Topological descriptors for 3D surface analysis
This work addresses 3D surface analysis for applications like computer vision or materials science, but it appears incremental as it builds on existing topological methods.
The paper tackled the problem of classifying 3D surfaces based on geometric structure by investigating topological descriptors, finding that they are robust, achieve state-of-the-art performance, and enhance classification when combined with non-topological descriptors.
We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical filtration. In the next step we investigate different topological descriptors and measure their ability to discriminate structurally different 3D surface patches. We evaluate their sensitivity to different parameters and compare the performance of the resulting topological descriptors to alternative (non-topological) descriptors. We present a comprehensive evaluation that shows that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis and (iii) improve classification performance when combined with non-topological descriptors.