Maximal Planes and Multiscale Tangential Cover of 3D Digital Objects

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 de- fine 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.

Proc. Int. Workshop Combinatorial Image Analysis (IWCIA2011), volume 6636 of Lecture Notes in Computer Science, pp 132-143, Springer