Persistence Codebooks for Topological Data Analysis

Topological data analysis, such as persistent homology has shown beneficial properties for machine learning in many tasks. Topological representations, such as the persistence diagram (PD), however, have a complex structure (multiset of intervals) which makes it difficult to combine with typical machine learning workflows. We present novel compact fixed-size vectorial representations of PDs based on clustering and bag of words encodings that cope well with the inherent sparsity of PDs. Our novel representations outperform state-of-the-art approaches from topological data analysis and are computationally more efficient.

A Study on Topological Descriptors for the Analysis of 3D Surface Texture

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.