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An Invitation to the Euler Characteristic Transform
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The Euler characteristic transform (ECT) is a simple to define yet powerful representation of shape. The idea is to encode an embedded shape using sub-level sets of a a function defined based on a given direction, and then returning the Euler characteristics of these sublevel sets. Because the ECT has been shown to be injective on the space of embedded simplicial complexes, it has been used for applications spanning a range of disciplines, including plant morphology and protein structural analysis. In this survey article, we present a comprehensive overview of the Euler characteristic transform, highlighting the main idea on a simple leaf example, and surveying its its key concepts, theoretical foundations, and available applications.
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Cited by 3 Pith papers
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For two embeddings of the same finite simplicial complex, the integrated distance between their Euler Characteristic Transforms is bounded by a constant times the total vertex displacement, and SELECT obeys an analogo...
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