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The optimization problem can now be rewritten as
:<math>E = \iint_\Omega \Psi(I_x u + I_y v + I_t) + \alpha \Psi(|\nabla u|) + \alpha \Psi(|\nabla v|) dx dy. </math>
For the choice of <math>\Psi(x) = x^2</math>, this method is the same as the [[Horn-Schunck method]].<ref name="Horn_1980"/>
Of course, other choices of cost function have been used such as <math>\Psi(x) = \sqrt{x^2 + \epsilon^2}</math>, which is a differentiable variant of the [[Taxicab geometry |<math>L^1</math> norm]].<ref name="Fortun_Survey_2015" />
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