Informative Descriptor Preservation via Commutativity for Shape Matching

Speaker: Dorian Nogneng   Ecole Polytechnique Palaiseau, France

Date: Thursday, March 23, 2017

Place: USI Lugano Campus, room SI-003, informatics building (Via G. Buffi 13)

Time: 14:30

Abstract:

We consider the problem of non-rigid shape matching, and specifically the functional mapsframework that was recently proposed to find correspondences between shapes. A key step in thisframework is to formulate descriptor preservation constraints that help to encode the information(e.g., geometric or appearance) that must be preserved by the unknown map. We showthat considering descriptors as linear operators acting on functions through multiplication,rather than as simple scalar-valued signals, allows to extract significantly more information froma given descriptor and ultimately results in a more accurate functional map estimation. Namely, weshow that descriptor preservation constraints can be formulated via commutativity withrespect to the unknown map, which can be conveniently encoded by considering relations betweenmatrices in the discrete setting. As a result, when the vector space spanned by the descriptorshas a dimension smaller than that of the reduced basis, our optimization may still provide afully-constrained system leading to accurate point-to-point correspondences, while previousmethods might not. We demonstrate on a wide variety of experiments that our approach leads tosignificant improvement for functional map estimation by helping to reduce the number of necessarydescriptor constraints by an order of magnitude, even given an increase in the size of the reducedbasis.

Biography:

Dorian Nogneng studied at Ecole Polytechnique and did his master in Paris Diderot (master of research in computer science: https://wikimpri.dptinfo.ens-cachan.fr/doku.php).He is now a PhD student of Pr. Maks Ovsjanikov in Ecole Polytechnique (Palaiseau, FRANCE) and works on shape matching, in particular using functional maps.

Host: Prof. Michael Bronstein