Neural implicit functions including signed distance functions (SDFs) and unsigned distance functions (UDFs) have shown powerful ability in fitting the shape geometry. However, inferring continuous distance fields from discrete unoriented point clouds still remains a challenge. The neural network typically fits the shape with a rough surface and omits fine-grained geometric details such as shape edges and corners. In this paper, we propose a novel non-linear implicit filter to smooth the implicit field while preserving high-frequency geometry details. Our novelty lies in that we can filter the surface (zero level set) by the neighbor input points with gradients of the signed distance field. By moving the input raw point clouds along the gradient, our proposed implicit filtering can be extended to non-zero level sets to keep the promise consistency between different level sets, which consequently results in a better regularization of the zero level set. Since the unsigned distance function is non-differentiable at the zero level set and lacks a stable gradient field, we further propose a gradient immutable training schema to migrate the filter to the unsigned distance function learned from point clouds. By leveraging the UDF training schema, we also improve sparse-view reconstruction results. We conduct comprehensive experiments in surface reconstruction from objects, complex scene point clouds, and multi-view images, and we further extend to the point normal estimation and point cloud upsampling tasks. The numerical and visual comparisons demonstrate our improvements over the stateof- the-art methods under the widely used benchmarks.
Li et al. (Wed,) studied this question.