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• W2892388036 abstract "Abstract We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices." @default.
• W2892388036 created "2018-10-05" @default.
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• W2892388036 date "2019-01-21" @default.
• W2892388036 modified "2023-10-16" @default.
• W2892388036 title "Functional Maps Representation On Product Manifolds" @default.
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• W2892388036 doi "https://doi.org/10.1111/cgf.13598" @default.
• W2892388036 hasPublicationYear "2019" @default.
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