Unsupervised geodesic convex combination of shape dissimilarity measures

Dissimilarity or distance metrics are the cornerstone of shape matching and retrieval algorithms. As there is no unique dissimilarity measure that gives good performances in all possible configurations, these metrics are usually combined to provide reliable results. In this paper we propose to compute the best linear convex, or weighted, combination of any set of measured shape distances to enhance shape matching algorithms. To do so, a database is represented as a graph, where nodes are shapes and the edges carry the convex combination of dissimilarity measures. Weights are chosen to maximize the weighted distances between the query shape and shapes in the database. The optimal weights are solutions of a linear programming problem. This fully unsupervised method improves the outcomes of any set of shape similarity measures as shown in our experimental results performed on several popular 3D shape benchmarks.