimization

Innovation

• DARB-溅射技术
• DARBFs
• 3D重建