3D object recognition using fully intrinsic skeletal graphs

Abstract

ABSTRACT In this paper, we propose a new topology extraction approach for 3D objects. We choose a normalized robustand simpli“ed geodesic-based Morse function to de“ne skeletal Reeb graphs of 3D objects. In addition to scaleinvariance, we ensure, by using a geodesic distance, the invariance of these graphs to all isometric transforms.In our Reeb graph construction procedure, we introduce important improvements and advantages over existingtechniques. We de“ne an ecient sampling rate based on the characteristic resolution intrinsic to each 3D object.Then, we provide a geometry preserving approach by replacing the traditional intervals of a Morse function byits exact level curves. Moreover, we take advantage of the resulting ordered adjacency matrices that describe ourReeb graphs, to introduce a new measure of similarity between the corresponding objects. Experimental resultsillustrate the computational simplicity and eciency of the proposed technique for topological Reeb graphsextraction. The experiments also show the robustness of this approach against noise and object remeshing.Keywords: 3D object, topological modeling, Morse theory, Reeb graph, GGF.