An invariant descriptor map for 3D objects matching

Meshes and point clouds are traditionally used to represent and match 3D shapes. The matching prob-lem can be formulated as finding the best one-to-one correspondence between featured regions of two shapes. This paper presents an efficient and robust 3D matching method using vertices descriptors de-tection to define feature regions and an optimization approach for regions matching. To do so, we compute an invariant shape descriptor map based on 3D surface patches calculated using Zernike coef-ficients. Then, we propose a multi-scale descriptor map to improve the measured descriptor map quali-ty and to deal with noise. In addition, we introduce a linear algorithm for feature regions segmentation according to the descriptor map. Finally, the matching problem is modelled as sub-graph isomorphism problem, which is a combinatorial optimization problem to match feature regions while preserving the geometric. Finally, we show the robustness and stability of our method through many experimental re-sults with respect to scaling, noise, rotation, and translation.