%0 Journal Article
%T Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes
%A Daniel J. Tward
%A Jun Ma
%A Michael I. Miller
%A Laurent Younes
%J International Journal of Biomedical Imaging
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/205494
%X This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is on robust diffeomorphic mapping methods based on parameterized surface representations of subcortical template structures. Our parametrization of the GDAS evolution is via the initial momentum representation in the tangent space of the template surface. The dimension of this representation is constrained using principal component analysis generated from training samples. In this work, we seek to use template surfaces to generate segmentations of the hippocampus with three data attachment terms: surface matching, landmark matching, and inside-outside modeling from grayscale T1 MR imaging data. This is formulated as an energy minimization problem, where energy describes shape variability and data attachment accuracy, and we derive a variational solution. A gradient descent strategy is employed in the numerical optimization. For the landmark matching case, we demonstrate the robustness of this algorithm as applied to the workflow of a large neuroanatomical study by comparing to an existing diffeomorphic landmark matching algorithm. 1. Introduction There have been many approaches to segmentation in medical imaging, including both the active shape methods pioneered by Kass et al. [1] and template based approaches pioneered by Dann et al. [2]. For studying images made up of simple homogeneous structures such as anatomical structures, local active evolution methods [1, 3¨C5] which are encoded through their boundary representations are natural. In such methods, the complexity of the representation is reduced from an encoding based on the dimension of the extrinsic background space containing the object, to the dimension of the boundary. Given the line of work in template based computational anatomy which has emphasized the important role of diffeomorphisms for defining bijective correspondence between coordinate systems, it is natural to constrain the iterative methods of active shapes so that shape evolution preserves the original topology of the template. This is the intention of the diffeomorphic active contour (DAC) approaches taken by Younes et al. [6¨C8], including in the local evolution equations the diffeomorphism constraint. DAC methods, in a form similar to the
%U http://www.hindawi.com/journals/ijbi/2013/205494/