Numerical Implementations Of Two Variational Models For Image Segmentation

Image segmentation is one of fundamental and important tasks in image analysis and computer vision. For an image, the segmentation goal is to separate the image domain into different regions, each of which has a consistent trait(intensity, color or texture, etc) that is different from other regions in the image. Recently, variational models for image segmentation have been widely paid attention by many researchers, because of their variable form, flexible structure and excellent performance. In general, variational models that are composed of several energy functionals, each of which reflects some of the characteristics of image to be segmented(gray, edge, color and texture, etc.), can also be subject to the shape and characteristics of the target of a priori knowledge. Minimizing the energy function makes segmentation curve(or surface) evolve, and improve the alignment between the current image segmentation and image data, thus obtain the desired segmentation result finally.In this thesis, two known variational models for image segmentation are again implemented by using different methods from the original ones. The main works are as follows:(1) By using radial basis function interpolation, we resolve a known convex variational level set model for two-phase image segmentation.This convex variational model was proposed in the journal [Signal Processing]. This authors designed a numerical method to solve the corresponding equation Euler-Lagrange. We resolve the model by using the method of Radial basis function interpolation, which converts the evolution of level set function process into the solution of system of linear equations. The proposed method needs less iteration numbers than the original method, while the level set function obtained by our method better approximates to a binary function.(2) Borrowing from the idea of barrier methods, we resolve a constraint convex variational models for image segmentation.This constraint variational model was proposed in the journal [SIAM J. Appl. Math.]. Borrowing from the idea of barrier methods, we add two barrier functions into the energy functional of the original model. The original constraint variational model is thus converted into an unconstrained optimization problem, which is solved by using the alternate minimization scheme. The experiment results show that the proposed method is better than the split Bregman algorithm that is used in the original model.