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Constant brightness assumption

Let $ \Omega\subset \mathbb{R}^2$ be the rectangular domain where the images are defined. The motion between the instants $ t_0$ and $ t_1$ where the images are $ I_0$ and $ I_1$ is then the vector field $ (u,v)$ such that for every point $ (x,y)\in\Omega$ ,

$\displaystyle I_1(x+u(x,y),y+v(x,y)) = I_0(x,y).$ (4.1)

A vector field satisfying equation (4.1) is not unique, this is known as the aperture problem in optical flow. Moreover, measurement errors make the equality (4.1) unlikely to be strictly satisfied.


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