Partial Differential Equation-based Image Enhancement And Segmentation

Image processing technology is an interdisciplinary topic combined with many other subjects such as electronics, optics, mathematics, computer and so on. It has been applied to a lot of fields such as biomedicine, communications, remote sensing, transportation, military and public security. Currently, the main methods of image processing can be divided into three categories:the algorithm based on probability theory, the algorithm based on wavelet transform theory and the algorithm based on partial differential equations. The algorithm based on partial differential equations has developed rapidly because of its complete mathematical theory foundation and relatively close conjunction with engineering applications. By using this method, the image problems can be regarded as the mathematical model. The image evolves under the guidance of partial differential equations. Ultimately, we will obtain the desired image processing result. It has been widely used in many fields such as image denoising, image enhancement, image fusion, image restoration and image segmentation. This thesis focuses on some key issues of the partial differential equations in image enhancement and image segmentation. The main work and contribution are listed as follows.For the image with low contrast and blurred details, we propose an algorithm of histogram specification with maximum entropy in each dynamic sub-layer. The basic idea is that based on the gray features of different image area, a method of hierarchical histogram stretch and gray value range remapping is introduced. It can enhance the contrast of image by redefining sub-layer range based on the probability density of the sub-layer. Further, by using the histogram specification method to remap the gray value in sub-layer according to the guiding function, the region with important information will be extended. Finally, we can achieve the purpose of enhancing image details.For the image with a low noise ratio and contrast, the edge detail is often buried in the background or noise. Human vision is sensitive to the changes of local image details which are actually image gradients. And by adjusting image gradients, image details can be enhanced. Based on theoretical framework of gradient field reconstruction, we propose gradient histogram enhancement based on bimodal Gaussian function fitting model. Firstly, we use the Gaussian mixture model to estimate the gradient histogram distribution and divide the gradient histogram into two parts corresponding to the weak edge detail and clear edge detail, respectively. Then, we extend the scope of these two gradients adaptively, with the gradient magnitude expansion of faint edge details larger than that of sharp edge details. This will enhance the faint details while preventing the clear edge details from over-enhancement. In order to quickly rebuild the enhanced image from gradient transformation field, we use the method based on sine transform matrix. In order to enhance the image while avoiding enhancing the noise, we further improve the gradient field reconstruction algorithm by using Gaussian mixture model. We also use the Gaussian mixture model to estimate the gradient histogram distribution. Due to the presence of noise in the image, we divide the gradient fields into three parts respectively corresponding to the weak details, the noise and the clear details. Then, we construct piecewise functions to increase the gradient of the faint detail and reduce noise gradient. The Anisotropic Diffusion Constraints is adopted in the reconstruction of the enhanced image to suppress noise. Finally, the image edge details are enhanced and the noise in the image is suppressed.As an important image processing technology, image segmentation is the most basic and important research in computer vision. The main purpose of this technology is to separate the object from the background in the image, while obtain the object boundary. In this paper, we focus on discussing the image segmentation method based on partial differential equations. In order to segment the image with high noise, low contrast and weak edges effectively, we propose a guide filter-based gradient vector flow module for image segmentation (GFGVF). In the methods based on gradient vector flow model, the quality of the edge map determines the accuracy of the segmentation results but the presence of noise in the image affects the construction of the edge map. Firstly, a guide filter is exploited to construct a novel edge map, providing characteristics of the image edge while excluding the effects of noise. This alleviates the possibility of edge leakage caused by using the traditional edge map. Then, a novel weighting function is constructed to effectively handle the extended capture range and the edge preserving even with noise existing. Finally, the variational problem is converted into the partial differential equations and the evolution curve stops at the boundary of target in the iterative processing.Level set method is a new method for image processing based on partial differential equations. It is easier to handle curves'topology with high precision and stability. In this paper, we also focus on the image segmentation of partial differential equations based on level set. In order to segment the image with intensity inhomogeneity and complex composition effectively, we propose a novel method which uses local region statistics and multi-parameter intensity fitting as well. The basic idea of this method is as follows. By replacing the original local region statistics with the novel local region statistics after bias field correction, the effect of intensity inhomogeneity can be eliminated. Furthermore, in order to characterize the features of each local region effectively, two parameters are used to fit the average intensity inside and outside of the counter, respectively. This can well handle the images with complex composition, such as larger gray difference even in the same region. Then we devise a maximum likelihood energy function based on the distribution of each local region. Segmentation and bias field estimation can be jointly obtained by minimizing the proposed energy function related with the level set function.