OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation

Pascal Zille, Thomas Corpetti

2012

Abstract

This paper is concerned with the multi-resolution issue used in many computer vision applications. Such approaches are very popular to optimize a cost function that, in most of the situations, has been linearized for mathematical facility reasons. In general, a multi-resolution setup consists in a redefinition of the problem at a different resolution level where the mathematical assumptions (usually linearity) hold. Following a coarseto- fine strategy, a usual process consists in 1) optimizing the large scales and 2) use this result as an initial condition for the estimation at finer scales. Such process is repeated until the plain image resolution. One of the main drawbacks of such downscaling approach is its incapacity to correct the eventual errors that have been made at larger scales. These latter are indeed propagated along the scales and disturb the final result. In this paper, we suggest a new formulation of the multi-resolution setup where we exploit some smoothing techniques issued from optimal control theory and in particular variational data assimilation. The time is here artificial and is related to the various scales we are dealing with. Following a consistent mathematical framework, we define an original downscaling/upscaling technique to perform the multi-resolution. We validate this approach by defining a simple optical flow estimation technique based on Lucas-Kanade. Experimental results on synthetic data demonstrate the efficiency of this new methodology.

Paper Citation

in Harvard Style

Zille P. and Corpetti T. (2012). OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012) ISBN 978-989-8565-04-4, pages 134-143. DOI: 10.5220/0003841401340143

in Bibtex Style

@conference{visapp12,
author={Pascal Zille and Thomas Corpetti},
title={OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)},
year={2012},
pages={134-143},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003841401340143},
isbn={978-989-8565-04-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)
TI - OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation
SN - 978-989-8565-04-4
AU - Zille P.
AU - Corpetti T.
PY - 2012
SP - 134
EP - 143
DO - 10.5220/0003841401340143