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.
Bibliographical noteKAUST Repository Item: Exported on 2022-06-10
Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: The authors thank the anonymous reviewers for their valuable comments. This work is supported by the KAUST OSR Award No. CRG-2017-3426, a gift from the NVIDIA Corporation, the ERC Starting Grant No. 758800 (EXPROTEA), NSF grants IIS-1528025 and DMS-1546206, a Vannevar Bush Faculty Fellowship, and a gift from the Autodesk Corporation.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Computer Networks and Communications