Topological descriptors for 3D surface analysis

TL;DR

This paper explores the use of topological descriptors derived from persistence diagrams for classifying 3D surface patches, demonstrating their robustness and superior performance compared to non-topological methods.

Contribution

It introduces a comprehensive evaluation of topological descriptors for 3D surface analysis, showing their effectiveness and how they enhance classification when combined with other descriptors.

Findings

Topological descriptors are robust to parameter variations.

They achieve state-of-the-art classification performance.

Combining topological and non-topological descriptors improves results.

Abstract

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.