Regularized implicit surface reconstruction from points and normals

Abstract

We consider the problem of surface reconstruction of a geometric object from a finite set of sample points with normals. Our contribution is to present a new scheme for implicit surface reconstruction. Similarly to the multilevel partition of unity (MPU) method we hierarchically divide the domain obtaining local approximation for the object on each part, and then patch all together obtaining a global description of the object. Our new scheme uses ridge regression and weighted gradient one fitting techniques to get better stability on local approximations. The method behaves reasonably on sparse set of points and data with holes as those which comes from 3D scanning of real objects.

Implicit B-Spline Surface Reconstruction

“…Moving least squares (MLS), for instance, is based on a weighted least squares defined in a local neighborhood [27]. Multi-level Partition of Unity is another local fitting method that is widely used for surface reconstruction [15], [28], [29]. Generally speaking, MPU describes the object based on a set of small patches that blend together in a smooth way.…”

“…Finally, all these local approximations are smoothly integrated into a global function. In [28] the authors use the gradient-one algorithm and ridge regression techniques to obtain a better result for a local description. In this work we show how the proposed IBS fitting equipped with an efficient weighting function provides a good trade-off between global and local fitting methods.…”