GPU Computation of the Euler Characteristic Curve for Imaging Data

TL;DR

This paper presents an optimized GPU implementation for computing the Euler characteristic curve of 2D and 3D imaging data, demonstrating its efficiency and highlighting GPU programming techniques for topological data analysis.

Contribution

It introduces a practical GPU-based algorithm for ECC computation in imaging, showcasing performance and providing insights into GPU programming for topological analysis.

Findings

GPU implementation significantly speeds up ECC computation

The method is effective for large 2D and 3D imaging datasets

Highlights common GPU programming pitfalls and solutions

Abstract

Persistent homology is perhaps the most popular and useful tool offered by topological data analysis, with point-cloud data being the most common setup. Its older cousin, the Euler characteristic curve (ECC) is less expressive, but far easier to compute. It is particularly suitable for analyzing imaging data, and is commonly used in fields ranging from astrophysics to biomedical image analysis. These fields are embracing GPU computations to handle increasingly large datasets. We therefore propose an optimized GPU implementation of ECC computation for 2D and 3D grayscale images. The goal of this paper is twofold. First, we offer a practical tool, illustrating its performance with thorough experimentation, but also explain its inherent shortcomings. Second, this simple algorithm serves as a perfect backdrop for highlighting basic GPU programming techniques that make our implementation so efficient, and some common pitfalls we avoided. This is intended as a step towards a wider usage of GPU programming in computational geometry and topology software. We find this is particularly important as geometric and topological tools are used in conjunction with modern, GPU-accelerated machine learning frameworks.