Computing the Euler characteristic and related additive functionals of digital objects from their bintree representation

✍ Scribed by H Bieri

• Publisher: Elsevier Science
• Year: 1987
• Weight: 703 KB
• Volume: 40
• Category: Article
• ISSN: 0734-189X
• DOI: 10.1016/0734-189x(87)90059-4

✦ Synopsis

A recursive algorithm for the computation of the Euler characteristic 5, the volume V, the surface S, the mean width M, and other properties (i.e., quermassintegrals) of digital pictures is presented. Full generality with respect to dimension is achieved by understanding digital pictures as (nondegenerate) polyhedra c Rd-that is why we call them "digital objects"-and the respective properties as additive functionals on sets of digital objects. In preparation, we discuss the bintree representation of digital objects which our algorithm will presuppose as the underlying data structure.