Sparse Ellipsoidal Radial Basis Function Network for Point Cloud Surface Representation

Point cloud surface representation is a fundamental problem in computer graphics and vision. This paper presents a machine learning approach for approximating the signed distance function (SDF) of a point cloud using sparse ellipsoidal radial basis function networks, enabling a compact and accurate surface representation. Given the SDF values defined on the grid points constructed from the point cloud, our method approximates the SDF accurately with as few ellipsoidal radial basis functions (ERBFs) as possible, i.e., represent the SDF of a point cloud by sparse ERBFs. To balance sparsity and approximation precision, a dynamic multi-objective optimization strategy is introduced, which adaptively adds the regularization terms and jointly optimizes the weights, centers, shapes, and orientations of ERBFs. To improve computational efficiency, a nearest-neighbor-based data structure is employed, restricting function calculations to points near each Gaussian kernel center. The computations for each kernel are further parallelized on CUDA, which significantly improves the optimization speed. Additionally, a hierarchical octree-based refinement strategy is designed for training. Specifically, the initialization and optimization of network parameters are conducted using coarse grid points in the octree lattice structure. Subsequently, fine lattice points are progressively incorporated to accelerate model convergence and enhance training efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our method outperforms previous sparse representation approaches in terms of accuracy, robustness, and computational efficiency. The corresponding code is publicly available at https://github.com/lianbobo/SE-RBFNet.git.