Abstract. This paper presents a novel method for surface recovery from discrete 3D point data sets. In order to produce improved reconstruction results, the algorithm presented in this paper combines the advantages of a parametric approach to model local surface structure, with the generality and the topological adaptability of a geometric flow approach. This hybrid method is specifically designed to preserve discontinuities in 3D, to be robust to noise, and to reconstruct objects with arbitrary topologies. The key ideas are to tailor a curvature consistency algorithm to the case of a set of points in 3D and to then incorporate a flux maximizing geometric flow for surface reconstruction. The approach is illustrated with experimental results on a variety of data sets.
IntroductionSurface reconstruction from incomplete data sets is a classical problem in computer vision. The problem consists of finding a surface S that approximates a physical surface P by using a set of point coordinates sampled from the surface P. These point coordinates may be corrupted with noise, due to imperfections in the acquisition of the data. Like many other problems in computer vision, the problem of surface reconstruction is ill-posed. Prior knowledge about the world and the data acquisition process must therefore be used in order to make it solvable. A good algorithm for surface reconstruction should be robust to noise and result in smooth surfaces, while recovering important structural information from the data, such as edges, ridges and holes. The presence of such structural information in the reconstructed 3D model is very important for further, higher-level processing tasks, such as shape segmentation into parts, object recognition, etc. It should impose as little restrictions on the topology of the reconstructed object as possible. These issues are taken into consideration in the research presented in this paper. The approach to surface reconstruction presented in this article combines two different philosophies, namely that of a parametric reconstruction approach, and that of a geometric flow reconstruction approach. Many algorithms for surface recovery are based on either one of the two types of approaches, but few have attempted to