SYMMETRIC SHAPE AVERAGING IN THE DIFFEOMORPHIC SPACE

We provide a method for symmetric (unbiased) computation of optimal shape templates in the diffeomorphic space (Diff). We explicitly minimize the Diff metric distance by allowing an unbiased statistical evolution of the initial conditions defining the set of diffeomorphisms at time zero. This procedure is distinct from related methods that do not explicitly compute symmetric shape averages or only average the appearance component (intensity) in an unbiased way. Explicitly minimizing the diffeomorphic metric distance improves the sharpness and accuracy of the derived template. We illustrate this accuracy by computing optimal templates from a simple dataset of ellipses. Our shape optimizing method yields results that reproduce the analytically known optimal template. A related method that uses diffeomorphisms to find an unbiased optimal intensity template does not yield the theoretical result. We show that the improved performance occurs not only in synthetic studies but also when deriving templates from real data