The field of computational anatomy has developed rigorous frameworks for analyzing anatomical shape, based on diffeomorphic transformations of a template. However, differences in algorithms used for template warping, in regularization parameters, and in the template itself, as well as in other variables, lead to different representations of the same anatomy. Variations of these parameters are considered as confounding factors, since they lead to different descriptions of the same exact shape. Recently, extensions of the conventional computational anatomy
framework to account for such confounding variations has shown that learning the equivalence class derived from the multitude of representations of an individual anatomy can lead to improved and more stable morphological
descriptors. Herein, we follow that approach, estimating the morphological appearance manifold obtained by varying parameters of the template warping procedure. Our approach parallels work in the computer vision field, in which variations lighting, pose and other parameters leads to image appearance manifolds representing the exact same figure in different ways. The proposed framework is then used for groupwise registration and statistical analysis of biomedical images,
which employs a minimum variance criterion to perform manifold walking, i.e. to traverse each individual’s morphological appearance manifold until the representations of all individuals in a group come as close to each other as possible. Effectively, this process removes the aforementioned confounding effects and potentially
leads to morphological representations that reflect purely underlying biological variations, instead of variations introduced by modeling assumptions and parameter settings. The nonlinearity of a morphological appearance
manifold is treated via local linear approximations of the manifold via PCA.
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