Study On Image Segmentation And Restoration Based On Variational Method

Human are very familiar with images. Image can be captured by optical imaging or human vision system. There is a saying "One picture is worth a thousand words". This means that image contains much information about the things represented by it. With the development of computer technology, digital image technology has been widely used in science research, industry, medical treatment, education, entertainment and communica-tion. Therefore, the research on image technology is of great significance.In this dissertation,we focus on two problems based on variational method:image segmentation and image restoration. Image segmentation is the preprocessing of object recognition and image understanding, its goal is to partition the image into meaningful regions. Due to imperfections in the imaging and capturing process, the recorded image invariably represents a degraded version of the original scene. Actually, both problems can be viewed as one of image estimation where the segmentation map or underlying image is to be estimated from the processing image. After analyzing the advantages and disadvantages of the existing algorithms, we try to propose some effective algorithms for image segmentation and restoration. The main contributions of this dissertation are as follows:(1) Image segmentation method based on variational method usually refers to active contour model. After analyzing the existing models for segmenting image with intensity inhomogeneity, we find that, most of them are non-convex. Thus, they can-not guarantee global minimizers and the corresponding algorithms may stop at local minimizers. Although the global active contour model based on local intensity means has achieved faster convergence, the local intensity means sometimes can-not provide enough information for accurate segmentation. Therefore, assume that the intensities of pixels in a window follow Gaussian distribution, we give a convex model. Then using the optimization method to solve the proposed model, we get an efficient algorithm which can find the global minimizer of the model. Numerical experiments show the good performance of the proposed algorithm. In addition, since second-order statistics contain part of the information about texture, we use the proposed algorithm to segment texture image.(2) Considering the second-order statistics can-not provide enough information for tex- ture segmentation, we propose a convex active contour model based on local feature histogram. To get better descriptors for texture image, we use a semi-local region descriptor to extract texture information. Moreover, the pixel intensity is also very important feature of texture image. Thus, we use those two features as features of texture image, and use feature histograms to represent regions. Since cross-bin distance matches perceptual similarity better than the bin-to-bin distance, we use a cross-bin distance, named Quadratic-Chi histogram distance, to measure the dis-tance between histograms. Finally, we get a convex model for texture segmentation. Experimental results for images show the effective of the proposed method.(3) For image restoration model based on variational method, we first study a TV dictionary model. It takes the TV regularization as the objective function, uses the constraints based on wavepacket decomposition to restrict the solution space. Since wavepacket decomposition algorithm provides multi-scale representation for images, TV dictionary model can achieve better preservation of texture than the classical ROF model. However, it is not easy to solve this model. Although some-one uses Uzawa method to solve it, the resulting algorithm is not stable. From the statistical view, we add a data-fidelity term to TV dictionary model. Then we can restrict the solution space from both time and frequency domain, and get a con-vex model. Then we prove the existence of the solution. To solve the proposed model, we discuss that on two cases:one approach is that we directly solve the constrained model, however, the resulting algorithm can only efficiently work on denoising problem; in the other approach, we first change the model to an uncon-strained model via Lagrange multiplier method, then solve the model, the result-ing algorithm can be applied to many applications. Experimental results show the effective of our algorithm. Furthermore, we replace the TV regularization by the nonlocal total variation regularization, and the resulting model reaches much higher restored quality.(4) We propose an algorithm for image deblurring under impulse noise based on sparse representation over learned dictionary. Since the patch-based approach may intro-duce some artifacts to the recovered image, and the pixel-based TV regularization term can locally smooth the recovered image, we combine this regularization to our model. Considering the special characteristics of the impulse noise:some pix-els are noise-free, we use the two-phase method to recover the image:the first phase is to identify the noise candidates which are likely to be corrupted by im- pulse noise; the second phase is to recover the image via the patch-based model in which the data-fidelity term only uses the noise-free pixels. However, the resulting algorithm just works well for image deblurring under salt-and-pepper noise. Since the detection for random-valued noise is usually unreliable, which introduces much difficulty, the two-phase method cannot work well. To get better recovered results from the blurred images with random-valued noise, we combine the two separate phases together to simultaneously detect the impulse noise positions and restore image. The numerical experiments demonstrate the good performance of the pro-posed methods.(5) In the image capturing process, kinds of noise appear. To tackle the image de-blurring under Poisson noise, we extend the idea of the above algorithm for image deblurring under impulse noise to get a new model for deblurring under Poisson noise. Furthermore, when the multiplicative noise follows Gamma distribution, the model for deblurring under Poisson noise can be used to deblur image with mul-tiplicative noise. Therefore, we use the proposed algorithm to deblur image with Poisson or multiplicative noise. The experimental results demonstrate the good performance of the proposed method.