Improvement Of Active Contour Models And Optimization Based On Sobolev Gradient

Image segmentation is a fundamental and important problem in image analysis and computer vision. The segmentation results have a direct impact on image analysis and understanding of other high-level follow-up processing. The purpose of image segmentation is dividing regions into non-overlapping areas based on gray-scale, color, texture, shape and other characteristics of the image. These characteristics show a significant difference in different regions, but show similarity in the same areas. Among the existing image segmentation methods, partial differential equation has become a hot research with experts and scholars at home and abroad. Because there are various forms, flexible structure, high precision and edge preserving continuity. The basic idea of PDE image segmentation method is:designing energy functional of partial differential equation according to the image feature, and then minimizing the energy functional through variational level set method, thus the resulting evolution equation is the boundary of the target object.In this paper, we first introduce the research background, purpose, and significance of the PDE-based image segmentation methods. Then we briefly describe a few classical active contour models with their mathematical theory, and a detailed analysis of the advantages and disadvantages of them. Based on the above analysis, this paper mainly has done the following aspects of work:(1) In this paper, we improve Li’s model, and propose an adaptive active contour model for weak boundary extraction. Besides, the adaptive force is proved to be bi-directional. The mean gray value of the image is added in the coefficient of the proposed model, so that the adaptive force can shrink or expand adaptively according to the position of the evolution curve. The experimental results show that the proposed method could overcome the problem of Li’s model, which is that the initial contours must be fully enclosed by or contained within the target object. It is robust with the position of the initial contour and noise, and can segment multi-target images.(2)The LBF model can segment images with intensity inhomogeneity because it fits the local energy by adopting the neighborhood information of each pixel. However, without considering the global information, LBF only considers the local information which leads to the sensitive with the size, shape and position of the selected initial contours. In this paper, we combine the local and global information of images and propose a "two-stage" active contour model. On the first stage, we utilize the global information of the image to roughly but quickly locate the target. On the second stage, we employ the local information to obtain a more accurately segmentation result. The experimental results show that our method keeps the advantage of the LBF model:effective for inhomogeneous images, and meanwhile possess other improvement:robust to the selection of initial contours and to noise.(3)Due to that CV can segment images with homogeneous foreground and background, but cannot handle intensity inhomogeneous images. The LBF can perform well with intensity inhomogeneous images, but it is highly sensitive with the initialization and noise. In combination with the CV and LBF model, we propose a hybrid active contour model, using the L2+Sobolev gradient method to achieve the evolution PDE equation. Experimental results show that the proposed model can segment images with homogeneous background and inhomogeneous foreground, and also can segment the simple multi-target images, while it is less sensitive with the initialization and noise.