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A Variational Method and its Mathematical Study in Image Sequence Analysis

G. Aubert 1 Rachid Deriche Pierre Kornprobst
1 ROBOTVIS - Computer Vision and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This article deals with the problem of restoring and motion segmenting noisy image sequences with a static background. Usually, motion segmentation and image restoration are tackled separately in image sequence restoration. Moreover, motion segmentation is often noise sensitive. In this article, the motion segmentation and the image restoration parts are performed in a coupled way, allowing the motion segmentation part to positively influence the restoration part and vice-versa. This is the key of our approach that allows to deal simultaneously with the problem of restoration and motion segmentation. To this end, we propose a theoretically justified optimization problem that permits to take into account both requirements. The model is theoretically justified. Existence and unicity are proved in the space of bounded variations. A suitable numerical scheme based on half quadratic minimization is then proposed and its convergence and stability demonstrated. Experimental results obtained on noisy synthetic data and real images will illustrate the capabilities of this original and promising approach.
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https://hal.inria.fr/inria-00073274
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Submitted on : Wednesday, May 24, 2006 - 12:24:18 PM
Last modification on : Saturday, January 27, 2018 - 1:31:28 AM
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  • HAL Id : inria-00073274, version 1

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G. Aubert, Rachid Deriche, Pierre Kornprobst. A Variational Method and its Mathematical Study in Image Sequence Analysis. [Research Report] RR-3415, INRIA. 1998. ⟨inria-00073274⟩

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