基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

A geometric flow approach for region-based image segmentation-theoretical analysis

In this paper, we analyze the well-posedness of an image segmentation model. The main idea of that segmentation model is to minimize one energy functional by evolving a given piecewise constant image towards the image to be segmented. The evolution is controlled by a serial of mappings, which can be represented by B-spline basis functions. The evolution terminates when the energy is below a given threshold. We prove that the correspondence between two images in the segmentation model is an injective and surjective mapping under appropriate conditions. We further prove that the solution of the segmentation model exists using the direct method in the calculus of variations. These results provide the theoretical support for that segmentation model.     

A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-Shah segmentation problems

In this paper, we propose a fast primal-dual algorithm for solving bilaterally constrained total variation minimization problems which subsume the bilaterally constrained total variation image deblurring model and the two-phase piecewise constant Mumford-Shah image segmentation model. The presence of the bilateral constraints makes the optimality conditions of the primal-dual problem semi-smooth which can be solved by a semi-smooth Newton’s method superlinearly. But the linear system to solve at each iteration is very large and difficult to precondition. Using a primal-dual active-set strategy, we reduce the linear system to a much smaller and better structured one so that it can be solved efficiently by conjugate gradient with an approximate inverse preconditioner. Locally superlinear convergence results are derived for the proposed algorithm. Numerical experiments are also provided for both deblurring and segmentation problems. In particular, for the deblurring problem, we show that the addition of the bilateral constraints to the total variation model improves the quality of the solutions.     

A variational formulation for physical noised image segmentation

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others,these results show that our proposed model and algorithms are effective.     

Noisy image segmentation based on nonlinear diffusion equation model

This paper addresses the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.     

Image segmentation by level set evolution with region consistency constraint

Image segmentation is a key and fundamental problem in image processing, computer graphics, and computer vision. Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation. However, poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation. In this paper, we present a region consistency constraint term to measure the regional consistency on both sides of the boundary, this term defines the boundary of the image within a range, and hence increases the stability of the level set model. The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary. Furthermore, this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour. The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.     

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation,Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging. An interactive implementation tool for MRF is described, and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently, rather than with the use of continuous techniques, such as PDE methods, which restrict the type of functions used and furthermore, can only guarantee convergence to a local minimum.     

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.     

Two-Stage Image Segmentation Scheme Based on Inexact Alternating Direction Method

Image segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, and the segmentation is then obtained by applying the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and brain MRI images.     

基于改进C-V水平集模型的SAR图像分割

本文研究了SAR图像分割的问题.利用一种加入图像边缘信息且无需重新初始化的改进水平集方法,获得了比传统C-V模型分割速度更快、准确度更高的分割结果.推广了C-V水平集模型分割灰度不均匀的SAR图像以及零水平集曲线的初始化等结果.     

Adaptive Segmentation Model for Images with Intensity Inhomogeneity based on Local Neighborhood Contrast

Segmentation of images with intensity inhomogeneity is a significant task in the field of image processing, especially in medical image processing and analysis. Some local region-based models work well on handling intensity inhomogeneity, but they are always sensitive to contour initialization and high noise. In this paper, we present an adaptive segmentation model for images with intensity inhomogeneity in the form of partial differential equation. Firstly, a global intensity fitting term and a local intensity fitting term are constructed by employing the global and local image information, respectively. Secondly, a tradeoff function is defined to adjust adaptively the weight between two fitting terms, which is based on the neighborhood contrast of image pixel. Finally, a weighted regularization term related to local entropy is used to ensure the smoothness of evolution curve. Meanwhile, a distance regularization term is added for stable level set evolution. Experimental results show that the proposed model without initial contour can segment inhomogeneous images stably and effectively, which thereby avoiding the influence of contour initialization on segmentation results. Besides, the proposed model works better on noise images comparing with two relevant segmentation models.     

A Retinex-based total variation approach for image segmentation and bias correction

Image segmentation methods usually suffer from intensity inhomogeneity problem caused by many factors such as spatial variations in illumination (or bias fields of imaging devices). In order to address this problem, this paper proposes a Retinex-based variational model for image segmentation and bias correction. According to Retinex theory, the input inhomogeneous image can be decoupled into illumination bias and reflectance parts. The main contribution of this paper is to consider piecewise constant of the reflectance, and thereby introduce the total variation term in the proposed model for correcting and segmenting the input image. This is different from the existing model in which the spatial smoothness of the illumination bias is employed only. The existence of the minimizers to the variational model is established. Furthermore, we develop an efficient algorithm to solve the model numerically by using the alternating minimization method. Our experimental results are reported to demonstrate the effectiveness of the proposed method, and its performance is competitive with that of the other testing methods.     

