Theory Of Variational Level Set Method And Its Application To Medical Image Segmentation

Medical image segmentation is a key technique and extracts the objective of interest, that is, the abnormal anatomic structures from medical images. It is an important component of computer-aided diagnosis used by the clinic doctors.The variational level set method is a class of curve evolution methods based on the geometry active contour model without parameters. The level set segmentation, essentially, embeds the geometrical evolution problem of lower dimension into higher dimension. And it is numerically stable and capable of describing the topology change of the contour. And so it can segment the medical image with complex topological changes, high noise and lower contrast.This dissertation is deeply developed around the improvement of level set segmentation method for the complicated medical images. The main contributions can be summarized as follows:(1) An improved level set segmentation model without re-initialization is developed in the energy function respect. Liver segmentation on computed tomography (CT) images is a challenging task due to the anatomic complexity and the imaging system noise. So, we develop a region-based level-set approach, which has many advantages over the conventional active contour models by combining C-V model and Li's model. First, the improved model can get much smoother contour by adding a signed distance preserving term to evolution PDE and has good robustness to the presence of weak boundaries and strong noise. Second, the difference scheme can be chosen freely and enhance the algorithm flexibility. Third, we can obtain accurate extracted liver image by morphological filters. Therefore, our algorithm can be applied to detect the internal malignant structure of liver image. This modified level set function speeds up the segmentation process significantly. Experimental results show that the proposed method gives automatic and accurate liver structure segmentation.(2) A new level set method for fast segmentation based on a single parameter is presented in the evolving PDE respect. The traditional level set methods for image segmentation need inevitably too many parameter adjustment and have usually lower computationally implementation. To solve this problem, the proposed method improves the Chan-Vese (C-V) PDE model based on the Mumford- Shah Model, by adding a penalized energy term and replacing the dirac function with the norm of level function gradient, and so it constructs a new PDE model with better globe optimization and no re-initialization. Besides, only the parameter of the length term is reserved in the model and an evolution criterion is introduced for the sake of the value rules of this single parameter as well as the accuracy of segmentation and semi-automation. The experimental results of synthesized and biomedical images show that the new method is faster and more robust. Moreover, the new method has more extensive adaptability on account of the zero level set function being set anyplace freely and the single parameter adjustment convenience.(3) A new iteration algorithm for an improved level set method is proposed. At the beginning, to the given method based on C-V model, the adding operator split (AOS) algorithm is introduced for the evolution. And then we develop new semi-implicit schemes to shorten the time of every loop without matrix-inversion. An evolutional criterion for ending segmentation is introduced during the iterating process. Experimentations for synthesized, biomedical images and video sequences show that the new approach is faster and more accurate than the traditional level set methods, and satisfy the real time requirement. Moreover, the initial level set curve can be set freely and the parameter can be adjusted conveniently, and so the proposed approach can be applied in practice more flexibly and interactivity.(4) A fast global minimization segmentation model based on total variation is presented around function modeling and algorithm constructing. First, an Active region contour model is developed by Maximum A-posterior Probability (MAP), and then a total variation model based on gradient information is constructed by the hint of geodesic active contour (GAC) model. So a new segmentation model is given by combining the two models. We establish theorems with proofs to determine the existence of the global minimum of this active contour model. From a numerical point of view, we propose a new practical way to solve the propagation problem toward object boundaries through a dual formulation of the total variation norm. It avoids the usual drawback of initializing and re-initializing. We apply our segmentation algorithms on medical images, and the model is found the convergence steady, good adaptability, high precision and well processing to lower contrast medical image.