Entropic metric alignment for correspondence problems
Solomon, Justin; Peyré, Gabriel; Kim, Vladimir G.; Sra, Suvrit (2016), Entropic metric alignment for correspondence problems, 43rd international conference and exhibition on Computer Graphics & Interactive Techniques (SIGGRAPH 2016), 2016-07, Anaheim, Etats-Unis
TypeCommunication / Conférence
External document linkhttps://hal.archives-ouvertes.fr/hal-01305808
Conference title43rd international conference and exhibition on Computer Graphics & Interactive Techniques (SIGGRAPH 2016)
Journal nameACM Transactions on Graphics
MetadataShow full item record
Abstract (EN)Many shape and image processing tools rely on computation of correspondences between geometric domains. Efficient methods that stably extract "soft" matches in the presence of diverse geometric structures have proven to be valuable for shape retrieval and transfer of labels or semantic information. With these applications in mind, we present an algorithm for probabilistic correspondence that optimizes an entropy-regularized Gromov-Wasserstein (GW) objective. Built upon recent developments in numerical optimal transportation, our algorithm is compact, provably convergent, and applicable to any geometric domain expressible as a metric measure matrix. We provide comprehensive experiments illustrating the convergence and applicability of our algorithm to a variety of graphics tasks. Furthermore, we expand entropic GW correspondence to a framework for other matching problems, incorporating partial distance matrices, user guidance, shape exploration, symmetry detection, and joint analysis of more than two domains. These applications expand the scope of entropic GW correspondence to major shape analysis problems and are stable to distortion and noise.
Subjects / Keywordsentropy; Gromov-Wasserstein; optimal transport; matching
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