Computation of an Average Atlas using LDDMM and Geodesic Shooting

January 31, 2006
Location: SFU, EAA 1100
Presenter: Dr. Faisel Beg, Assistant Professor of School of Engineering Science, SFU

Average 3D digital atlases are important in various aspects of Computational Anatomy (CA). Typical applications of digital atlases include their use in providing a template anatomy for registration of the other members in the anatomical ensemble and establishing a standard coordinate system (akin to an origin) for statistical analysis of structural and functional variations observed in the population. Preceding the statistical study of anatomical variation in CA, transformations that allow the placement of different members of the anatomical ensemble into a common coordinate system are computed. The provisional template image to which the ensemble is transformed has often been chosen, for the lack of an averaged template, to be one representative member of the ensemble. However, an important feature of good atlases is that they are representative of the entire population, and include information from a set of images acquired from the population rather than being based on a single chosen proviso-template, and choosing and basing statistical analyses on a single image is said to introduce bias to this preferred common coordinates, specially in settings where the transformations are non-invertible. Therefore, averaged-atlas computation must involve the averaging of the anatomical ensemble in a meaningful way to ensure that the outcome remains representative of the topological and shape characteristics of the ensemble.

In this talk, I will discuss the challenges in atlas computation and describe the computation of an average atlas using Large Deformation Diffeomorphic Metric Mapping (LDDMM) and geodesic shooting where the velocity vector fields transforming a provisional template to the ensemble are averaged and evolved via shooting using the equation for the geodesic conservation of momentum to give the average atlas. This guarantees that the averaged atlas so computed remains within the permissible shape space of the anatomical ensemble being averaged.

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