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

dc.contributor.authorHuang, Ruqien_US
dc.contributor.authorAchlioptas, Panosen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorBommes, David and Huang, Huien_US
dc.description.abstractWe 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.en_US
dc.description.sectionheadersShape Collections and Analysis
dc.description.seriesinformationComputer Graphics Forum
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectComputing methodologies → Spectral methods
dc.subjectShape analysis
dc.titleLimit Shapes - A Tool for Understanding Shape Differences and Variability in 3D Model Collectionsen_US