Deformable Radial Kernel Splatting

TL;DR

Deformable Radial Kernel Splatting (DRK) introduces a flexible, learnable planar primitive that generalizes Gaussian splatting by employing radial bases with lengths $s_k$ and angles $\theta_k$, combined via an adaptive $L1$/$L2$ blending weight $\eta$ and a boundary-sharpening parameter $\tau$. The rendering pipeline integrates ray-primitive intersections on a tangent plane, along with rasterization optimizations such as low-pass filtering, polygonal kernel culling, and cache-based sorting to enable real-time performance. Across DiverseScenes and Mip-NeRF360, DRK achieves state-of-the-art rendering quality with significantly fewer primitives than Gaussian baselines, and supports seamless mesh-to-DRK conversion for asset integration. While DRK shows some vulnerability to camera noise, its expressive deformation capabilities and efficient rendering make it a strong candidate for rapid, high-fidelity 3D scene representation in VR/AR and related applications.

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.

Figures (15)

• Figure 1: Gaussian Splatting vs. Our Deformable Radial Kernel (DRK) Splatting: Gaussian splatting requires thousands of Gaussians to approximate detailed textures and shapes. In contrast, our kernel efficiently fits the target pattern with just 30 primitives, achieving superior results.
• Figure 2: Comparison of 3D-GS versus a single DRK: DRK achieves superior geometric fidelity with just one primitive compared to multiple Gaussians. We visualize the contours of 3D-GS and DRK to better illustrate primitive count, scale, and position.
• Figure 3: Illustration of general planar kernel splatting: UV coordinates of ray-plane intersections are mapped to density values via a kernel function that determines the primitive's shape.
• Figure 4: DRK defines a deformable shape using radial basis functions characterized by lengths $s_k$ and polar angles $\theta_k$, with parameters $\eta$ and $\tau$ governing the shape's curvature and sharpness respectively.
• Figure 5: Sharpening function illustration.