A detail preserving variational model for image Retinex

In this paper, we propose a detail preserving variational model for Retinex to simultaneously estimate the illumination and the reflectance from an observed image. Most previous models use the log-transform as pretreatment which results in loss of details in reflectance. From this observation, a detail preserving variational method is proposed for better decomposition. Different from the log-transform based models, the proposed model performs the decomposition directly in the image domain. Mathematically, we prove the existence of a solution for the proposed model. Numerically, we derive an efficient iterative algorithm by utilizing alternating direction method of multipliers (ADMM) method. Experimental results demonstrate the effectiveness of the proposed method. Compared with other closely related Retinex methods, the proposed method achieves competitive results on both subjective and objective assessments.     

A Retinex modulated piecewise constant variational model for image segmentation and bias correction

In this paper, we propose a novel Retinex induced piecewise constant variational model for simultaneous segmentation of images with intensity inhomogeneity and bias correction. Firstly, we obtain an additive model by decomposing the original image into a smooth bias component and a structure part based on the Retinex theory. Secondly, the structure part can be modeled by the piecewise constant variational model and thus deduced a new data fidelity term. Finally, we formulate a new energy functional by incorporating the data fidelity term into the level set framework and introducing a GL-regularizer to the level set function and a smooth regularizer to model the bias component. Based on the alternating minimization algorithm and the operator splitting method, we present a numerical scheme to solve the minimization problem efficiently. Experimental results on images from diverse modalities demonstrate the competitive performances of the proposed model and algorithm over other representative methods in term of efficiency and robustness.     

A variational model with hybrid Hyper-Laplacian priors for Retinex

Retinex aims at estimating real reflectance images by removing the effect of illumination. We propose a nonconvex variational model for Retinex with novel priors for reflectance and illumination. Based on the statistics of the gradients of reflectance and illumination, we use the hyper-Laplacian prior to characterize the gradients of reflectance, and the hybrid hyper-Laplacian and Tikhonov prior to characterize the gradients of illumination. An efficient alternating direction method of multipliers (ADMM) is developed to solve the proposed model. Extensive numerical experiments show that the proposed method is comparable to the state-of-the-art methods quantitatively and qualitatively.     

A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.     

基于双分数阶变分光流模型的运动目标检测方法

变分光流法是常用的运动目标检测方法,应用场景中的光照变化会极大影响现存变分光流法的稳定性及准确率,提出基于分数阶的变分光流模型来提高光照变化鲁棒性.该模型将分数阶导数同时应用于经典变分光流模型的数据项及平滑项中;根据图像的数据特征,采用图像函数及光流向量函数的有限离散二重分数阶导数近似拟合求导结果计算光流向量,进而将光照变化的影响按比例分摊到了各周边像素点中,弱化了光流向量计算过程中光照变化对光流模型的影响.为避免同一像素点的二重分数阶导数覆盖了不同光流向量区域的问题,采用超像素分割来舍弃不在同一光流向量区域的像素点,从而保证了同一光流向量区域的整体性,从而进一步提高模型的光流估计准确率.在三大常用数据库及户外视频序列中进行实验,实验证明,在应用场景存在光照变化的前提下,基于双分数阶的变分光流模型优于其他算法;对比其他算法,文中算法的运算速度适中.     

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.     

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.     

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.     

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.     

Non-convex and non-smooth variational decomposition for image restoration

The variational image decomposition model decomposes an image into a structural and an oscillatory component by regularization technique and functional minimization. It is an important task in various image processing methods, such as image restoration, image segmentation, and object recognition. In this paper, we propose a non-convex and non-smooth variational decomposition model for image restoration that uses non-convex and non-smooth total variation (TV) to measure the structure component and the negative Sobolev space $H^{-1}$ to model the oscillatory component. The new model combines the advantages of non-convex regularization and weaker-norm texture modeling, and it can well remove the noises while preserving the valuable edges and contours of the image. The iteratively reweighted l¹ (IRL1) algorithm is employed to solve the proposed non-convex minimization problem. For each subproblem, we use the alternating direction method of multipliers (ADMM) algorithm to solve it. Numerical results validate the effectiveness of the proposed model for both synthetic and real images in terms of peak signal-to-noise ratio (PSNR) and mean structural similarity index (MSSIM).     

A novel enhancement method for low illumination images based on microarray camera

It is difficult but important to get clear information from the low illumination im-ages. In recent years the research of the low illumination image enhancement has become a hot topic in image processing and computer vision. The Retinex algorithm is one of the most popular methods in the field and uniform illumination is necessary to enhance low illumination image quality by using this algorithm. However, for the diff erent areas of an image with contrast brightness diff erences, the illumination image is not smooth and causes halo artifacts so that it cannot retain the detail information of the original images. To solve the problem, we gen-eralize the multi-scale Retinex algorithm and propose a new enhancement method for the low illumination images based on the microarray camera. The proposed method can well make up for the deficiency of imbalanced illumination and significantly inhibit the halo artifacts as well. Experimental results show that the proposed method can get better image enhancement eff ect compared to the multi-scale Retinex algorithm of a single image enhancement. Advantages of the method also include that it can significantly inhibit the halo artifacts and thus retain the details of the original images, it can improve the brightness and contrast of the image as well. The newly developed method in this paper has application potential to the images captured by pad and cell phone in the low illumination environment.     

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.     

Statistical shape priors for level set segmentation

Starting in the early 1990's level set methods have become a popular mathematical framework for variational image segmentation. In many applications of segmentation, however, cost functionals which merely take into account the intensity information of the input image will not give rise to the desired segmentation results. To cope with missing or misleading image information, researchers have proposed to impose statistical shape priors into the segmentation process. Such shape priors favor the evolving embedding function to remain similar to embedding functions associated with a collection of training shapes. As a consequence, one can obtain shape-consistent segmentation despite large amounts of noise, background clutter and partial occlusion of the object of interest. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

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.     

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.     

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.     

视频车辆分类与计数的模型与应用

由于受形态变化、光照变化、视觉碰撞和视觉模糊的影响,基于监控视频的车辆分类和计数一直都是待解决的复杂问题。为了更好地解决这个问题,本文提出新的模型来更好的提取前景。详细来讲,在初次前景提取中,建立模型判断是否存在车辆碰撞,对存在碰撞的车辆通过灰度空间双阀值和YCbCr图像空间处理后,对前景进行更准确的再提取。并在此基础上针对碰撞车辆,定义间隙特征向量将车辆分割问题转换为寻找分割点的优化问题,从而给出高效的车辆分割算法,对发生碰撞的车辆进行准确分割。之后利用神经网络对车辆分类,并设计一种基于已正确对碰撞车辆分割的算法对车辆计数。实验结果表明,本文提出的模型在视频车辆的分类和计数中取得优异的表现,并且数据处理速度能够满足及时性。比起人为计算车流量或建立三维模型等进行分析车辆碰撞情况下的车辆分类与计数,此方法兼顾了准确性与时效性,效率提高,成本减少。