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→Parametric Models: Started the parametric model section in earnest |
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==== Parametric Models ====
Instead of applying the regularization constraint on a point by point basis as per a regularized model, one can group pixels into regions and estimate the motion of these regions.
This is known as a ''parametric model'', since the motion of these regions is [[parameter|parameterized]].
In formulating optical flow estimation in this way, one makes the assumption that the motion field in each region be fully characterised by a set of parameters.
Therefore, the goal of a parametric model is to estimate the motion parameters that minimise a loss function which can be written as,
:<math>
\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" />
A straightforward choice for the data cost term <math>\rho()</math> is...
===Learning Based Models===
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