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HAIT Journal of Science and Engineering C Volume 4, Issues 1-2, pp. 178-193 © 2007 Holon Institute of Technology | |||||
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A variational approach for correspondence finding between three rectified images
Jeremy Yrmeyahu Kaminski1,*, Michael Belhdeb2, and Mina Teicher2
1Computer Science Department, Holon Institute of Technology, | 52 Golomb St., Holon 58102, Israel 2Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel *Corresponding author: kaminsj@hit.ac.il Received 10 May 2007, accepted 16 May 2007
| We present a variational approach for the computation of dense correspondence between three rectified images. Using rectification allows reducing the problem to a single parameter functional. Classically, the functional is composed of a data term and a regularization term. We introduce an improved model, where the pixel wise data term is combined with a template matching approach, which is well adapted to the case of rectified images. This modification increases the accuracy very significantly. The minimization is practically handled by solving the Euler-Lagrange equation. In our setting, the Euler-Lagrange equation is replaced by a parabolic evolution equation. Under general assumptions, we prove that this equation has a single asymptotic state, that is obtained by any initial guess.
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