Study On Medical Image Segmentation Based On Partial Differential Equations And Graph Theory

With the development of economy and technology as well as much more attention paid to public health by the government, medical imaging examination has been more and more popular. It is definitely necessary to assist doctors by giving the diagnosis through the exact and repeatable information that computer draws from the medical images. As a rising intercross subject, medical imaging analysis is developing nowadays and aiming at fulfilling this requirement. As one of most foundational and key issues, medical imaging segmentation has significant academic and practical value.In recent years, there are a great deal of improvements in image segmentation, restoration and enhancement along with the introduction of partial differential equations and graph theory. In this paper, we study on the geometric active contour model in image segmentation based on partial differential equations and the graph cuts method in image segmentation based on graph theory. For sake of minimizing complexity of algorithm and improving the veracity of segmentation, we propose two improved geometric active contour models and validate the efficiency and effectivity of our methods through the simulation images and clinical knee images. Finally we improve graph cuts algorithm based on the fuzzy c-means clustering for the bone tumor MRI segmentation. The main jobs we complete are as follows:(1) We propose a multiphase Chan-Vese model incorporating gradient information. Compared to the original Chan-Vese model, there are two improvements. First, we add the gradient information into the region information, so the new level sets methods will settle the segmentation problem of inhomogeneous images. Second, we can maintain a signed distance function around the zero level set completely without the re-initialization process in the level sets evolution.(2) An intergrated active model is proposed by blending geodesic active contour (GAC) model with the regional statistic information. First we compute the Bhattacharyya distance between object and background pixels during the evolution and receive the global likelihood information. After that, in the framework of functional derivative and Variational level sets, we construct the velocity of evolution based on regional distribution which is combined with the geodesic active contour model. It's turning out that with the operation of new restriction, the intergrated model will improve the drawback of boundary leaking problem from GAC model as well as the performance of anti-noise. Finally three-dimensional knee model is completed with the results of segmentation.(3) Because of the gradient descent method which is used in the partial differential equations method for minimizing energy functional, it's prone to plunge into the local optimal solution. To overcome this problem, we realize the graph cuts method to process global optimization, improve the data energy function by fuzzy c-means clustering and do some elementary research on the bone tumor segmentation for computer aided diagnoses.