Functional maps

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…

• NS
  National Science Foundation

  Award: FODAVA 0808515IIS 0914833CCF 1011228
• DO
  Division of Computing and Communication Foundations

  Award: FODAVA 0808515IIS 0914833CCF 1011228
• DO
  Division of Information and Intelligent Systems

  Award: FODAVA 0808515IIS 0914833CCF 1011228