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Continuous-domain assignment flows

Published online by Cambridge University Press:  01 September 2020

F. SAVARINO
Affiliation:
Image and Pattern Analysis Group, Heidelberg University, Heidelberg, Germany emails: fabrizio.savarino@iwr.uni-heidelberg.de; schnoerr@math.uni-heidelberg.de, URL: https://ipa.math.uni-heidelberg.de
C. SCHNÖRR
Affiliation:
Image and Pattern Analysis Group, Heidelberg University, Heidelberg, Germany emails: fabrizio.savarino@iwr.uni-heidelberg.de; schnoerr@math.uni-heidelberg.de, URL: https://ipa.math.uni-heidelberg.de

Abstract

Assignment flows denote a class of dynamical models for contextual data labelling (classification) on graphs. We derive a novel parametrisation of assignment flows that reveals how the underlying information geometry induces two processes for assignment regularisation and for gradually enforcing unambiguous decisions, respectively, that seamlessly interact when solving for the flow. Our result enables to characterise the dominant part of the assignment flow as a Riemannian gradient flow with respect to the underlying information geometry. We consider a continuous-domain formulation of the corresponding potential and develop a novel algorithm in terms of solving a sequence of linear elliptic partial differential equations (PDEs) subject to a simple convex constraint. Our result provides a basis for addressing learning problems by controlling such PDEs in future work.

Type
Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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