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where <math>\Omega</math> is the extent of the images <math>I(x, y)</math>, <math>\nabla</math> is the gradient operator, <math>\alpha</math> is a constant, and <math>\Psi()</math> is a [[loss function]].
<ref name="Fortun_Survey_2015" /><ref name="Brox_2004" />
This optimisation problem is difficult to solve owing to its non-linearity.
To address this issue, one can use a ''variational approach'' and linearise the brightness constancy constraint using a first order [[Taylor series]] approximation. Specifically, the brightness constancy constraint is approximated as,
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