Image Segmentations Based On Partial Differential Equations

Image segmentation means extracting interested objects from an image, and it is one of the key issues in image processing. Firstly, image segmentation is a process that segment image domain into a set of connected regions, each region having the same or similar features. Feature of an image means a remarkable attribute of an image.There are many different methods for image segmentation, and the segmentation method based on PDE is one of the most popular at present. Compared to traditional image segmentation, PDE-based method involves too many calculations. But the flexible numerical method has good stability when discretizing PDE. Besides, it can carry out high-quality image restoration and precise image segmentation. Active contour models based on variational method and level set method reflect the advantages of PDE method. Thus, the active contour models have gained more and more attentions in image processing field, and are widely used in other areas of imaging.In this dissertation, we first review a relative knowledge of mathematics and image segmentation. And then, we present respectively the improvement of C-V model and the model based on inter-dissimilar.The main results of this dissertation are summarized as follows:(1) Fast C-V models. We find that the evolving speed of the contour is closely related to the absolute difference between the two regions (foreground and background). Therefore, we propose a fast C-V model by magnifying the absolute difference between foreground and background. The experimental results show that this model has faster convergence and it reduced a lot of iterations.(2) C-V incorporated with local entropy. Intensity changes are crucial for accurate segmentation of many images, thus we propose a new model which incorporates local entropy into C-V. The experimental results show that this model can obtain better results with respect to images with noise, complex background or inhomogeneous.