Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval

In content-based image retrieval a major problem is the presence of noisy shapes. Noise can present itself not only in the form of continuous deformations, but also as topological changes. It is well known that persistent Betti numbers are a shape descriptor that admits dissimilarity distances stable under continuous shape deformations. In this paper we focus on the problem of dealing with noise that alters the topology of the studied objects. We present a general method to turn persistent Betti numbers into stable descriptors also in the presence of topological changes. Retrieval tests on the Kimia-99 database show the effectiveness of the method.

► Persistent homology is shown to be tolerant to noisy domains.
► Domain information is encoded into a function.
► Stability of persistent homology with respect to functions perturbation is exploited.
► Multidimensional persistent homology is crucial for the proposed method.