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GPU Computation of the Euler Characteristic Curve for Imaging Data

Authors Fan Wang, Hubert Wagner, Chao Chen

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Author Details

Fan Wang
  • Stony Brook University, NY, US
Hubert Wagner
  • University of Florida, Gainesville, FL, US
Chao Chen
  • Stony Brook University, NY, US

Funding

This work was partially supported by grants NSF IIS-1909038 and CCF-1855760.

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Fan Wang, Hubert Wagner, and Chao Chen. GPU Computation of the Euler Characteristic Curve for Imaging Data. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SoCG.2022.64

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • topological data analysis
  • Euler characteristic
  • Euler characteristic curve
  • Betti curve
  • persistent homology
  • algorithms
  • parallel programming
  • algorithm engineering
  • GPU programming
  • imaging data

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