Abstract The paper presents a variational framework to compute first and second order statistics of an ensemble of shapes undergoing deformations. Geometrically “meaningful ” correspondence between shapes is established via a kernel descriptor that characterizes local shape properties. Such a descriptor allows retaining geometric features such as high-curvature structures in the average shape, unlike conventional methods where the average shape is usually smoothed out by generic regularization terms. The obtained shape statistics are integrated into segmentation as a prior knowledge. The effectiveness of the method is demonstrated through experimental results with synthetic and real images.

Key Words: 2D medical image, image segmentation, deformable models Medical image segmentation is one of the most actively studied fields in the past few decades. As the development of modern imaging modalities such as magnetic resonance imaging (MRI) and computed tomography (CT), physicians and technicians nowadays have to process the increasing number and size of medical images. Therefore, efficient and accurate computational segmentation algorithms become necessary to extract the desired information from these large data sets. Moreover, sophisticated segmentation algorithms can help the physicians delineate better the anatomical structures presented in the input images, enhance the accuracy of medical diagnosis and facilitate the best treatment planning. However, due to the specific and complex requirements of biomedical image segmentations, general image segmentation algorithms are either not applicable or need to be revised for accomplishing this image analysis task. Combining the medical knowledge with the techniques from modern mathematics, physics and biomechanics,