Generative Topology for Shape Synthesis
Keywords: Topological Data Analysis, TDA, Euler Characteristic, Topology, Topological Deep Learning, Geometric Deep Learning.
TL;DR: A topological model for the synthesis and reconstruction of shapes.
Abstract: The _Euler Characteristic Transform_ (ECT) is a powerful invariant for assessing geometrical and topological characteristics of a large variety of objects, including graphs and embedded simplicial complexes. Although the ECT is invertible in theory, no explicit algorithm for general data sets exists. In this paper, we address this lack and demonstrate that it is possible to _learn_ the inversion, permitting us to develop a novel framework for shape generation tasks on point clouds. Our model exhibits high quality in reconstruction and generation tasks, affords efficient latent-space interpolation, and is orders of magnitude faster than existing methods.
Primary Area: generative models
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Submission Number: 9765
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