Functional Maps: A Flexible Representation of Maps (with Applications)

author: Maks Ovsjanikov, Laboratoire d'Informatique, École Polytechnique
published: March 5, 2013,   recorded: February 2013,   views: 5635


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In this talk, I will discuss a representation of maps between pairs of 3D shapes (represented as triangle meshes) that generalizes of the standard notion of a map to include correspondences that are not necessarily point-to-point. This representation is compact, and yet allows for efficient inference (shape matching) and enables a number of applications, including algebraic map manipulation such as computing map sums and differences. The key aspect of this representation is that many constraints on a map, including landmark correspondences, part preservation and operator commutativity become linear. This means, in particular, that shape matching can be phrased as a simple linear system of equations. I will describe the main properties of this representation and give a few examples of applications that include improving existing correspondence, segmentation transfer without establishing point-to-point matches and efficient map compression and visualization.

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