Geometric measures on arbitrary dimensional digital surfaces

Abstract

This paper proposes a set of tools to analyse the geometry of multidimensional digital surfaces. Our approach is based on several works of digital topology and discrete geometry: representation of digital surfaces, bel adjacencies and digital surface tracking, 2D tangent computation by discrete line recognition, 3D normal estimation from slice contours. The main idea is to notice that each surface element is the crossing point of n - 1 discrete contours lying on the surface. Each of them can be seen as a 4-connected 2D contour. We combine the directions of the tangents extracted on each of these contours to compute the normal vector at the considered surface element. We then define the surface area from the normal field. The presented geometric estimators have been implemented in a framework able to represent subsets of n-dimensional spaces. As shown by our experiments, this generic implementation is also efficient. © Springer-Verlag Berlin Heidelberg 2003.