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Cost function

We propose then a leat square optimization to replace the exact equality (4.1):

$\displaystyle J(u,v) = \frac{1}{2}\int_\Omega \left[ F(I_0,I_1;u,v)(x,y)\right]^2\, dx dy + \frac{1}{2} \alpha R(u,v),$ (4.2)

where $ R(u,v)$ is a spatial regularization term, and $ \alpha>0$ is the regularization factor. Finally, $ F$ is the following function:

$\displaystyle F(I_0,I_1;u,v)(x,y) = I_1(x+u(x,y),y+v(x,y))-I_0(x,y).$ (4.3)


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