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where S is a regularization parameter, typically a differential smoothness penalty. This optimization problem is solved

FIGURE 10 The finite element model of Young et al. [7] divides the LV into 16 elements, shown here before and after deformation. [Courtesy of A. Young.] From [7] with permission. © 1995 IEEE.

simultaneously for all corner points because different elements share common corner points.

Finally, Park et al. [41] propose a hybrid method in which a few global motions are defined as in field fitting, but the parameters defining those motions vary from element to element. The global motion terms reflect basic LV motions such as radial contraction and twisting. The fine scale variation in motion is determined by the spatial variation of the parameters.

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