Approximating Signed Distance Fields With Sparse Ellipsoidal Radial Basis Function Networks: A Dynamic Multi-Objective Optimization Strategy

TL;DR

This paper introduces a novel method for approximating signed distance functions of implicit surfaces using a sparse set of ellipsoidal radial basis functions, optimized through a dynamic multi-objective strategy for efficient and accurate 3D shape representation.

Contribution

It presents a new learning approach that uses a multi-objective optimization to sparsely approximate SDFs with ERBFs, improving compactness and accuracy over existing methods.

Findings

Achieves significantly fewer parameters for SDF representation.

Demonstrates improved accuracy and robustness on benchmark datasets.

Enhances computational efficiency with CUDA acceleration and hierarchical refinement.

Abstract

Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for approximating precomputed SDF fields of implicit surfaces by a relatively small number of ellipsoidal radial basis functions (ERBFs). The SDF values could be computed from various sources, including point clouds, triangle meshes, analytical expressions, pretrained neural networks, etc. Given SDF values on spatial grid points, our method approximates the SDF using as few ERBFs as possible, achieving a compact representation while preserving the geometric shape of the corresponding implicit surface. To balance sparsity and approximation precision, we introduce a dynamic multi-objective optimization strategy, which adaptively incorporates regularization to enforce sparsity and jointly optimizes the weights, centers, shapes, and orientations of the ERBFs. For computational efficiency, a nearest-neighbor-based data structure restricts computations to points near each kernel center, and CUDA-based parallelism further accelerates the optimization. Furthermore, a hierarchical refinement strategy based on SDF spatial grid points progressively incorporates coarse-to-fine samples for parameter initialization and optimization, improving convergence and training efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our method can represent SDF fields with significantly fewer parameters than existing sparse implicit representation approaches, achieving better accuracy, robustness, and computational efficiency. The corresponding executable program is publicly available at https://github.com/lianbobo/SE-RBFNet.git