Existence and regularity of minimizers of a functional for unsupervised multiphase segmentation

We consider a variational model for image segmentation proposed in Sandberg et al. (2010) [12]. In such a model the image domain is partitioned into a finite collection of subsets denoted as phases. The segmentation is unsupervised, i.e., the model finds automatically an optimal number of phases, which are not required to be connected subsets. Unsupervised segmentation is obtained by minimizing a functional of the Mumford–Shah type (Mumford and Shah, 1989 [1]), but modifying the geometric part of the Mumford–Shah energy with the introduction of a suitable scale term. The results of computer experiments discussed in [12] show that the resulting variational model has several properties which are relevant for applications. In this paper we investigate the theoretical properties of the model. We study the existence of minimizers of the corresponding functional, first looking for a weak solution in a class of phases constituted by sets of finite perimeter. Then we find various regularity properties of such minimizers, particularly we study the structure of triple junctions by determining their optimal angles.     

基于直方图初始化的有效的多区域Mumford-Shah图像分割方法（英文）

The Mumford-Shah energy functional is a successful image segmentation model. It is a non-convex variational problem and lacks of good initialization techniques so far. In this paper, motivated by the fact that image histogram is a combination of several Gaussian distributions, and their centers can be considered as approximations of cluster centers, we introduce a histogram-based initialization method to compute the cluster centers. With this technique, we then devise an effective multi-region Mumford-Shah image segmentation method, and adopt the recent proximal alternating minimization method to solve the minimization problem. Experiments indicate that our histogram initialization method is more robust than existing methods,and our segmentation method is very effective for both gray and color images.     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

A new multi-threshold image segmentation approach using state transition algorithm

Thresholding plays an important role in image segmentation and image analysis. In this paper, the normalized histogram of an image is fitted by a linear combined normal distribution functions and each normal distribution function represents a class of pixels, whereas the parameters like the mean, the variance and the weights in the fitting function are undetermined. By transforming the fitting problem into a nonlinear and non-convex optimization problem, the state transition algorithm (STA) which is a new global optimization method is used to choose the optimal parameters of the fitting function. The effectiveness of proposed approach in multilevel thresholding problems is tested by several experimental results. By comparing with OTSU, particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE) algorithm, it has shown that STA has competitive performance in terms of both optimization results and thresholding segmentation.     

Idempotent Block Splitting on Partial Partitions,I: Isotone Operators

Image segmentation algorithms can be modelled as image-guided operators (maps) on the complete lattice of partitions of space, or on the one of partial partitions (i.e., partitions of subsets of the space). In particular region-splitting segmentation algorithms correspond to block splitting operators on the lattice of partial partitions, in other words anti-extensive operators that act by splitting each block independently. This first paper studies in detail block splitting operators and their lattice-theoretical and monoid properties; in particular we consider their idempotence (a requirement in image segmentation). We characterize block splitting openings (kernel operators) as operators splitting each block into its connected components according to a partial connection; furthermore, block splitting openings constitute a complete sublattice of the complete lattice of all openings on partial partitions. Our results underlie the connective approach to image segmentation introduced by Serra. The second paper will study two classes of non-isotone idempotent block splitting operators, that are also relevant to image segmentation.     

低分辨率医学图像的多图谱分割方法

基于多图谱的图像分割方法因其分割精度高和鲁棒性强,在医学图像分割领域被广泛研究,主要包含图像配准和标签融合两个步骤.目前对多图谱分割方法的研究通常都是在图谱图像和待分割目标图像具有相同分辨率的情况下展开的.然而,由于受图像采集时间,采集设备等影响,临床实践中采集的影像大多是低分辨率数据,使得目前在影像研究中广泛使用的方法无法有效应用于临床实践.因此,针对这一问题,我们结合图像超分辨率恢复方法,提出了精确鲁棒的低分辨率医学图像的多图谱分割方法,实验结果显示提出的方法显著地提高了多图谱分割方法的分割精度.     

A fast algorithm for image segmentation based on fuzzy region competition

Variational models for image segmentation are usually solved by the level set method, which is not only slow to compute but also dependent on initialization strongly. Recently, fuzzy region competition models or globally convex segmentation models have been introduced. They are insensitive to initialization, but contain TV-regularizers, making them difficult to compute. Goldstein, Bresson and Osher have applied the split Bregman iteration to globally convex segmentation models which avoided the regularization of TV norm and speeded up the computation. However, the split Bregman method needs to solve a partial differential equation (PDE) in each iteration. In this paper, we present a simple algorithm without solving the PDEs proposed originally by Jia et al. (2009) with application to image segmentation problems. The algorithm also avoids the regularization of TV norm and has a simpler form, which is in favor of implementing. Numerical experiments show that our algorithm works faster and more efficiently than other fast schemes, such as duality based methods and the split Bregman scheme.