Variational Level Set Models For Image Segmentation

With the rapid development of the information and computational science, there are a large number of digital images in application. How to take an effective and quick way to extract useful information, e.g., image segmentation, becomes a very important issue. Level set methods have shown their effectiveness in image segmentation. The basic idea is to deform a curve, surface or image under a partial differential equation (PDE) with initial and boundary conditions, and obtain the desired segmentation results as the solution of the equation. The evolution PDE of level set function can be obtained from the problem of minimizing a certain energy functioned defined on the level set functions, such methods are known as variational level set methods.This thesis concentrates on variational level set methods for image segmentation; our studies are concentrated in the following three topics:1. Study on the initialization problem of level set function. An adaptive variational level set model is proposed.A problem with most of level set models is contour initialization. Because the segmentation results typically depend on the selection of initial contours, these methods need user intervention to define the initial contours professionally. This means that they may be fraught with the problems of how and where to define the initial contours. Up to now, it is still a great challenge to find an efficient way to tackle the initialization problem.We propose an adptive variational level set model to address this problem, in which a novel variational formulation (external energy) for the level set function is presented. This external energy forces the level-set function to have the opposite sign along the edges at convergence. It is then incorporated into a variational level-set formulation with two extra regularization terms (internal energy). The resulting evolution of the level-set function is the gradient flow that minimizes the overall energy functional. Because of the external energy, the level-set function can be initialized to any bounded function (e.g., a constant function), which completely eliminates the need of initial contours. This implies that the new formulation is robust to initialization or even free of manual initialization.2. Study on the regularization problem of the zero level curves. A weighted p(x)-Dirichlet integral regularized variational level set model is proposed. As we known, level set methods must impose some constraints on zero level curves usually due to noise. Length regularization, H 1 regularization , W 1,∞regularization and weighted p-Dirichlet integral regularization are popular choices of the geometric constraint on zero level set, but these regularizations cannot reflect the local property of image. This problem has limited their applications in pratice. We propose a novel variational level set formulation for image segmentation. A weighted p(x)-Dirichlet integral is presented as a geometric constraint on zero level set, which is used to diminish the influence of image noise on level set evolution while ensuring the active contours not to pass through weak object boundaries. The idea behind the new energy integral is that the amount of regularization on the zero level set can be adjusted automatically by the variable exponent p(x) to fit the image data. The proposed model has been applied to a wider range of medical images with intensity inhomogeneity with promising results.3. Study on the problem of infrared images segmentation. A tensor diffusion level set model is proposed.As a key technique in infrared (IR) alert and automatic target recognition system, IR targets detection has became one of the most important topics in the field of IR image processing. However, IR targets detection is yet a difficult task. This difficult can be arises from the fact that most IR images are characterized by complexbackground.A tensor diffusion level set method is presented to extract infrared (IR) targets contour under a sky-mountain-water complex background. The proposed model combines tensor diffusion operator and the eigenvalues of tensor-image into a common energy minimization level set framework. By incorporating the information of image tensor diffusion operator into the external energy term, the level set function can move in a specific way. And eigenvalues of tensor-image are used for the regularization of zero level curves in order to diminish the influence of image"clutter"and noise. An additional benefit of the proposed method is robust to initial conditions. Experimental results show very good performance of the proposed model for IR targets contours extraction.