Functional maps: a flexible representation of maps between shapes

We present a novel representation of maps between pairs of shapes that allows for efficient inference and manipulation. Key to our approach is a generalization of the notion of map that puts in correspondence real-valued functions rather than points on the shapes. By choosing a multi-scale basis for the function space on each shape, such as the eigenfunctions of its Laplace-Beltrami operator, we obtain a representation of a map that is very compact, yet fully suitable for global inference. Perhaps more remarkably, most natural constraints on a map, such as descriptor preservation, landmark correspondences, part preservation and operator commutativity become linear in this formulation. Moreover, the representation naturally supports certain algebraic operations such as map sum, difference and composition, and enables a number of applications, such as function or annotation transfer without establishing pointto-point correspondences. We exploit these properties to devise an efficient ...

• Type: Journal
• Year: 2012
• Where: TOG
• Authors: Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, Leonidas J. Guibas
• Keywords: Algebraic Operations, Communications, Natural Constraints, Point Correspondences, TOG 2012