Multi-scale surface reconstruction based on a curvature-adaptive signed distance field

This paper presents a multi-scale method for surface reconstruction from oriented point sets. The method is based on building and fitting an adaptive signed distance field. The adaptive signed distance field is built on an adaptive octree grid whose local grid interval is determined by the principal curvatures estimated on the input point set. In this way, scale-varying geometric details can be faithfully represented by the adaptive signed distance field. Next, a set of multi-scale B-spline basis functions are adopted to define the implicit function that globally and optimally fits the adaptive signed distance field. Because these basis functions are selected carefully, the fitting problem is reduced to a well-conditioned sparse linear system. As a result, a CI-continuous field function is generated. The fitted field function is a good approximation of the signed distance field, and thus, its nonzero level sets can also approximate the offsets of the underlying surface well. Experimental results show that the proposed method can faithfully reconstruct crack-free adaptive triangular meshes from oriented point sets. Meanwhile, it is efficient in both running time and memory. (C) 2017 Elsevier Ltd. All rights reserved.