Limit Shapes – A Tool for Understanding Shape Differences and Variability in 3D Model Collections

Ruqi Huang, Panos Achlioptas, Leonidas Guibas, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We propose a novel construction for extracting a central or limit shape in a shape collection, connected via a functional map network. Our approach is based on enriching the latent space induced by a functional map network with an additional natural metric structure. We call this shape-like dual object the limit shape and show that its construction avoids many of the biases introduced by selecting a fixed base shape or template. We also show that shape differences between real shapes and the limit shape can be computed and characterize the unique properties of each shape in a collection – leading to a compact and rich shape representation. We demonstrate the utility of this representation in a range of shape analysis tasks, including improving functional maps in difficult situations through the mediation of limit shapes, understanding and visualizing the variability within and across different shape classes, and several others. In this way, our analysis sheds light on the missing geometric structure in previously used latent functional spaces, demonstrates how these can be addressed and finally enables a compact and meaningful shape representation useful in a variety of practical applications.
Original languageEnglish (US)
Pages (from-to)187-202
Number of pages16
JournalComputer Graphics Forum
Volume38
Issue number5
DOIs
StatePublished - Aug 12 2019
Externally publishedYes

ASJC Scopus subject areas

  • Computer Networks and Communications

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