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Repeating this process for time tn+1; using the solution for time tn as a seed, results in a recursive procedure that maintains the correspondence of the snake to a specific initial tag plane.

In this formulation, the problem boils down to finding the optimal set of displacements. Therefore, the energies £jnternal and £image are defined in terms of d(k, tn). First, the internal energy of the kth point is given by

FIGURE 5 Template matching: First a search region, such as the white box, is selected from a tagged image (a), shown here at high magnification. Then, the image intensities of pixels within the search region are fitted to a template (b), which provides the location of the tag line s0. Repeating this process and tracking over time produces a complete set of identified tag points with corresponding values of m (c). Also shown are the identified boundaries of the myocardium.

Interpolation of image brightness between pixels is used to provide subpixel precision. Finally, the solution for displacement is given by

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