Deformable Radial Kernel Splatting

2024-12-16

arXiv.org

AI Summary

Gaussian splatting suffers from radial symmetry, making it inefficient for representing complex geometries—requiring thousands of ellipsoids to approximate fine details, thereby compromising model compactness and edge fidelity. To address this, we propose Deformable Radial Kernels (DRKs), which break radial symmetry via learnable angular modulation and scale adaptation, enabling explicit control over edge sharpness and boundary curvature. Furthermore, we introduce the first analytical ray-primitive intersection solver tailored for planar primitives, coupled with a depth-aware kernel culling strategy. Our method achieves significant PSNR/SSIM improvements over state-of-the-art methods—including Gaussian Splatting—on NeRF synthetic datasets, while reducing primitive count by an order of magnitude. It simultaneously supports real-time rasterization and high-fidelity rendering, unifying gains in geometric representation efficiency and visual quality.

Technology Category

• Machine Learning: Kernel Methods
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search

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
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. iven DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count.

Problem

• Extends Gaussian splatting for complex 3D shapes
• Enables precise control over edge sharpness
• Improves rendering efficiency and quality

Innovation

• Deformable Radial Kernel for flexible 3D representation
• Learnable radial bases with adjustable angles and scales
• Efficient ray-primitive intersection and kernel culling