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We propose a novel shape representation useful for analyzing and processingshape collections, as well for a variety of learning and inference tasks.Unlike most approaches that capture variability in a collection by using atemplate model or a base shape, we show that it is possible to construct a fullshape representation by using the latent space induced by a functional map net-work, allowing us to represent shapes in the context of a collection withoutthe bias induced by selecting a template shape. Key to our construction is anovel analysis of latent functional spaces, which shows that after properregularization they can be endowed with a natural geometric structure, givingrise to a well-defined, stable and fully informative shape representation. Wedemonstrate the utility of our representation in shape analysis tasks, such ashighlighting the most distorted shape parts in a collection or separatingvariability modes between shape classes. We further exploit our representationin learning applications by showing how it can naturally be used within deeplearning and convolutional neural networks for shape classi cation orreconstruction, signi cantly outperforming existing point-based techniques.

Latent Space Representation for Shape Analysis and Learning