Volume xx (200y), Number z, pp. 1–15 Partial Functional Correspondence

Figure 1: Partial functional correspondence between two pairs of shapes with large missing parts. For each pair we show the matrix C representing the functional map in the spectral domain, and the action of the map by transferring colors from one shape to the other. The special slanted-diagonal structure of C induced by the partiality transformation is first estimated from spectral properties of the two shapes, and then exploited to drive the matching process. In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford-Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings