# Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

## TL;DR

This paper introduces the first streaming algorithm for computing Euler characteristic curves of multidimensional images, enabling efficient processing of large-scale data without extensive memory requirements.

## Contribution

It presents a novel streaming algorithm for Euler characteristic curves, scalable with multiple cores, and connects the concept to computational topology and persistence diagrams.

## Key findings

- Handles terabyte-scale images on commodity hardware
- Scales well with processor cores due to lock-free parallelism
- Provides open-source software for practical use

## Abstract

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Our software---CHUNKYEuler---is available as open source on Bitbucket. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.