@inproceedings{ad2d0234869a42129da5846abf0ca1fb,
title = "Time Discrete Extrapolation in a Riemannian Space of Images",
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.",
author = "Alexander Effland and Martin Rumpf and Florian Sch{\"a}fer",
year = "2017",
doi = "10.1007%2F978-3-319-58771-4_38",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "473--485",
booktitle = "International Conference on Scale Space and Variational Methods in Computer Vision",
note = "6th International Conference on Scale Space and Variational Methods in Computer Vision : SSVM 2017 ; Conference date: 05-06-2017 Through 08-06-2017",
}