Classification of digital images using topological signatures

Abstract

Topological Data Analysis (TDA) is a new area of Applied Mathematics that has become increasingly popular in recent years. TDA utilizes Persistent Homology, a mathematical tool that analyzes the topology of data sets. The focus of this paper is on using Persistent Homology to extract topological signatures from digital images and investigate how these signatures can improve image classification. In this short paper there are some preliminary results obtained on real world digital image datasets. There are improvement in evaluation metrics from 19% to 37%, using topological signatures.