# Topological signature for periodic motion recognition

## TL;DR

This paper introduces a topological signature based on persistent homology for recognizing periodic motions, demonstrating robustness and effectiveness across various activities and partial body data.

## Contribution

The paper presents a novel topological signature method for periodic motion recognition that is robust to perturbations and independent of the number of motion cycles.

## Key findings

- Effective in gait recognition using only lower body silhouette
- Applicable to various periodic motions like running and jumping
- Proven robustness to data perturbations

## Abstract

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of the object that models the motion. Two topological signatures are compared simply by the angle between the corresponding vectors. With respect to gait recognition, we have tested our method using only the lowest fourth part of the body's silhouette. In this way, the impact of variations in the upper part of the body, which are very frequent in real scenarios, decreases considerably. We have also tested our method using other periodic motions such as running or jumping. Finally, we formally prove that our method is robust to small perturbations in the input data and does not depend on the number of periods contained in the periodic motion sequence.