| Contents |
| We consider the segmentation problem for some motion analysis in computer vision. In the variational framework the segmentation of images mainly results from the minimization of the Mumford-Shah functional. This is performed by solving some nonlinear elliptic PDEs (e.g. the Ambrosio and Tortorelli approximation formulation). A second class of methods is based on TV-model where the segmentation is achieved with piecewise constant solution. For the optic flow estimation, such methods of segmentation extend with an additional difficulty relying to the vectoriel character of the problem.
We develop a different approach based on the minimization of a linear functional with a spatially varying regularization parameter. The regularization varying parameter acts as a phase field function and is determined by an adaptive method which allows us to select locally its values and to achieve the segmentation of the optic flow.
We analyze the method in the framework of the $\Gamma$-convergence to explain why such an approach leads to the minimization of the Mumford-Shah functional.
In the same spirit we consider the problem of edge-enhancement with the total variation and show that our method allows us to obtain pre-segmented flow. |
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