Image Segmentation Based On Partial Differential Equation

Image segmentation is one of the key problems in Computer Vision. The purpose of image segmentation is to separate the interested objects from the image and obtain the edges of the objects. Many segmentation methods are available now while few can apply for any type of images. Recently, variational methods and partial differential equation (PDE) methods bring new vitality for image segmentation and many successful models have been proposed.In this thesis, image segmentation methods based on PDE are studied. First, some prerequisite mathematical foundations and classical variational segmentation models are introduced. Then an improved method for level set evolution without re-initialization is proposed. Numerical experiments show the new method can detect multiple edges in the image precisely and efficiently. Finally, by incorporating the histogram information of interested objects, a new model for tracking moving objects is presented in video. Further, the image segmentation models for two-phase texture image and four-phase texture image are proposed with the help of histogram matching. And carefully designed algorithms are given by solving these models. The algorithms have many advantages, for example, simple structure of level set, without re-initialization, fast segmentation speed, high precision. Experimental results for real images and images created by computer show the performance of the algorithms.