A technique for modeling shape changes in a time series of biological images of arbitrary dimension is described. The technique consists of first segmenting the image to locate the specimen, and then parametrizing the specimen in the initial image with an orthogonal material coordinate system. The deformation of the material coordinate system caused by the changing shape of the specimen is then solved for by minimizing an energy functional. The energy functional is a linear combination of a brightness continuity term and a shape change term. A parameter lambda, weights the brightness continuity against the shape change smoothness. The best value to use for lambda is chosen as the value that minimizes the mean square error between the image derived from the calculated shape change parameters and the corresponding actual image. A two-dimensional implementation by finite differences is given. Results from both two-dimensional confocal images, and two-dimensional synthetic images are presented. Our early work on a three-dimensional implementation is given.