Time Discrete Extrapolation in a Riemannian Space of Images

Alexander Effland*, Martin Rumpf, Florian Schäfer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paper

Abstract

The Riemannian metamorphosis model introduced and analyzed in [7, 12] is taken into account to develop an image extrapolation tool in the space of images. To this end, the variational time discretization for the geodesic interpolation proposed in [2] is picked up to define a discrete exponential map. For a given weakly differentiable initial image and a sufficiently small initial image variation it is shown how to compute a discrete geodesic extrapolation path in the space of images. The resulting discrete paths are indeed local minimizers of the corresponding discrete path energy. A spatial Galerkin discretization with cubic splines on coarse meshes for image deformations and piecewise bilinear finite elements on fine meshes for image intensity functions is used to derive a fully practical algorithm. The method is applied to real images and image variations recorded with a digital camera.
Original languageEnglish
Title of host publicationInternational Conference on Scale Space and Variational Methods in Computer Vision
Pages473-485
ISBN (Electronic)978-331958770-7
DOIs
Publication statusPublished - 2017
Externally publishedYes
Event6th International Conference on Scale Space and Variational Methods in Computer Vision: SSVM 2017 - Kolding, Denmark
Duration: 5 Jun 20178 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Volume10302
ISSN (Electronic)0302-9743

Conference

Conference6th International Conference on Scale Space and Variational Methods in Computer Vision
CountryDenmark
CityKolding
Period5/06/178/06/17

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