  Methods from computational topology are becoming more and more popular in
computer vision and have shown to improve the state-of-the-art in several
tasks. In this paper, we investigate the applicability of topological
descriptors in the context of 3D surface analysis for the classification of
different surface textures. We present a comprehensive study on topological
descriptors, investigate their robustness and expressiveness and compare them
with state-of-the-art methods including Convolutional Neural Networks (CNNs).
Results show that class-specific information is reflected well in topological
descriptors. The investigated descriptors can directly compete with
non-topological descriptors and capture complementary information. As a
consequence they improve the state-of-the-art when combined with
non-topological descriptors.
