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.
Additional Information
© Springer International Publishing AG 2017.Additional details
- Eprint ID
- 86847
- DOI
- 10.1007/978-3-319-58771-4_38
- Resolver ID
- CaltechAUTHORS:20180606-130533228
- Created
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2018-06-06Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Series Name
- Lecture Notes in Computer Science
- Series Volume or Issue Number
- 10302