Abstract

Topological data analysis offffers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernelbased learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive defifinite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classifification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.