# Regularization Terms for Motion Estimation - Links with Spatial Correlations

### Yann Lepoittevin, Isabelle Herlin

#### Abstract

Motion estimation from image data has been widely studied in the literature. Due to the aperture problem, one equation with two unknowns, a Tikhonov regularization is usually applied, which constrains the estimated motion field. The paper demonstrates that the use of regularization functions is equivalent to the definition of correlations between pixels and the formulation of the corresponding correlation matrices is given. This equivalence allows to better understand the impact of the regularization with a display of the correlation values as images. Such equivalence is of major interest in the context of image assimilation as these methods are based on the minimization of errors that are correlated on the space-time domain. It also allows to characterize the role of the errors during the assimilation process.

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#### Paper Citation

#### in Harvard Style

Lepoittevin Y. and Herlin I. (2016). **Regularization Terms for Motion Estimation - Links with Spatial Correlations** . In *Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)* ISBN 978-989-758-175-5, pages 456-464. DOI: 10.5220/0005712104560464

#### in Bibtex Style

@conference{visapp16,

author={Yann Lepoittevin and Isabelle Herlin},

title={Regularization Terms for Motion Estimation - Links with Spatial Correlations},

booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)},

year={2016},

pages={456-464},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005712104560464},

isbn={978-989-758-175-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)

TI - Regularization Terms for Motion Estimation - Links with Spatial Correlations

SN - 978-989-758-175-5

AU - Lepoittevin Y.

AU - Herlin I.

PY - 2016

SP - 456

EP - 464

DO - 10.5220/0005712104560464