The Differentiable Euler Characteristic Transform (DECT) overcomes limitations of the ECT by enabling task-specific representations through end-to-end learning. It provides efficient and scalable performance in shape classification tasks for graphs, point clouds, and meshes. The ECT and Persistent Homology Transform (PHT) are based on multi-scale topological descriptors for shapes. DECT is differentiable with respect to directions and coordinates, allowing integration into deep neural networks. The method offers a flexible framework for shape representation and optimisation based on topological constraints.
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by Ernst Roell,... at arxiv.org 03-18-2024
https://arxiv.org/pdf/2310.07630.pdfDeeper Inquiries