ArticleProceedings of the National Academy of Sciences of the United States of America2025
Digital tools for analyzing nondiffeomorphic shapes.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze nondiffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of directions and heights, which results in potential loss of information, as well as problems in inverting the transform. In this work, we present a fully digital algorithm for computing the ECT exactly, up to computer precision; we introduce the Ectoplasm package that implements this algorithm, and we demonstrate that this is fast and convenient enough to compute distances in real-life datasets. We also discuss the implications of this algorithm to related problems in shape analysis, such as shape inversion and subshape selection. We also show a proof-of-concept application for solving the shape alignment problem with gradient descent and adaptive grid search, which are two powerful methods, neither of which is possible using the discretized transform.
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