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Groupwise registration and statistical analysis of medical images are of fundamental importance in computational
anatomy, where healthy and pathologic anatomies are compared relative to their differences with a common
template. Accuracy of such approaches is primarily determined by the ability of finding perfectly conforming
shape transformations, which is rarely achieved in practice due to algorithmic limitations arising from biological
variability. Amount of the residual information not reflected by the transformation is, in fact, dictated by
template selection and is lost permanently from subsequent analysis. In general, an attempt to aggressively
minimize residual results in biologically incorrect correspondences, necessitating a certain level of regularity in
the transformation at the cost of accuracy.
In this paper, we introduce a framework for groupwise registration and statistical analysis of biomedical images
that optimally fuses the information contained in a diffeomorphism and the residual to achieve completeness of
representation. Since the degree of information retained in the residual depends on transformation parameters
such as the level of regularization, and template selection, our approach consists of forming an equivalence class
for each individual, thereby representing them via nonlinear manifolds embedded in high dimensional space. By
employing a minimum variance criterion and constraining the optimization to respective anatomical manifolds,
we proceed to determine their optimal morphological representation. A practical ancillary benefit of this approach
is that it yields optimal choice of transformation parameters, and eliminates respective confounding variation in
the data. Resultantly, the optimal signatures depend solely on anatomical variations across subjects, and may
ultimately lead to more accurate diagnosis through pattern classification.
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