Generative Topology for Shape Synthesis

• URL: http://arxiv.org/abs/2410.18987v1
• Date: Wed, 09 Oct 2024 17:19:22 GMT
• Title: Generative Topology for Shape Synthesis
• Authors: Ernst Röell, Bastian Rieck,
• Abstract summary: We 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, and is orders of magnitude faster than existing methods.
• Score: 13.608942872770855
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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