Organ Shape Modeling Based on the Laplacian Deformation Framework for Surface-Based Morphometry Studies

Recently, shape analysis of human organs has achieved much attention, owing to its potential to localize structural abnormalities. For a group-wise shape analysis, it is important to accurately restore the shape of a target structure in each subject and to build the inter-subject shape correspondences. To accomplish this, we propose a shape modeling method based on the Laplacian deformation framework. We deform a template model of a target structure in the segmented images while restoring subject-specific shape features by using Laplacian surface representation. In order to build the inter-subject shape correspondences, we implemented the progressive weighting scheme for adaptively controlling the rigidity parameter of the deformable model. This weighting scheme helps to preserve the relative distance between each point in the template model as much as possible during model deformation. This area-preserving deformation allows each point of the template model to be located at an anatomically consistent position in the target structure. Another advantage of our method is its application to human organs of non-spherical topology. We present the experiments for evaluating the robustness of shape modeling against large variations in shape and size with the synthetic sets of the second cervical vertebrae (C2), which has a complex shape with holes.