A Quantum Particle Swarm Optimization and Genetic Algorithm approach to the correspondence problem

Finding correspondences between deformable objects has wide application in many domains. In information retrieval, researchers may be interested in finding similar objects, while computer animation experts may be considering ways to morph shapes. The correspondence problem is especially challenging when the objects under consideration are suspect to non-rigid deformations, noise and/or distortions. In this paper, a novel method using Quantum Particle Swarm Optimization (QPSO) and Genetic Algorithms (GA) is presented to address this issue. In our QPSO-GA algorithm we formulate the problem of correspondence detection as an optimization problem over all possible mapping in between the geodesic distance matrices associated with two sets of point clouds. We proceed to identify the optimal mapping, by first applying Quantum Particle Swarm Optimization to the permutation matrices associated with their geodesic distance matrices and then employing Genetic Algorithms in order to guide the search. Experimental results suggest that our QPSO-GA algorithm is fast, scalable, and robust. Our method accurately identifies the correspondences between objects, even in the presence of noise and distortion.