A Novel Ant Colony Shape Matching Algorithm Based on the Gromov-Wasserstein Distance

Shape matching has always been and still is an important task in the graphics and imaging research. The optimization of the minimum distance among the feature points on two surfaces of the same topological types, is a core to match shapes. Therefore, we propose in the present paper a novel ant colony shape matching algorithm based on the Gromov-Wasserstein distance. Firstly, the Gromov-Wasserstein distance is calculated using the geodesic distance of sampling points. Secondly, we make appeal to the geometric distance optimization method to establish the Gromov-Wasserstein distance model based on the ant colony algorithm, that is a quadratic convex optimization model. Next, we relax the constraint of the model by the “one-to-one matching” principle. Finally, in order to find the minimum distance, the ant colony algorithm is improved by the use of the exponent distance accumulation strategy and constraint. The proposed shape matching algorithm was tested on following data sets: TOSCA, McGill and D-FAUST. Though comparing with other algorithms, it shows that the matching effect is highly efficient and stable, as well as displays good robustness and noise resistance.