where S is a regularization parameter, typically a differential smoothness penalty. This optimization problem is solved
simultaneously for all corner points because different elements share common corner points.
Finally, Park et al.  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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