Variational And Discrete Variational Level Set Models For Image Segmentation

With the rapid development of computer vision and information science,image processing has achieved great success in some fields.Image segmentation,as a fundamental and important component in image processing,has become a hot problem in image analysis and computer vision.For a given image,the goal of segmentation is to partition the image domain into two or more dissimilar regions so that each subregion is uniform and homogeneous regarding one or more characteristics(intensity,color or texture,etc.)in order to extract the regions of interest.In recent years,variational methods have been widely used in the field of image segmentation due to their outstanding performance.Variational methods for image segmentation usually have two steps as follows:first,one establishes an energy functional which consists of data term containing image features and regularization term.The data term is used to drive the evolution curve(or surface)toward the target,and the regularization term is used to smooth the evolution curve(or surface).Then one minimizes the energy functional typically by the gradient descent method to make evolution curve move towards the desired locations and finally get the desired segmentation result.This thesis concentrates on variational models for image segmentation.By analyzing some specific problems in image segmentation,we propose three region-based variational models and design some effective numerical implementation methods.The main contents of our studies are summarized as follows:1.For noisy images,we present a variational image segmentation model with kernel metric-based data termIn real word,images are often degraded by noise due to the technical limitations of imaging,transmission,storage and conversion.Noise has great influence on the accuracy of segmentation,thus segmentation for noisy images has always been a very challenging task.The data term in region-based variational models is usually defined via certain data fidelity metric.In most cases,it is(often implicitly)assumed that the image is degraded by additive Gaussian noise,therefore,the ~2L-norm metric has been widely used for the data term in variational level set models.The L~1-norm metric is used to minimize the effect of salt&pepper noise in image denoising and has been successfully used to deal with the segmentation problem of images with salt&pepper noise.The data fidelity metrics mentioned above can handle specific noise,but they may be only appropriate for one type of noise.In this thesis,we present a variational model with kernel metric-based data term,in which the data term is defined by the kernel metric based on the Gaussian radial basis function.This kernel metric can adaptively emphasize the contribution of pixels close to the mean intensity value inside(or outside)the evolution curve and so reduce the influence of noise.Moreover,this kernel metric is a quite flexible alternative to several metrics and can be appropriate for some different types of noise.We prove that the proposed model is strictly convex and has a unique minimizer in BV(?).In the numerical implementation,we design a three-step splitting scheme to solve the evolution equation of level set function.Experimental results show that the proposed method is very robust to some types of noise(i.e.,salt&pepper,Gaussian and mixed noises).2.We propose a binary level set variational model with L~1 data termDue to the malfunctioning pixels in camera sensors or transmission in a noisy channel,the impulse noise often occurs in the images,which greatly influences the accuracy of segmentation.So far,segmentation of images with impulse noise is still a very challenging task.To segment images with impulse noise,we propose a binary level set variational model with L~1 data term.In our model,the data term is defined by the L~1-norm metric,which enables our model to segment images with impulse noise or low contrast.In order to tackle the constraint,we introduce a penalty functional and then transform constrained minimization problem into unconstrainted minimization problem.Then we design a three-step splitting scheme to numerically solve the gradient descent flow of level set function efficiently.Experimental results show that the proposed model is very robust to impulse noise(salt&pepper and random-valued noises)and can better deal with some types of real images.3.For the regularization problem of level set function,we propose a L~0-regularized discrete variational level set methodIn the variational level set models,it is often necessary to use some kind of regularization term to smoothen the level set function or its zero-level set.There are some common regularization terms,such as length regularization term,area regularization term,H~1 regularization term,TV regularization term and so on.In recent years,L~0-based regularizers have been successfully applied to some fields of image processing.However,there are few studies that directly useL~0-based regularizers on level set function for image segmentation.This thesis proposes a L~0-regularized discrete variational level set method.We use the 0.5-level set of a ternary function whose values are within{0,0.5,1}to implicitly represent the evolution curve and use L~0 counting operator to discretely measure the length of evolution curve and the area of the region inside evolution curve.The proposed model can be regarded as a discrete form of the well-known Chan-Vese model.We design an alternating minimization algorithm to solve the proposed model efficiently.The algorithm can ensure that each subproblem has the closed-form solution and has fast convergence rate.Experimental results show that the proposed method has good performance for segmentation of images with severe noise,outliers or low contrast.