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\hat{\boldsymbol{\alpha}} = \arg \min_{\boldsymbol{\alpha}} \sum_{(x, y) \in \mathcal{R}} g(x, y) \rho(x, y, I_1, I_2, u_{\boldsymbol{\alpha}}, v_{\boldsymbol{\alpha}}),
</math>
where <math>{\boldsymbol{\alpha}}</math> is the set of parameters determining the motion in the region <math>\mathcal{R}</math>, <math>\rho()</math> is data cost term, <math>g()</math> is a weighting function that determines the influence of pixel <math>(x, y)</math> on the total cost, and <math>I_1</math> and <math>I_2</math> are frames 1 and 2 from a pair of consecutive frames.<ref name="Fortun_Survey_2015" />
The simplest parametric model is the [[Lucas-Kanade method]]. This uses rectangular regions and parameterises the motion as purely translational. The Lucas-Kanade method uses the original brightness constancy constrain as the data cost term and selects <math>g(x, y) = 1</math>.
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