Reeb graph based segmentation of articulated components of 3D digital objects

Abstract

Segmentation of the articulated components of digital objects by a fast and efficient algorithm is presented in this paper. Given a 3D object in the form of a triangulated mesh, the approach involves representation of the mesh in a topological space and relating quotient spaces, containing the topologically invariant sections of the object, to weighted Reeb graphs along each of yz-, zx-, and xy-planes. It is followed by segmentation of the Reeb graphs where the concept of exponential averaging for dynamic thresholding ensures natural segmentation with a relatively high degree of accuracy. The segmented quotient spaces corresponding to the three Reeb graphs are subsequently related to each other and transformed topologically to report the segmented object in an appropriate topological space. The segmentation is carried out in a framework of 3D grid so as to exploit the topological relation between the triangulated object and its tight isothetic cover, and hence involves efficient computation and storage. The accuracy of segmentation at different grid resolutions, its robustness w.r.t. rotation, and pose-invariance for a reasonable range of postures are demonstrated by experimental results on a variety of objects.