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.     

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 new stochastic variational PDE model for soft Mumford-Shah segmentation

In this paper, a new stochastic variational PDE model is developed, using instead of hard segmentation soft segmentation. In this way, each pixel is allowed to belong to each image pattern with some probability. Our work proposes a functional with variable exponent, which provides a more accurate model for image segmentation and denoising. The diffusion resulting from the proposed model is a combination between TV-based and isotropic smoothing. The modeling procedure, computational implementation and results are explored in detail and numerical examples of real and synthetic images are presented.     

车牌识别机器学习方法的数学建模与实现

首先,针对不同光照、复杂背景和投影失真的车牌图像建立基于Adaboost算法和改进Haar特征的车牌检测模型;然后,运用Radon变换进行车牌校正,并结合3次B样条小波变换和识别反馈模型对字符进行粗和精分割;最后,根据汉字和数字字母的不同结构特征,采用不同的算法提取特征,特别是针对车牌字符特点,训练汉字、字母和数字字母3种神经网络模型用于建立字符识别模型.实验结果表明该模型是实用的.     

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.     

Asymptotics of generalized derangements

An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed.     

基于改进支持向量机的高端装备制造业供应商分类研究

针对现有供应商分类方法应用于高端装备制造业供应商所存在的局限性,从相互依赖视角构建了高端装备制造业供应商分类指标体系,提出了基于改进支持向量机的高端装备制造业供应商分类模型。该模型根据供应商误分代价不同,设计代价敏感支持向量机分类器,利用粒子群算法优化分类器的参数,并采用概率输出方法对多个优化的二类分类器的结果进行组合以实现多类分类。实验结果表明,该模型提高了现有方法的分类效果,可以降低总体误分代价,有效识别出对高端装备制造企业具有重大影响的供应商,为高端装备制造企业实施供应商分类管理提供了依据。     

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.     

Variational image inpainting

Inpainting is an image interpolation problem with broad applications in image and vision analysis. Described in the current expository paper are our recent efforts in developing universal inpainting models based on the Bayesian and variational principles. Discussed in detail are several variational inpainting models built upon geometric image models, the associated Euler‐Lagrange PDEs and their geometric and dynamic interpretations, as well as effective computational approaches. Novel efforts are then made to further extend this systematic variational framework to the inpainting of oscillatory textures, interpolation of missing wavelet coefficients as in the wireless transmission of JPEG2000 images, as well as light‐adapted inpainting schemes motivated by Weber's law in visual perception. All these efforts lead to the conclusion that unlike many familiar image processors such as denoising, segmentation, and compression, the performance of a variational/Bayesian inpainting scheme much more crucially depends on whether the image prior model well resolves the spatial coupling (or geometric correlation) of image features. As a highlight, we show that the Besov image models appear to be less interesting for image inpainting in the wavelet domain, highly contrary to their significant roles in thresholding‐based denoising and compression. Thus geometry is the single most important keyword throughout this paper. © 2005 Wiley Periodicals, Inc.     

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.     

A variational model and its numerical solution for local,selective and automatic segmentation

Variational region-based segmentation models can serve as effective tools for identifying all features and their boundaries in an image. To adapt such models to identify a local feature defined by geometric constraints, re-initializing iterations towards the feature offers a solution in some simple cases but does not in general lead to a reliable solution. This paper presents a dual level set model that is capable of automatically capturing a local feature of some interested region in three dimensions. An additive operator spitting method is developed for accelerating the solution process. Numerical tests show that the proposed model is robust in locally segmenting complex image structures.     

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.     

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.     

统计模型在中文文本挖掘中的应用

本文讨论了中文文本挖掘的三个问题:分词、关键词提取和文本分类。对分词问题,介绍了基于层叠隐马尔可夫模型的ICTCLAS分词法,以及将词与词之间的分隔视为缺失数据并用EM算法求解的WDM方法;对关键词提取问题,提出了贝叶斯因子法,并介绍了使用稀疏回归的CCS方法;对文本分类问题,介绍了根据关键词频率建立分类器的方法,以及先建立主题模型再根据主题概率建立分类器的方法。本文通过两组文本数据对上述方法进行比较,并给出使用建议。     

On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl. Math.) on dividing a general surface into piecewise smooth sub-surfaces. A central idea of models based on this work is to minimize the length of feature’s boundaries (i.e., H1 Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize L2 Lebesgue measure of the γ-neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method.     

Recent advances of variational model in medical imaging and applications to computer aided surgery

In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging: image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.     

Unsupervised construction of fuzzy measures through self-organizing feature maps and its application in color image segmentation

The paper presents a framework for the segmentation of multi-dimensional images, e.g., color, satellite, multi-sensory images, based on the employment of the fuzzy integral, which undertakes the classification of the input features. The framework makes use of a self-organizing feature map, whereby the coefficients of the fuzzy measure are determined. This process is unsupervised and therefore constitutes one of the main contributions of the paper.The performance of the framework is shown by successfully realizing the segmentation of color images in two different applications. First, the features of the framework and its parameterization are analyzed by segmenting different images used as benchmark in image processing. Finally, the framework is applied in the segmentation of different images taken under difficult illumination conditions. The images serve the development of an automated cashier system, where the weak segmentation constitutes the first step for the identification of different market items. The presented framework succeeds in the segmentation of all these color images.     

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.     

Rolling element bearing diagnosis based on probability box theory

Feature extraction leads to the loss of statistical information of raw data and ignores the sampling uncertainty and the fluctuations in the signal over time in mechanical fault diagnosis. In this paper, novel modeling methods for mechanical signals based on probability box theory were proposed to solve the above problem. First, the type of random distribution of the bearing signals were analyzed. Then, a Dempster-Shafer structure was obtained to establish a probability box model. To address the identification difficulty of the type of random distribution for the bearing signals, a second probability box model was established based on a vector consisting of features from the bearing signals. If the data are not found to follow a random distribution, a third modeling method based on the definition of probability boxes was proposed. The effectiveness and applicability of the three proposed models were compared with experimental data from rolling element bearings. The combination of probability box theory and mechanical fault diagnosis theory can open up a new research direction for mechanical fault diagnosis.