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While neural representations for static 3D shapes are widely studied,representations for deformable surfaces are limited to be template-dependent orlack efficiency. We introduce Canonical Deformation Coordinate Space (CaDeX), aunified representation of both shape and nonrigid motion. Our key insight isthe factorization of the deformation between frames by continuous bijectivecanonical maps (homeomorphisms) and their inverses that go through a learnedcanonical shape. Our novel deformation representation and its implementationare simple, efficient, and guarantee cycle consistency, topology preservation,and, if needed, volume conservation. Our modelling of the learned canonicalshapes provides a flexible and stable space for shape prior learning. Wedemonstrate state-of-the-art performance in modelling a wide range ofdeformable geometries: human bodies, animal bodies, and articulated objects.

CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism