Characterizing the shape of anatomical structures with Poisson's equation

@article{citeulike:2754558, abstract = {Poisson's equation, a fundamental partial differential equation in classical physics, has a number of properties that are interesting for shape analysis. In particular, the equipotential sets of the solution graph become smoother as the potential increases. We use the displacement map, the length of the streamlines formed by the gradient field of the solution, to measure the "complexity" (or smoothness) of the equipotential sets, and study its behavior as the potential increases. We believe that this function complexity=f(potential), which we call the shape characteristic, is a very natural way to express shape. Robust algorithms are presented to compute the solution to Poisson's equation, the displacement map, and the shape characteristic. We first illustrate our technique on two-dimensional synthetic examples and natural silhouettes. We then perform two shape analysis studies on three-dimensional neuroanatomical data extracted from magnetic resonance (MR) images of the brain. In the first study, we investigate changes in the caudate nucleus in Schizotypal Personality Disorder (SPD) and confirm previously published results on this structure . In the second study, we present a data set of caudate nuclei of premature infants with asymmetric white matter injury. Our method shows structural shape differences that volumetric measurements were unable to detect.}, author = {Haidar, H. and Bouix, S. and Levitt, J. J. and Mccarley, R. W. and Shenton, M. E. and Soul, J. S. }, booktitle = {Medical Imaging, IEEE Transactions on}, citeulike-article-id = {2754558}, doi = {http://dx.doi.org/10.1109/TMI.2006.881378}, journal = {Medical Imaging, IEEE Transactions on}, keywords = {poisson, shape-representation}, number = {10}, pages = {1249--1257}, posted-at = {2008-05-04 23:05:35}, priority = {2}, title = {Characterizing the shape of anatomical structures with Poisson's equation}, url = {http://dx.doi.org/10.1109/TMI.2006.881378}, volume = {25}, year = {2006} }

TY - JOUR ID - citeulike:2754558 L3 - citeulike-article-id:2754558 TI - Characterizing the shape of anatomical structures with Poisson's equation T2 - Medical Imaging, IEEE Transactions on JF - Medical Imaging, IEEE Transactions on VL - 25 IS - 10 SP - 1249 EP - 1257 N2 - Poisson's equation, a fundamental partial differential equation in classical physics, has a number of properties that are interesting for shape analysis. In particular, the equipotential sets of the solution graph become smoother as the potential increases. We use the displacement map, the length of the streamlines formed by the gradient field of the solution, to measure the "complexity" (or smoothness) of the equipotential sets, and study its behavior as the potential increases. We believe that this function complexity=f(potential), which we call the shape characteristic, is a very natural way to express shape. Robust algorithms are presented to compute the solution to Poisson's equation, the displacement map, and the shape characteristic. We first illustrate our technique on two-dimensional synthetic examples and natural silhouettes. We then perform two shape analysis studies on three-dimensional neuroanatomical data extracted from magnetic resonance (MR) images of the brain. In the first study, we investigate changes in the caudate nucleus in Schizotypal Personality Disorder (SPD) and confirm previously published results on this structure . In the second study, we present a data set of caudate nuclei of premature infants with asymmetric white matter injury. Our method shows structural shape differences that volumetric measurements were unable to detect. KW - poisson KW - shape-representation AU - Haidar, H AU - Bouix, S AU - Levitt, JJ AU - Mccarley, RW AU - Shenton, ME AU - Soul, JS PY - 2006/// UR - http://dx.doi.org/10.1109/TMI.2006.881378 ER -