Surface Reconstruction of Defective Point Clouds Based on Dual Off-Set Gradient Functions

Surface reconstruction is an interesting and challenging task in extensively applied fields including rapid prototype manufacturing, computer vision, virtual reality and computer aided design (CAD). A typical reconstruction procedure begins with scanning, in which the point data are sampled from physical objects by digitizing measurement systems (such as laser-range scanners and hand-held digitizers). And then, the point data are generated as a smooth, water-tight and proper resulting surface by a suitable reconstruction method. In industry the most difficulty comes from the defective samples that are subject to the noise, holes and overlapping regions. The defective samples are often unavoidable due to the sampling inaccuracy, scan mis-registration and accessibility constraints of scanning device. They often make most existing reconstruction methods not practical for engineering application because the oriented or neighbour information of points, which the most methods are highly based on, are hard to evaluate. For instance, many methods rely on consistent normals, or pose the demand on triangular meshes generated from point data. However, the holes and overlapping samples confuse the point’s neighbour relationship, some jagged, self-intersect regions could exist in the corresponding triangular mesh or the estimation of consistent normals becomes an ill-posed problem. Only a few methods need not such specific information, but they have to resort to some complex or time-consuming steps, like re-sampling, distance-computing, mesh-smooth or deformable models. Even if these methods can generate a water-tight resulting surface, the reasonableness of fitting overlapping samples and holes is not guaranteed. In fact, such issues, especially “badscanning” data, often lead long scanning time, massive manual work and poor model quality. Given these challenges, this paper propose a novel surface reconstruction method that takes as input defective point clouds without any specific information and output a smooth and water-tight surface. The main idea is that (1) this technique is based on implicit function, because implicit reconstruction is convenient to guarantee a water-tight result; (2) the approach is indirect, two off-set surfaces are generated to best fit the point clouds instead of direct approximation. As shown in Fig.1 (1D situation for simple expression), the point