  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.
