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Variational Methods

In Imaging and Geometric Control

Ed. by Bergounioux, Maïtine / Peyré, Gabriel / Schnörr, Christoph / Caillau, Jean-Baptiste / Haberkorn, Thomas

Series:Radon Series on Computational and Applied Mathematics 18

eBook (PDF)
Publication Date:
January 2017
Copyright year:
2017
ISBN
978-3-11-043039-4
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5. Convective regularization for optical flow

Iglesias, José A. / Kirisits, Clemens

Abstract

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field v we consider the convective acceleration vt +∇vv which describes the acceleration of objects moving according to v. Consequently, we investigate the suitability of the nonconvex functional ‖vt + ∇vv‖2L 2 as a regularization term for optical flow. We demonstrate that this term acts as both a spatial and a temporal regularizer and has an intrinsic edge-preserving property. We incorporate it into a contrast invariant and time-regularized variant of the Horn-Schunck functional, prove the existence of minimizers and verify experimentally that it addresses someof the problems of basic quadratic models. For the minimization we use an iterative scheme that approximates the original nonlinear problem with a sequence of linear ones.We believe that the convective acceleration may be gainfully introduced in a variety of optical flow models.

Citation Information

Variational Methods

In Imaging and Geometric Control

Edited by Bergounioux, Maïtine / Peyré, Gabriel / Schnörr, Christoph / Caillau, Jean-Baptiste / Haberkorn, Thomas

De Gruyter

2016

Pages: 184–201

ISBN (Online): 9783110430394

DOI (Chapter): https://doi.org/10.1515/9783110430394-005

DOI (Book): https://doi.org/10.1515/9783110430394

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