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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

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Publication Date:
January 2017
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5. Convective regularization for optical flow

Iglesias, José A. / Kirisits, Clemens


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

José A. Iglesias, Clemens Kirisits (2016). 5. Convective regularization for optical flow. In Maitine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn (Eds.), Variational Methods: In Imaging and Geometric Control (pp. 184–201). Berlin, Boston: De Gruyter. https://doi.org/10.1515/9783110430394-005

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

Online ISBN: 9783110430394

© 2016 Walter de Gruyter GmbH, Berlin/Munich/BostonGet Permission

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