Abstract
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. Â
Highlights
The convergence between computer science, audiovisual, and internet leads to widen visual information
We present a robust method for finding a geometric correspondence between 3D shapes
We presented a robust method for 3D objects matching
Summary
The traditional matching problem between two graphs can be formulated using the Euclidean matrix from equation (17) as (18). The graph isomorphism is reduced to the problem of finding the permutation matrix that minimizes equation (18). To apply simulated annealing algorithm in the matching process, we should define the states and their transitions with associated energy changes. The matching problem between two graphs and can be formulated as finding a subgraph of isomorphic to and minimizes the criteria in equation (21). Simulated annealing algorithm can be formulated using the property of graphs matching where we consider a state and the states spaces respectively as an isomorphism and the set of possible isomorphism. The state transition can be done by changing two vertices correspondents within a mapping to produce a new one. The system energy that controls the simulated annealing is defined as:
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