Phase-field guided surface reconstruction based on implicit hierarchical B-splines

Constructing smooth surface representations from point clouds is a fundamental problem in geometric modeling and computer graphics, and a wealthy of literature has focused on this problem. Among the many approaches, implicit surface reconstruction has been a central topic in the past two decades due to its ability to represent objects with complicated geometry and topology. Recently, the problem of reducing the storage requirement for implicit representations has attracted much attention. In this paper, we propose a phase-field guided implicit surface reconstruction method to tackle this problem. The implicit function of our method behaves like the phase-field of a binary system, in which it takes distinct values (i.e., −1 and 1) in each of the phases with a smooth transition between them. Given an unorganized point cloud, we present a method to construct a phase-filed function represented by a hierarchical B-spline whose zero level set approximates the point cloud as much as possible. Unlike previous approaches, our mathematical model avoids the use of the normal information of the point cloud. Furthermore, as demonstrated by experimental results, our method can achieve very compact representation since we mainly need to save the coefficients of the hierarchical B-spline function within a narrow band near the point cloud. The ability of our method to produce reconstruction results with high quality is also validated by experiments.