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Limit Shapes – A Tool for Understanding Shape Differences and Variability in 3D Model Collections
Author(s) -
Huang Ruqi,
Achlioptas Panos,
Guibas Leonidas,
Ovsjanikov Maks
Publication year - 2019
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13799
Subject(s) - shape analysis (program analysis) , active shape model , limit (mathematics) , representation (politics) , computer science , range (aeronautics) , artificial intelligence , topological skeleton , object (grammar) , pattern recognition (psychology) , mathematics , segmentation , static analysis , mathematical analysis , materials science , politics , political science , law , composite material , programming language
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.