Abstract: Persistent homology is commonly applied to study the shape of high dimensional data sets. In this talk we consider two low-dimensional data scenarios in which both geometry and topology are of importance. We study 2D and 3D images of prostate cancer tissue, in which glands form cycles or voids. Treatment decisions for prostate cancer patients are largely based on the pathological analysis of the geometry and topology of these data. As a second scenario we consider the comparison of road networks.