Recognition of digital hyperplanes and level layers with forbidden points

Abstract

We consider a new problem of recognition of digital primitives - digital hyperplanes or level layers - arising in a new practical application of surface segmentation. Such problems are usually driven by a maximal thickness criterion which is not satisfactory for applications as soon as the dimension of the primitives becomes greater than 1. It is a good reason to introduce a more flexible approach where the set to recognize (whose points are called inliers) is given along with two other sets of outliers that should each remain on his own side of the primitive. We reduce this problem of recognition with outliers to the separation of three point clouds of ℝ d by two parallel hyperplanes and we provide a geometrical algorithm derived from the well-known GJK algorithm to solve the problem. © 2011 Springer-Verlag Berlin Heidelberg.