Image Segmentation Technology Based On Curve Evolution And Applications

The researches on image processing based on Partial Differential Equation (PDEs) began in the 1960s' and 1970s', and PDEs were introduced for the perspective of noise removal and image restoration. However, it was not until 1990s' that PDEs were systematicly introduced to the field of image processing, and formed a relatively integrated theory system combined with mathematic morphology and affine geometry. Now, PDEs have been widely used in many aspects of image processing and computer vision, including image segmentation, tracking moving objects, object edges detection, image interpolation and so on, which have obtained many expected results.The "Snake" model, proposed by M. Kass in 1987, provides not only a powerful tool for the image analysis, but also an effective framework for the computer vision problem. The "Snake" model changes the mode of traditional image processing method. It accomplishes the image processing task using the curve evolution model, which is described as the minimization of an energy function. With the development of the method, the deficiency of the "Snake" model is exposed in the process of expression to the image and the numerical algorithm. How to modify and perfect the curve evolution method, and speed the velocity of the computation become the hotspot of the field.The paper discusses the devlopment of the model, and analyzes the principle and deficiency of the "Snake" model. Geometric and geodesic active contours based on the level set theory are concerned. The active contours without edges are emphasized, which are proposed by Chan and Vese, and their implementation is developed.In this paper, beginning from the fundamental level set theory, many problems are discussed here, such as the level set expression on the PDE and the numerical algorithm for the level set method. The emphasis is on the fast scheme for solving the level set method and numeric implementation. Two new methods are presented in the paper, one combines the developed fast marching method and narrow band to inplement initialization of the level set, and the other presents the new difference scheme-the additive operator splitting, to reduce the computation complexity. And then, the discussion in the paper validates the scheme. Besides, these methods have been accomplished in some models, especially in multi-phase level set method.