Image Segmentation Technology Based On Partial Differential Equation And Its Applications

Images reflect the world and its objects. The target of image segmentation is to isolate the objects in an image, and get the boundaries of the objects. There are large research works about how to detect the objects in an image quickly and accuracy in the fields of medicine, Military and industry. Recently years, with the support of the Partial Differential Equations theories, image segmentation have entered into a new study field. The major goal of this dissertation is to explore and discuss the edge detection function in the active contour models and apply the research results into the software developed with the active contour models.In the beginning of this paper, we made a survey in image segmentation and classified the existing segmentation methods in classic approaches. After this chapter, we discussed the relationship between the mathematic models with the image segmentation and explained the work principles of the active contour models based on the snakes model of Kass et al,. We selected the geometric and geodesic active contour model of Caselles as our researching objects in next steps . According to the capacity of the stopping function in the two models, we made a specific discuss about its function and then analyzed how to select a functions as the edge detector. In many literatures about the active contour models, the edge detection function is only defined a regular monotonic decreasing function. In our study, different functions are specified as the edge detectors for the images with different boundaries characteristics based on our research works.We added a new control parameter into the stopping function in order to make the image processing using active contour models can get better results. As for the images with different boundaries, we can set the responding control parameter and edge detector to deal with the actual situation. At the same time, operation explains and theory discussions were presented.Besides the level-sets numerical algorithm, AOS(additive operator splitting) schemes were introduced to implement implicit active contour models. The strictly diagonally dominant tridi-agonal linear systems which imported from AOS schemes can be solved very efficiently with a Thomas algorithm. This algorithm makes up the low efficiency result from the level-set's big compute works to some extent.While studying on active contour models and improving the edge detect function, we accomplished the related algorithms with C++ tool on the Windows platform, and designed a application system based on geometric and geodesic active models. Using this application system we compared the classic image segmentation approaches with the PDE's. And validate our discussion about the proposed edge detectors and control parameter selection by present some experimental results and data samplings.