A Curvature and Density‐based Generative Representation of Shapes

• DOI: 10.1111/cgf.14094
• Publication Date: 2020-10-12T20:58:59Z
• Authors: Z. Ye; N. Umetani; T. Igarashi; T. Hoffmann
• Keywords: Autoencoder; Rigid transformation; Representation

Abstract This paper introduces a generative model for 3D surfaces based on representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared existing machine learning frameworks, our substantially reduces the influence translation rotation. In addition, local structure will be more precisely captured, since is explicitly encoded in model. Specifically, every surface first conformally mapped to canonical domain, such as unit disk or sphere. Then, it represented by two functions: half‐density vertex density, over this domain. Assuming that input follow certain distribution latent space, we use variational autoencoder learn space representation. After learning, can generate variations randomly sampling space. Surfaces triangular meshes reconstructed from generated data applying isotropic remeshing spin transformation, given Dirac equation. We demonstrate effectiveness datasets man‐made biological compare results other methods.