Maximal planes and multiscale tangential cover of 3D digital objects

Abstract

The sequence of maximal segments (i.e. the tangential cover) along a digital boundary is an essential tool for analyzing the geometry of two-dimensional digital shapes. The purpose of this paper is to define similar primitives for three-dimensional digital shapes, i.e. maximal planes defined over their boundary. We provide for them an unambiguous geometrical definition avoiding a simple greedy characterization as previous approaches. We further develop a multiscale theory of maximal planes. We show that these primitives are representative of the geometry of the digital object at different scales, even in the presence of noise. © 2011 Springer-Verlag Berlin Heidelberg.