Volume 16, Issue 1
​A Space-Time Parallel Method for the Optic Flow Estimation in Large Displacements and Varying Illumination Case

Diane Gilliocq-HirtzZakaria Belhachmi

Int. J. Numer. Anal. Mod., 16 (2019), pp. 116-138.

Published online: 2018-10

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  • Abstract

We consider a unified variational PDEs model to solve the optic flow problem for large displacements and varying illumination. Although, the energy functional is nonconvex and severely nonlinear, we show that the model offers a well suited framework to extend the efficient methods we used for small displacements. In particular, we resort to an adaptive control of the diffusion and the illumination coefficients which allows us to preserve the edges and to obtain a sparse vector field. We develop a combined space-time parallel programming strategy based on a Schwarz domain decomposition method to speed up the computations and to handle high resolution images, and the parareal algorithm, to enhance the speedup and to achieve a lowestenergy local minimum. This full parallel method gives raise to several iterative schemes and allows us to obtain a good balance between several objectives, e.g. accuracy, cost reduction, time saving and achieving the "best" local minimum. We present several numerical simulations to validate the different algorithms and to compare their performances.

  • Keywords

Optic flow estimation large dislacements variable illumination adaptive finite elements parallel and parareal computations domain decomposition.

  • AMS Subject Headings

35K15 35K55 65M22 65M55 68Y05 68U10 65D18.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

diane.gilliocq-hirtz@uha.fr (Diane Gilliocq-Hirtz)

zakaria.belhachmi@uha.fr (Zakaria Belhachmi)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-116, author = {Gilliocq-Hirtz , Diane and Belhachmi , Zakaria}, title = {​A Space-Time Parallel Method for the Optic Flow Estimation in Large Displacements and Varying Illumination Case}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {1}, pages = {116--138}, abstract = {

We consider a unified variational PDEs model to solve the optic flow problem for large displacements and varying illumination. Although, the energy functional is nonconvex and severely nonlinear, we show that the model offers a well suited framework to extend the efficient methods we used for small displacements. In particular, we resort to an adaptive control of the diffusion and the illumination coefficients which allows us to preserve the edges and to obtain a sparse vector field. We develop a combined space-time parallel programming strategy based on a Schwarz domain decomposition method to speed up the computations and to handle high resolution images, and the parareal algorithm, to enhance the speedup and to achieve a lowestenergy local minimum. This full parallel method gives raise to several iterative schemes and allows us to obtain a good balance between several objectives, e.g. accuracy, cost reduction, time saving and achieving the "best" local minimum. We present several numerical simulations to validate the different algorithms and to compare their performances.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12796.html} }
TY - JOUR T1 - ​A Space-Time Parallel Method for the Optic Flow Estimation in Large Displacements and Varying Illumination Case AU - Gilliocq-Hirtz , Diane AU - Belhachmi , Zakaria JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 116 EP - 138 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12796.html KW - Optic flow estimation KW - large dislacements KW - variable illumination KW - adaptive finite elements KW - parallel and parareal computations KW - domain decomposition. AB -

We consider a unified variational PDEs model to solve the optic flow problem for large displacements and varying illumination. Although, the energy functional is nonconvex and severely nonlinear, we show that the model offers a well suited framework to extend the efficient methods we used for small displacements. In particular, we resort to an adaptive control of the diffusion and the illumination coefficients which allows us to preserve the edges and to obtain a sparse vector field. We develop a combined space-time parallel programming strategy based on a Schwarz domain decomposition method to speed up the computations and to handle high resolution images, and the parareal algorithm, to enhance the speedup and to achieve a lowestenergy local minimum. This full parallel method gives raise to several iterative schemes and allows us to obtain a good balance between several objectives, e.g. accuracy, cost reduction, time saving and achieving the "best" local minimum. We present several numerical simulations to validate the different algorithms and to compare their performances.

​Diane Gilliocq-Hirtz & Zakaria Belhachmi. (2020). ​A Space-Time Parallel Method for the Optic Flow Estimation in Large Displacements and Varying Illumination Case. International Journal of Numerical Analysis and Modeling. 16 (1). 116-138. doi:
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