Physics-based Deformable Modeling For Medical Image Segmentation

Medical image segmentation, as the first step of medical image analysis, is fundamental to surgical planning and simulation. It is the key to the 3D construction of normal or abnormal structure and quantitive analysis such as structure analysis and motion analysis. It also forms the basis of 3D visualization, image guided surgery, motion estimation, image registration, tissue state assessment, etc. Accurate segmentation is important for the doctor to reach proper clinical diagnoses.Deformable model, especially Snake, a promising and vigorously researched computer-assisted medical image analysis technique is widely used in segmenting, matching, and motion tracking. Deformable modeling only takes the perspective of mathematics, which omits the important information from the characteristic of the material itself. Physics-based deformable model is introduced in this paper which combine geometry, physics, and approximation theory together by taking the characteristic of the material into consideration, such as Young's modulus and Poisson's ratio. Deformation process is governed by basic laws of non-rigid motion.As for the numerical method, we use FEM methods and meshfree methods respectively. The base idea of FEM is to discretize the domain of interests into elements which provide spatial relationships between the sampling nodes. The main computational power of the FEM results from the fundamental idea of replacing a continuous function defined over the entire domain by piecewise approximations over a set of finite number of geometrically simple domains. Meanwhile, the recently developed meshfree methods represent the interested spatial domains with only a set of nodal points but without any mesh constraints which eliminate at least part of the mesh structure by constructing the approximation of the field function and the discrete system equations entirely in terms of the nodes. They can more naturally handle very large deformation and discontinuity. Experiments on synthetic and real images show their robustness and accuracy in medical image segmentation.