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Control of the Effects of Regularization on Variational Optic Flow Computations

By Z Belhachmi and Frédéric Hecht

Abstract

International audienceWe consider a variational model for the determination of the optic-flow in a general setting of non-smooth domains. This problem is ill-posed and its solution with PDE techniques includes a regulariza-tion procedure. The goal of this paper is to study a method to solve the optic flow problem and to control the effects of the regularization by allowing, locally and adaptively the choice of its parameters. The regu-larization in our approach is not controlled by a single parameter but by a function of the space variable. This results in a dynamical selection of the variational model which evolves with the variations of this function. Such method consists of new adaptive finite element discretization and an a posteriori strategy for the control of the regularization in order to achieve a trade-off between the data and the smoothness terms in the energy functional. We perform the convergence analysis and the a posteriori analysis, and we prove that the error indicators provide, as, a by-product, a confidence measure which shows the effects of regu-larization and serves to compute sparse solutions. We perform several numerical experiments, to show the efficiency and the reliability of the method in the computations of optic flow, with high accuracy and of low density

Topics: 68U10 (65J20), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
Publisher: Springer Verlag
Year: 2011
DOI identifier: 10.1007/s10851-010-0239-x
OAI identifier: oai:HAL:hal-01279861v1
Provided by: Hal-Diderot

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