Euler Calculus with Applications to Signals and Sensing

TL;DR

This paper surveys Euler calculus, an integral based on Euler characteristic, and explores its applications in data analysis, sensing, networks, and imaging, highlighting its potential for diverse scientific fields.

Contribution

It provides a comprehensive overview of Euler calculus and demonstrates its applications across various domains, which is a novel integration of topology and data analysis.

Findings

Euler calculus offers a new approach to data integration.

Applications include improved sensing and imaging techniques.

Potential for broad impact in scientific data analysis.

Abstract

This article surveys the Euler calculus - an integral calculus based on Euler characteristic - and its applications to data, sensing, networks, and imaging.