| Locality is an important but oft-ignored aspect of shape asymmetry quantification, and segmentation is one method by which to make the locality of an analysis explicit. We have thus formulated an approach to surface registration and shape comparison which features an integrated segmentation component for the purpose of simultaneously identifying and separating regions by their evolving deformation characteristics. In the first instantiation, we achieve this effect through an adaptation of the Chan-Vese approach for image segmentation to the problem of segmenting the Riemannian structures of the very surfaces comprising the domain of the segmentation. We have successfully used the method's output on hippocampal pairs in an epilepsy classification problem, demonstrating improvement over global measures. Noting that a Chan-Vese-based approach to simultaneous segmentation and registration is inherently limited, we have also developed a unified approach to segmentation, smoothing, and nonrigid registration of images via extension of the Mumford-Shah functional, devised in such a way as to be applicable symmetrically and consistently to multiple (two or more) inputs. To conclude, we propose an extension of this unified framework (dubbed "USSR") to the previously considered problem of 2D surface shape analysis (asymmetry quantification and localization), conferring the benefits of unbiasedness, consistency, multiple input processing, and nontrivial data field reconstruction. |
