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Diffeomorphic density matching by optimal information transport

M. Bauer ; S. Joshi ; Klas Modin (Institutionen för matematiska vetenskaper, matematik)
SIAM Journal on Imaging Sciences Vol. 8 (2015), 3, p. 1718-1751.
[Artikel, refereegranskad vetenskaplig]

We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher–Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimensional manifold of diffeomorphisms. This optimal information transport, and modifications thereof, allow us to construct numerical algorithms for density matching. The algorithms are inherently more efficient than those based on optimal mass transport or diffeomorphic registration. Our methods have applications in medical image registration, texture mapping, image morphing, nonuniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.

Nyckelord: Density matching , Diffeomorphism groups , Fisher–rao metric , Image registration , Information geometry , Optimal transport , Random sampling



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Denna post skapades 2015-10-19. Senast ändrad 2016-01-20.
CPL Pubid: 224449

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Livsvetenskaper
Geometri
Beräkningsmatematik

Chalmers infrastruktur