Solving ill-posed Image Processing problems using Data Assimilation

Béréziat, Dominique; Herlin, Isabelle

doi:10.1007/s11075-010-9383-z

Cited by 26 publications

(37 citation statements)

References 25 publications

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“…The image is considered as a passive tracer moving with respect to the dynamics of the system, and more precisely with the motion field V . This approach, proposed in Béréziat and Herlin (2011), Papadakis and Mémin (2008) and Gorthi et al (2011), leads to the following image cost function:…”

Section: Observation Operators For Imagesmentioning

confidence: 99%

Toward the assimilation of images

Dimet

Souopgui

Titaud

et al. 2015

Nonlin. Processes Geophys.

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Abstract. The equations that govern geophysical fluids (namely atmosphere, ocean and rivers) are well known but their use for prediction requires the knowledge of the initial condition. In many practical cases, this initial condition is poorly known and the use of an imprecise initial guess is not sufficient to perform accurate forecasts because of the high sensitivity of these systems to small perturbations. As every situation is unique, the only additional information that can help to retrieve the initial condition are observations and statistics. The set of methods that combine these sources of heterogeneous information to construct such an initial condition are referred to as data assimilation. More and more images and sequences of images, of increasing resolution, are produced for scientific or technical studies. This is particularly true in the case of geophysical fluids that are permanently observed by remote sensors. However, the structured information contained in images or image sequences is not assimilated as regular observations: images are still (under-)utilized to produce qualitative analysis by experts. This paper deals with the quantitative assimilation of information provided in an image form into a numerical model of a dynamical system. We describe several possibilities for such assimilation and identify associated difficulties. Results from our ongoing research are used to illustrate the methods. The assimilation of image is a very general framework that can be transposed in several scientific domains.

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Section: Observation Operators For Imagesmentioning

confidence: 99%

Toward the assimilation of images

Dimet

Souopgui

Titaud

et al. 2015

Nonlin. Processes Geophys.

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show abstract

“…Equation (6) (7) and (8) using the adjoint variable and the adjoint variable is determined from Equations (5) and (6) using the state vector. To break this deadlock, an incremental method is applied, that is fully described in [3].…”

Section: Variational Formulationmentioning

confidence: 99%

Recovering Missing Data on Satellite Images

2011

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Abstract. Data Assimilation is commonly used in environmental sciences to improve forecasts, obtained by meteorological, oceanographic or air quality simulation models, with observation data. It aims to solve an evolution equation, describing the dynamics, and an observation equation, measuring the misfit between the state vector and the observations, to get a better knowledge of the actual system's state, named the reference. In this article, we describe how to use this technique to recover missing data and reduce noise on satellite images. The recovering process is based on assumptions on the underlying dynamics displayed by the sequence of images. This is a promising alternative to methods such as space-time interpolation. In order to better evaluate our approach, results are first quantified for an artificial noise applied on the acquisitions and then displayed for real data.

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“…For further details, the reader is referred to (Oliver, 1998;Tarantola, 2005;Béréziat and Herlin, 2008).…”

Section: The Evolution Model and Errormentioning

confidence: 99%

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

Béréziat¹,

Herlin

2009

Proceedings of the Fourth International Conference on Computer Vision Theory and Applications

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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.

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Solving ill-posed Image Processing problems using Data Assimilation

Cited by 26 publications

References 25 publications

Toward the assimilation of images

Toward the assimilation of images

Recovering Missing Data on Satellite Images

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

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