Research On Partial Differential Equation-based Image Processing Algorithms

In recent years, with the development of the electronics technology, the communication technology and the computer technology, image processing techniques have attracted serious concern and have been widely in the fields of astronomy, biomedicine, remote sensing, communication and video surveillance and so on. The basic research methods of image processing can be categorized into three types:the methods based on probability and statistics, the methods based on Fourier and wavelet transform and the methods based on the partial differential equations. Among these three methods, the methods based on the partial differential equations have achieved fast development because of their strong local adaptability, high flexibility. The research areas include:image denoising, image segmentation, image decomposition, image inpainting, image reconstruction and so on. This thesis focuses on the study of image denoising, image segmentation and their applications. The major research contents and productions are shown in the following areas:(1) An image denoising model based on local adaptive Lp norm constraints is formulated with attention to address the limitations of the adaptive p-Laplace model. Though the adaptive p-Laplace model can smooth images successfully, the staircase effect appears in the flat regions in the final images. This problem is closely associated with the poor scheme of the Lp norm of the adaptive p-Laplace model. In order to address the problem, we propose a new scheme which employs the inhomogeneity instead of the spatial gradient to detect the edges. The proposed mode can utilize the different Lp norm constraints exactly in the different regions of the image. Experimental results demonstrate that it has better performance than that of the adaptive p-Laplace model.(2) A geodesic active contour model based on edge diffusion information fitting is proposed with attention to address the problems associated with initialization and weak edges of the geodesic active contour model. First, a diffusion functional is defined, which is related to the second derivative in the normal direction of the edges of the image. Second, the edge diffusion information is obtained by solving this diffusion functional. Third, we utilize the edge diffusion information to construct a novel force field, which drives the active contour evolution and converges to desirable edges. An efficient numerical schema is used for the implementation of the proposed model in order to converge rapidly and avoid re-initialization. Experimental results on a series of real and synthetic images demonstrate that the proposed model is robust to the initial contour, and it can segment the objects with the weak edges successfully, as well as the objects with complex geometry shapes and the objects with interior and exterior boundaries. It has better segmentation performance than that of some traditional models.(3) A novel active contour model based on local image and global image information fitting energy is proposed with attention to address the problems associated with initialization of the local Gaussian distribution fitting model. According to the characteristic of the local intensity clustering, the bias field and a piecewise constant function are integrated to approximate the local image intensities, which make the proposed model can segment the objects with the initial contour being anywhere in the image. An efficient numerical schema is used for the implementation of the proposed model in order to converge rapidly and avoid re-initialization. Experimental results on a series of real and synthetic images demonstrate that the proposed model is robust to the initial contour and it can segment the images with intensity inhomogeneities effectively. It has better segmentation performance than that of some traditional models.(4) River detection in high resolution remote sensing image is one of the most popular topics of research in computer vision. A novel river detection algorithm in high resolution remote sensing by using support vector machine and level set is proposed. According to the characteristic of the river, we employ texture feature and benchmark information diffusion feature as the feature vectors to train the support vector machine classifiers in order to perform the coarse segmentation of rivers. Then the distance regularized level set evolution model which takes the results of the coarse segmentation as the initial curves is utilized to capture the desirable shapes of the rivers. Experiments are executed on IKONS 1m-resolution images and the results demonstrated superior performance of the proposed algorithm in terms of accuracy, efficiency and robustness.(5) A fundamental issue in sensor network is the coverage problem. Since the distributions of sensor nodes are not usually uniform due to random deployment and node failures, the coverage holes are hardly avoided in sensor network. And the coverage holes are important health indicators of the sensor network. We propose a level set based coverage holes detection algorithm for hybrid sensor network. First, we employ the Neyman-Pearson criterion based sensing model to construct the graph of the joint detection probability of the sensor nodes. Second, we apply the local intensity clustering model to segment this graph to estimate the number of holes and the size of the holes. Finally, we utilize the genetic algorithms which could leverage mobility to optimize the average coverage rate and the average movement distance of the mobile nodes to heal the hybrid sensor network. Simulation results show that the proposed method could detect the holes efficiently. The holes healing algorithm outperforms over the Random and Delaunay methods.