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A technique for modeling shape changes in microscopic images is described. The technique consists of first segmenting the image to locate the specimen and the parametrizing the specimen in the initial image with an orthogonal material coordinate system. The deformation of the material coordinate system caused by the motion of the specimen is then solved for by minimizing an energy functional which is derived here. Results from both synthetic and real two-dimensional images are presented. The foundations of a three-dimensional implementation are given. A two-dimensional implementation is demonstrated while keeping sufficient generality for an application to three-dimensional dynamic confocal microscope images.
Bartels et al. (Fri,) studied this question.