Image Segmentation And Fast Algorithm Based On PDE And Variation Methods

Image processing is an interdisciplinary subject, mainly related to optics, mathematics and computer technology. Mathematical methods in the field of image processing include stochastic modeling, wavelet analysis and partial differential equations (PDE). Over the last decade, PDE based image processing and variational methods have been developing. They have a high degree of flexibility and perform well in numerical implementation and have been widely applied to image processing research.Image segmentation is one of the crucial steps in the image processing. Its purpose is to segment the image into a finite number of semantically important regions, so that we can further analyze and understand the image. This paper studies the image segmentation methods based on PDE and variational method.In this paper, we propose two segementation models, i.e. the TVg-L1model and the weighted Chan-Vese model, and implement them with fast algorithms.The first model is the TVg-L1model, which combines the classic PDE denoising model---the Rudin-Osher-Fatemi (ROF, TV-L2) model and the geodesic active contour (GAC) model. We use the split Bregman algorithm to implement the model, and compare it to the traditional gradient descent method. The results show that the proposed algorithm has a good effect even the images are contaminated by certain noise.The second model is the weighted Chan-Vese model, which is a new convex Chan-Vese model and has the both advantanges of Chan-Vese model and GAC model. We explore the split Bregman algorithm to implement the convex Chan-Vese model, and show the results. Compared to other models, this model outperforms in terms of effects and computation-time.