Colloquium: Steve Pizer – “Representations of Anatomic Object Interior Shape to Produce Statistical Correspondence”

Representations of Anatomic Object Interior Shape to Produce Statistical Correspondence

Colloquium by Stephen M. Pizer, Kenan Professor of Computer Science

Co-sponsored by the Department of Statistics and Operations Research and the Biomedical Research Imaging Center

The input to most representations of object shape is the object boundary, and as a result many representations have been of the boundary geometry. Others have been of the deformations from a base boundary to the target boundary produced by diffeomorphic (LDDMM) methods. An improvement in producing correspondence of shape instances in a population, at least for anatomic shapes, comes from recognizing that the shape of the object interior, mediated by skeletal representations, yields important features provided by the deformation from a base shape, an ellipsoid, into the target shape. This yields a shape space made using fitted frames in the closure of the object interior in the form of vector lengths and directions and local rotations to which statistical methods are applied. The result on classifying the shape of an infant’s hippocampus as to whether some years later autistic behavioral symptoms will appear shows notably better performance than the LDDMM representation, which was thought to be the best previous scheme; the improvement is presumably due to the richer geometric features and inter-sample locational correspondences that our method provides. Moreover, my advisee Mohsen Taheri has shown that a particular form of this representation yields a shape space that includes only objects that are locally valid and thus, unlike any other representation, guarantees geometric validity of means and other important statistical measures.