The Study Of Level Set Methods And Their Applications In Image Segmentation

In information society, image has become an important way in which people can acquire and exchange information. So, the purpose of digital image processing on computer is to analyze the existing objects in images and acquire the essential information about the objects and give the related descriptions of image. Image segmentation has always been a most fundamental and important problem in the field of digital image processing. It is also the fundamental premise for the visual analysis and pattern recognition on the images. Generally speaking, image segmentation is to divide one image into some non-overlapping regions according to the intensity, color, texture and shape features. The segmentation result should make these features be homogeneous in the same region and obviously distinct in different regions.Recently, level set method has become a research hotspot in the field of image segmentation and achieved a good performance while addressing the image segmentation problem. Compared with the traditional image segmentation methods, level set method has some distinct advantages. First, it can segment the object with complicated shape in image since the evolving curve (surface) implicitly represented by the zero level set can naturally change its topological structure. Second, it can avoid the track procedure for the closed evolving curve (surface) and further transform the evolution problem of curve (surface) to the numerical solution to partial differential equation. Finally, it is theoretically supported by some strong mathematical backgrounds and can be easily extended to high dimensional case. Thus, it is very necessary to make a deep study on level set method. However, level set method is still staying in the developing stage, and the investigation of its theory and application should be enhanced and improved. In this thesis, the level set methods with their applications in image segmentation and further extensions have been deeply investigated. Some efficient algorithms have been proposed such as the hybrid level set model based on local information, multi-layer level set framework for multi-phase image segmentation, density-based clustering framework by using level set method, and prior information based plant leaf image segmentation methods.The main works in this thesis can be summarized as follows:(1) We proposed a new local Chan-Vese (LCV) model based on local statistical information. By incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented in few iterations. During the evolution process, the level set function can naturally maintain an approximate signed distance function by introducing a penalizing energy into the regularization term. Moreover, a termination criterion based on the length change of the evolving curve is proposed to ensure that the evolving curve can automatically stop on the true boundaries of objects. Particularly, an extended structure tensor (EST) was constructed for texture image segmentation. Combining the EST with the proposed LCV model, the texture image can be efficiently segmented no matter whether it presents intensity inhomogeneity or not. Finally, the experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. And the comparisons with the Chan-Vese (CV) model and local binary fitting (LBF) model also show that our LCV model can segment images with few iterations and be less sensitive to the location of initial contour and the selection of governing parameters.(2) By introducing a conception of image layer into the level set method, we proposed a new multi-layer level set framework. Different from traditional multiple level set segmentation schemes, the proposed multi-layer level set framework employs only one level set function with a hierarchical form to segment the multi-phase images. To keep the convergence speed, an adaptable evolution parameter update scheme was proposed. In addition, we also gave the termination criteria for level set evolution on single image layer and global evolution. It should be emphasized that no manual interventions are needed in the whole evolution process. Finally, the experiments on some synthetic and real images have demonstrated the efficiency of our multi-layer level set framework. And the comparisons with multi-phase Chan-Vese method also show that the proposed framework has a less time-consuming computation and much faster convergence.(3) We proposed finding the approximations of cluster centers through the level set evolution and constructed a density-based clustering framework by using level set method. Our framework can successfully extend image segmentation method to density-based clustering field. Unlike traditional level set methods, our level set evolution scheme can automatically compute the initial boundaries based on the characteristic of data space. In the evolution process, different types of contours would evolve in different ways to surround each cluster centers. To obtain the optimized level set boundary (LSB) surrounding the corresponding cluster center after the evolution process, the evolving boundary record (EBR) update criterion was defined. In addition, a termination criterion was presented to stop the evolution process when no more cluster centers can be found. Finally, a new level set density (LSD) was computed according to the level set boundary for clustering instead of traditional probability density. The experiments on some synthetic and real datasets show that the proposed framework works well while clustering the dataset with near cluster centers and detecting the outliers. The comparisons with some other density-based clustering methods further show that the proposed framework can successfully avoid the overfitting phenomenon and solve the confusion problem of cluster boundary points and outliers.(4) We proposed two efficient plant leaf image segmentation schemes based on the prior information. The common feature for two schemes is that the segmentation process can be divided into pre-segmentation procedure and formal segmentation procedure. The first segmentation scheme is based on level set evolution which uses the approximate symmetry of leaf as prior information. The second segmentation scheme is based on watershed algorithm in mathematical morphology which adopts the size of leaf as prior information. The experiments on some real leaf images show that two segmentation schemes can both achieve success while segmenting the leaf images with overlapping phenomenon and interference produced by branches and non-target leaves.