# SOLVING ILL-POSED PROBLEMS USING DATA ASSIMILATION - Application to Optical Flow Estimation

### Dominique Béréziat, Isabelle Herlin

#### Abstract

Data Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. Data Assimilation techniques require the resolution of a system with three components: one describing the temporal evolution of a state vector, one coupling the observations and the state vector, and one defining the initial condition. In this article, we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. A generic approach is defined to convert an ill-posed Image Processing problem in terms of a Data Assimilation system. This method is illustrated on the determination of optical flow from a sequence of images. The resulting software has two advantages: a quality criterion on input data is used for weighting their contribution in the computation of the solution and a dynamic model is proposed to ensure a significant temporal regularity on the solution.

#### References

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#### Paper Citation

#### in Harvard Style

Béréziat D. and Herlin I. (2009). **SOLVING ILL-POSED PROBLEMS USING DATA ASSIMILATION - Application to Optical Flow Estimation** . In *Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)* ISBN 978-989-8111-69-2, pages 595-602. DOI: 10.5220/0001792205950602

#### in Bibtex Style

@conference{visapp09,

author={Dominique Béréziat and Isabelle Herlin},

title={SOLVING ILL-POSED PROBLEMS USING DATA ASSIMILATION - Application to Optical Flow Estimation},

booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)},

year={2009},

pages={595-602},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001792205950602},

isbn={978-989-8111-69-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)

TI - SOLVING ILL-POSED PROBLEMS USING DATA ASSIMILATION - Application to Optical Flow Estimation

SN - 978-989-8111-69-2

AU - Béréziat D.

AU - Herlin I.

PY - 2009

SP - 595

EP - 602

DO - 10.5220/0001792205950602