Abstract

Computational Anatomy: Computing Metrics on Anatomical Shapes

M. Faisal Beg
Johns Hopkins University, Center for Imaging Science
Biomedical Engineering

Joint work by: M. Faisal Beg, Michael Miller, Laurent Younes

In this talk, I will present the problem of quantifying anatomical shape as represented in an image within the framework of the deformable template model. Briefly, the deformable template model approach involves selecting a representative shape to be the reference or the template representing prior knowledge of the shape of the anatomical sub-structures in the anatomy to be characterized and comparing anatomical shapes as represented in given images also called as the target to the image of the template. Comparison is done by computing infinite-dimensional diffeomorphisms (smooth and invertible transformations with a smooth inverse) as a flow between the images that will deform the template image to match the target image. The problem can be formulated as an optimization problem by defining a cost as comprised of a term representing the energy of the velocity of the flow field and a term that represents the amount of mismatch between images being compared. By estimating the velocity-fields that will minimize this cost, a diffeomorphic transformation between the images is computed. The construction of diffeomorphisms between the images allows metrics to be calculated in comparing shapes represented in image data. Transformations "far" from identity represent larger deviations in shape from the template than those "close" to the identity transformation.

I will present the Frechet derivative of the proposed cost functional and an algorithm to estimate the velocity fields that minimize the cost via a standard steepest descent technique. I will also discuss some computational and parallelization aspects of this algorithm and show some results on image matching and the metrics computed on mitochindrial and hippocampal shapes by using this approach. An example of the possible clinical applications of this work are in the area of diagnosis of neuropsychiatric disorders such as Alzheimer's disease, Schizophrenia, and Epilepsy by quantifying shape changes in the hippocampus.