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Time Discrete Extrapolation in a Riemannian Space of Images

Effland, Alexander and Rumpf, Martin and Schäfer, Florian (2017) Time Discrete Extrapolation in a Riemannian Space of Images. In: Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science. No.10302. Springer , Cham, Switzerland, pp. 473-485. ISBN 978-3-319-58770-7. http://resolver.caltech.edu/CaltechAUTHORS:20180606-130533228

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-319-58771-4_38DOIArticle
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Additional Information:© Springer International Publishing AG 2017.
Subject Keywords:Image extrapolation · Shape space · Elastic registration · Exponential map
Record Number:CaltechAUTHORS:20180606-130533228
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180606-130533228
Official Citation:Effland A., Rumpf M., Schäfer F. (2017) Time Discrete Extrapolation in a Riemannian Space of Images. In: Lauze F., Dong Y., Dahl A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science, vol 10302. Springer, Cham
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86847
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Jun 2018 20:47
Last Modified:06 Jun 2018 20:47

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