Vectorized Computation of Euler Characteristic Functions and Transforms
This work addresses a computational bottleneck for researchers in topological data analysis, providing a faster and more scalable tool for analyzing geometric structures, though it is incremental as it improves existing methods rather than introducing a new paradigm.
The paper tackles the problem of slow and non-scalable computation of weighted Euler characteristic transforms (WECT) and Euler characteristic functions (ECF) by introducing a vectorized framework optimized for GPUs, achieving speedups of up to 180x over existing methods on image datasets.
The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are neither optimized for speed nor do they scale to higher-dimensional settings. In this work, we present a vectorized framework for computing such topological transforms using tensor operations, which is highly optimized for GPU architectures and works in full generality across geometric simplicial complexes (or cubical complexes) of arbitrary dimension. Experimentally, the framework demonstrates significant speedups (up to $180 \times$) over existing methods when computing the WECT and ECF across a variety of image datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT.