Level Set Active Contour Models In Image Segmentation

In human life, image is always one of the important ways for people to acquire and exchange information. And in the modern information society, processing and analyzing images by computer becomes more and more import. Image segmentation is a fundamental task and an important precondition for image processing and analyzing. It is also an important precondition for computer vision and pattern recognition as well. Therefore, it has always got more attention from researchers. Generally speaking, image segmentation is to divide one image into several non-overlapped regions according to some similarity criteria, and in the same regions the image is homogeneous while in the different regions is obviously distinct.So far, there have been lots of image segmentation algorithms. Among these algorithms, active contour model is an outstanding model which attracted much researcher's attention. By this model, the problem of image segmentation was converted to an energy minimization problem, and was produced through a procedure of curve evolution. There are two basic types of active contour model:parameter-based active contour model and level-set based active contour model. Parameter-based active contour model, which is in the early stage of active contour model, represents curves and surfaces explicitly in there parametric forms. This kind of representation is simple to understand, but can't adapt topology changing during evolution, which make it hard to segment sophisticated images. Level-set based active contour model, on the other hand, combines level set method with active contour model, and performs image segmentation by updating level set function indirectly. Level-set based active contour model has some advantages:Firstly, it implicitly represent curve by level set function, which make it adapt topology naturally during evolution. Secondly, level-set based curve evolution is essentially to solve a partial different equation, which is theoretically supported by some strong mathematical backgrounds and can be easily extended to higher dimensional case.On the other hand, we also note that the research on the level-set based active contour model is on a primary stage, and there are many questions to be solved. So, it is essential to continue researching on this kind of model.The main works and innovations in this thesis can be summarized as follows:(1) We comprehensively introduced the research situation of the level-set based active contour model, summarized completely the mathematical principle of level set method and curve evolution theory.(2) According to the characteristic of level set iteration, we proposed a termination algorithm for level set iteration. The method to implementing curve evolution through level set method is essentially insert evolving curve into a higher level set function implicitly; achieving curve evolution through updating level set function. For it increased the dimension of problem space, this method suffered a defect of costly computation. Level-set based active contour model update the level set function through iterative process. The final segmentation result is depending on the number of iteration:on the one hand, with more iteration the result became better; on the other hand, with more iteration evolving curve moves more slightly while time consuming increases proportionally. Furthermore, the iteration process is apt to a local minimum. GCBAC algorithm, a globally optimal algorithm, gains a lower time complexity of o(n1,2) by converting the inner and outer contour into the single source and sink point for graph cuts. Then, we propose an iteration stopping algorithm that combining graph cuts method and level set method, which not only decreases the numbers of iteration effectively but also avoid the local minimum. And it provides us an approach to stop the level set iteration.(3) We proposed an improved geometric active contour model based on the region information. The traditional geometric active contour model, the first level-set based active contour model, controls the level set evolution (i.e. curve moving) by a gradient-based speed stopping function. Just because the speed stopping function got the value of 0 on the object's boundary that makes the evolving curve's driving force be 0 and the curve stop on the object's boundary. However, because the speed stopping function is based on the gradient of the image, this model can't segment the image with blurred boundaries and be sensitive to noise. We improved the traditional model by constructing a region-base signed pressure function, which has opposite value inside and outside of the object region. So, it can control the curve evolution:inside the object region expands the evolving curve and outside the object region shrink the curve. We then substitute this function for the speed stopping function in the traditional geometric active contour model. The experiments shows that the improved model not only segment the object with blurred edges, be immune to noise, but also can drive the evolving curve bi-directly.(4) We improve the Chan-Vese model by embedding an energy term based local image information. Chan-Vese model is a typical region-based active contour model. It is based on the energy function in Mumford-Shah model. It assumes that the region of object and background are intensity homogeneous, so that simplify the Mumford-Shah model by fitting the object and background area as constant value separately. Chan-Vese model is anti-noise and has the ability to detect the blurred edge and the inner edge of the object. But it gives poor performance on image with intensity inhomogeneity. To solve this problem, we constructed an energy term based on the local information and embedded it in the traditional Chan-Vese model to improve it. Furthermore, we introduced Li's penalizing term to force the level set function to be close to the signed distance function, which can eliminates the need of costly re-initialization procedure, improving the stability of the model.