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.     

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.     

一种无重新初始化的水平集方法的错觉轮廓捕捉新方法

在错觉轮廓捕捉模型建立前,我们要得到根据物体边界的符号距离函数时,用Eikonal方程不能实现的,我们用基于水平集方法的分割技术实现,扩大了模型的使用范围;在Zhu和Chan等人的错觉轮廓捕捉模型基础上引入了李纯明等人提出的符号距离约束信息,这就使得在水平集函数演化时不必对其重新初始化,并大大简化了模型的数值处理水平集函数的演化速度.并通过实验验证了该方法的优势.     

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.     

A fractional order derivative based active contour model for inhomogeneous image segmentation

Segmenting intensity inhomogeneous images is a challenging task for both local and global methods. Some hybrid methods have great advantages over the traditional methods in inhomogeneous image segmentation. In this paper, a new hybrid method is presented, which incorporates image gradient, local environment and global information into a framework, called adaptive-weighting active contour model. The energy or level set functions in the framework mainly include two parts: a global term and local term. The global term aims to enhance the image contrast, and it can also accelerate the convergence rate when minimizing the energy function. The local term integrates fractional order differentiation, fractional order gradient magnitude, and difference image information into the well-known local Chan–Vese model, which has been shown to be effective and efficient in modeling the local information. The local term can also enhance low frequency information and improve the inhomogeneous image segmentation. An adaptive weighting strategy is proposed to balance the actions of the global and local terms automatically. When minimizing the level set functions, regularization can be imposed by applying Gaussian filtering to ensure smoothness in the evolution process. In addition, a corresponding stopping criterion is proposed to ensure the evolving curve automatically stops on true boundaries of objects. Dice similarity coefficient is employed as the comparative quantitative measures for the segmented results. Experiments on synthetic images as well as real images are performed to demonstrate the segmentation accuracy and computational efficiency of the presented hybrid method.     

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.     

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 fast level set model of multi‐atlas labels fusion for 3D MRI tissues segmentation with application of split Bregman method

In this paper, we propose a new fast level set model of multi‐atlas labels fusion for 3D magnetic resonance imaging (MRI) tissues segmentation. The proposed model is aimed at segmenting regions of interest in MR images, especially the tissues such as the amygdala, the caudate, the hippocampus, the pallidum, the putamen, and the thalamus. We first define a new energy functional by taking full advantage of an image data term, a length term, and a label fusion term. Different from using the region‐scalable fitting image data term and length term directly, we define a new image data term and a new length term, which is also incorporated with an edge detect function. By introducing a spatially weight function into the label fusion term, segmentation sensitivity to warped images can be largely improved. Furthermore, the special structure of the new energy functional ensures the application of the split Bregman method, which is a significant highlight and can improve segmentation efficiency of the proposed model. Because of these promotions, several good characters, such as accuracy, efficiency, and robustness have been exhibited in experimental results. Quantitative and qualitative comparisons with other methods have demonstrated the superior advantages of the proposed model.     

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.     

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.     

A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images

We introduce a novel implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as possible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potential that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. We present a fast implementation that has been successfully applied to 3D medical and synthetic images.     

基于小波域的多尺度非参数图像分割方法

主要介绍了一种基于信息熵理论及图像多尺度信息来对图像进行非参数主动轮廓模型分割的有效方法.由于小波多分辨率特性的引入,可以最大程度地利用图像多尺度信息以确保分割的准确性和完整性.又由于小波变换的特性,低频信息的使用更是进一步降低了噪声影响.文中把图像分割问题定义为在分割区域边缘长度满足一定约束条件下,图像标记场与各个尺度图像像素值之间的互信息熵最大化过程.该方法可以有效地降低噪声对于分割的影响,及确保分割的准确性和完整性.     

Split Bregman method for minimization of improved active contour model combining local and global information dynamically

This paper presents an improved active contour model by combining the Chan–Vese model, the region-scalable fitting energy model, the globally convex segmentation method and the split Bregman method. A weight function that varies with the location of a given image is used to control the influence of the local and global information dynamically. We first present our model in a 2-phase level set formulation and then extend it to a multi-phase formulation. By taking the local and global information into consideration together, our model can segment more general images, especially images with intensity inhomogeneity. Our model has been applied to synthetic and real images with promising results. Numerical results show the advantages of our model compared with other models. The accuracy and efficiency are demonstrated by the numerical results. Besides, our model is robust in the presence of noise.     

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 level set evolution starting with a constant function

In this paper, we propose a novel level set evolution model in a partial differential equation (PDE) formulation. According to the governing PDE, the evolution of level set function is controlled by two forces, an adaptive driving force and a total variation (TV)-based regularizing force that smoothes the level set function. Due to the adaptive driving force, the evolving level set function can adaptively move up or down in accordance with image information as the evolution proceeds forward in time. As a result, the level set function can be simply initialized to a constant function rather than the widely-used signed distance function or piecewise constant function in existing level set evolution models. Our model completely eliminates the needs of initial contours as well as re-initialization, and so avoids the problems resulted from contours initialization and re-initialization. In addition, the evolution PDE can be solved numerically via a simple explicit finite difference scheme with a significantly larger time step. The proposed model is fast enough for near real-time segmentation applications while still retaining enough accuracy; in general, only a few iterations are needed to obtain segmentation results accurately.     

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.     

Using a level set approach for image segmentation under interpolation conditions

In this paper, we propose a new 2D segmentation model including geometric constraints, namely interpolation conditions, to detect objects in a given image. We propose to apply the deformable models to an explicit function using the level set approach (Osher and Sethian [24]); so, we avoid the classical problem of parameterization of both segmentation representation and interpolation conditions. Furthermore, we allow this representation to have topological changes. A problem of energy minimization on a closed subspace of a Hilbert space is defined and introducing Lagrange multipliers enables us to formulate the corresponding variational problem with interpolation conditions. Thus the explicit function evolves, while minimizing the energy and it stops evolving when the desired outlines of the object to detect are reached. The stopping term, as in the classical deformable models, is related to the gradient of the image. Numerical results are given. AMS subject classification 74G65, 46-xx, 92C55     

Using Conventional Edge Detectors and Postsmoothing for Segmentation of Spotted Microarray Images

Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot boundary curves separating foregrounds from backgrounds in a microarray image can be treated as edges. However, for generating gene expression data, segmentation methods for handling spotted microarray images are required to classify each pixel as either a foreground or a background pixel; most conventional edge detectors in the image processing literature do not have this classification property, because their detected edge pixels are often scattered in the whole design space and consequently the foreground or background pixels are not defined. In this article, we propose a general postsmoothing procedure for estimating spot boundary curves from the detected edge pixels of conventional edge detectors, such that these conventional edge detectors together with the proposed postsmoothing procedure can be used for segmentation of spotted microarray images. Numerical studies show that this proposal works well in applications.

Datasets and computer code are available in the online supplements.     

灰度图像复原的一种空间适应性向前向后扩散模型

该文考虑退化灰度图像复原问题. 首先, 作者利用时滞正则化方法定义退化图像去噪过程和去模糊过程之间的权重函数, 将激波过滤器边缘增强模型与水平集运动去噪模型相结合, 建立一种新的图像磨光增强偏微分方程. 然后, 证明该偏微分方程初值问题黏性弱解的存在唯一性. 最后, 给出该模型的部分数值算例.