Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Registering a multisensor ensemble of images
IEEE Transactions on Image Processing
Exploring cortical folding pattern variability using local image features
MCV'10 Proceedings of the 2010 international MICCAI conference on Medical computer vision: recognition techniques and applications in medical imaging
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Existing approaches to computational anatomy assume that a perfectly conforming diffeomorphism applied to an anatomy of interest captures its morphological characteristics relative to a template. However, biological variability renders this task extremely difficult, if possible at all in many cases. Consequently, the information not reflected by the transformation, is lost permanently from subsequent analysis. We establish that this residual information is highly significant for characterizing subtle morphological variations and is complementary to the transformation. The amount of residual, in turn, depends on transformation parameters, such as its degree of regularization as well as on the template. We, therefore, present a methodology that measures morphological characteristics via a lossless morphological descriptor, based on both the residual and the transformation. Since there are infinitely many [transformation, residual] pairs that reconstruct a given anatomy, which collectively form a nonlinear manifold embedded in a high-dimensional space, we treat them as members of an Anatomical Equivalence Class (AEC). A unique and optimal representation, according to a certain criterion, of each individual anatomy is then selected from the corresponding AEC, by solving an optimization problem. This process effectively determines the optimal template and transformation parameters for each individual anatomy, and removes respective confounding variation in the data. Based on statistical tests on synthetic 2D images and real 3D brain scans with simulated atrophy, we show that this approach provides significant improvement over descriptors based solely on a transformation, in addition to being nearly independent of the choice of the template.