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Abstract.This paper studies a variational formulation of the image matching problem. We consider a scenario in which a canonical representative image T is to be carried via a smooth change of variable into an image that is intended to provide a good fit to the observed data. where ||v|| is an appropriate norm on the velocity field v(-, •), and the second term attempts to enforce fidelity to the data. In this paper we derive conditions under which the variational problem described above is well posed. The key issue is the choice of the norm. Conditions are formulated under which the regularity of v(-, ■) imposed by finiteness of the norm guarantees that the associated flow is supported on a space of diffeomorphisms. The problem (0.2) can

Abstract.This paper studies mathematical methods in the emerging new discipline of Computational Anatomy. Herein we formalize the Brown/Washington University model of anatomy following the global pattern theory introduced in [1,2], in which anatomies are represented as deformable templates, collections of 0,1,2,3-dimensional manifolds. Typical structure is carried by the template with the variabilities accommodated via the application of random transformations to the background manifolds. The anatomical model is a quadruple (0,W, X,V), the background space f2 = \JaMa of 0,1,2,3-dimensional manifolds, the set of diffeomorphic transformations on the background space W :<-> O, the space of idealized medical imagery X, and V the family of probability measures on H. The group of diffeomorphic transformations H is chosen to be rich enough so that a large family of shapes may be generated with the topologies of the template maintained.For normal anatomy one deformable template is studied, with (f1,H,X) corresponding to a homogeneous space [3], in that it can be completely generated from one of its elements, X = Tiltemp-, hemp £ For disease, a family of templates Ua I"emp are introduced of perhaps varying dimensional transformation classes. The complete anatomy is a collection of homogeneous spaces Xtotai -UQ(^a> ~Ha )-There are three principal components to computational anatomy studied herein.(1) Computation of large deformation maps: Given any two elements 1,1' £ X in the same homogeneous anatomy (fl,7i,X), compute diffeomorphisms h from one h anatomy to the other I1I'. This is the principal method by which anatomical

Theories of the pathophysiology of schizophrenia have implicated the hippocampus, but controversy remains regarding hippocampal abnormalities in patients with schizophrenia. In vivo studies of hippocampal anatomy using high resolution magnetic resonance scanning and manual methods for volumetric measurement have yielded inconclusive results, perhaps because of the normal variability in hippocampal volume and the error involved in manual measurement techniques. To resolve this controversy, high dimensional transformations of a computerized brain template were used to compare hippocampal volumes and shape characteristics in 15 matched pairs of schizophrenia and control subjects. The transformations were derived from principles of general pattern matching and were constrained according to the physical properties of f luids. The analysis and comparison of hippocampal shapes based on these transformations were far superior to the comparison of hippocampal volumes or other global indices of hippocampal anatomy in showing a statistically significant difference between the two groups. In the schizophrenia subjects, hippocampal shape deformations were found to be localized to subregions of the structure that send projections to prefrontal cortex. The results of this study demonstrate that abnormalities of hippocampal anatomy occur in schizophrenia and support current hypotheses that schizophrenia involves a disturbance of hippocampalprefrontal connections. These results also show that comparisons of neuroanatomical shapes can be more informative than volume comparisons for identifying individuals with neuropsychiatric diseases, such as schizophrenia.