脑MR图像互信息最大的凸优化分割模型

脑MR图像中普遍存在灰度不均匀性,传统的分割方法无法得到理想的脑组织分割结果.为此提出一种基于互信息最大化准则的变分水平集凸优化分割模型.首先建立最大化图像灰度与标记之间互信息能量的分割模型,并融入偏移场信息;对模型进行水平集表示和凸优化后,再引入边缘指示函数加权的总变差范数;最后采用SplitBregman方法快速求解.实验结果表明,该模型可以得到较准确的脑组织分割和偏移场矫正结果,对噪声和灰度不均匀性有很好的鲁棒性.     

基于凸优化的自适应CV模型*

针对CV模型分割精度不高、分割速度缓慢和易陷于局部最优等缺点,提出了一种新的基于凸优化的自适应CV模型。首先,引入了自适应权重项,对拟合中心的计算采用加权平均,提高了拟合中心计算的准确性;然后,在模型中加入了凸优化技术,以获取模型的全局最优解;最后,采用了Split Bregman方法进行快速求解,有效地提高了分割效率。实验结果表明,基于凸优化的自适应CV模型有效地提高了分割精度和效率,对初始化也具有较好的鲁棒性。     

基于全变分的运动分割模型及分裂 Bregman 算法

提出了一种基于全变分的运动分割模型,可以适用于2D/3D视频.首先, 通过活动轮廓模型将分割与估计融合在同一能量函数中, 该模型能够同时进行分割曲面的演化和运动参数的估计. 其次,通过凸松弛方法将原始问题转化为等价的全变分模型, 克服了局部最小值问题.最后,采用分裂Bregman快速算法进行求解. 多组实验证明了本文方法对2D/3D视频的通用性和算法的高效性.     

Nonlocal variational image segmentation models on graphs using the Split Bregman

Variational functionals such as Mumford-Shah and Chan-Vese methods have a major impact on various areas of image processing. After over 10 years of investigation, they are still in widespread use today. These formulations optimize contours by evolution through gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In this paper, we propose an image segmentation model in a variational nonlocal means framework based on a weighted graph. The advantages of this model are twofold. First, the convexity global minimum (optimum) information is taken into account to achieve better segmentation results. Second, the proposed global convex energy functionals combine nonlocal regularization and local intensity fitting terms. The nonlocal total variational regularization term based on the graph is able to preserve the detailed structure of target objects. At the same time, the modified local binary fitting term introduced in the model as the local fitting term can efficiently deal with intensity inhomogeneity in images. Finally, we apply the Split Bregman method to minimize the proposed energy functional efficiently. The proposed model has been applied to segmentation of real medical and remote sensing images. Compared with other methods, the proposed model is superior in terms of both accuracy and efficient.     

基于凸松弛方法的医学 B 超图像快速分割

利用活动轮廓线方法进行图像分割的一个重要缺陷是目标函数是非凸的, 这不仅使得分割结果容易陷于局部极小, 而且还使得一些快速算法无法开展.本文首先从贝叶斯风险估计的方法出发,针对B超幅度图像, 给出一种基于Rayleigh分布的活动轮廓线模型. 然后结合凸松弛的方法,得到一个新的放松的凸模型.原有模型和放松后模型的关系可由定理1给出. 最后结合分裂Bregman算法, 给出基于B超分割模型的快速算法.与传统梯度下降法相比较,本文提出的算法不仅能得到全局最优解,而且在算法收敛速度上也 大大优于梯度下降法.     

区域拟合的背景去除图像分割模型

目的 图像分割是图像处理领域的重要研究内容之一,且应用广泛。在基于PDE和变分法的图像分割方法中,大部分图像分割模型的能量泛函均为非凸性,较容易陷入局部极小解,因而分割结果往往不尽如人意,且运算时间较慢。为此,本文根据背景去除模型的思想结合区域拟合的方法,提出了一种区域拟合的背景去除图像分割模型。方法 首先对背景去除模型进行改造;再结合区域拟合的方法对模型进行改进,并对改进模型进行凸优化处理;最后结合水平集和Split Bregman法对改进模型进行快速求解,获得全局最小值解。结果 针对改进模型在分割效果、计算效率及初始化位置对实验结果的影响这3个方面了进行数值实验,相较于ICV(improved Chan-Vese)模型、LK(Li-Kim)模型及CV(Chan-Vese)模型,本文模型能得到更优的分割效果,且在分割效果相似的情况下,本文模型较RSF(region-scalable fitting)模型耗时更短,同时当实验初始化位置不同时,实验亦能取得良好的分割效果。结论 在对于MRI(magnetic resonance imaging)图像以及合成图像等进行处理时,本文所给出的模型不仅能获得良好的分割效果,并且效率较高,而且从实验结果来看,本文模型具有一定的鲁棒性。     

Retinex theory based active contour model for segmentation of inhomogeneous images

Intensity inhomogeneity in images makes automated segmentation of these images difficult. As intensity inhomogeneity is often caused by inhomogeneous light reflection, the Retinex theory can be used to reduce inhomogeneity. We introduce the Retinex theory into the active contour model, which is commonly used for image segmentation. The segmentation procedure is then guided by the image intensity and light reflection. In order to solve the proposed model efficiently, we develop a new fast Split Bregman algorithm. Experimental results on a variety of real images with inhomogeneity validate the performance of the proposed methods.     

A Review of Statistical Approaches to Level Set Segmentation: Integrating Color,Texture, Motion and Shape

Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals. We point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.     

彩色纹理图像恢复的非局部TV模型及其特征保持

基于局部算子的不同形式的TV模型用于彩色图像噪声去除时往往存在边缘模糊、纹理模糊、阶梯效应、Mosaic效应等问题。本文基于非局部算子概念将传统的Tikhonov模型、TV模型、MTV模型、CTV模型推广到NL-CT模型、NL-LTV模型、NL-MTV模型、NL-CTV模型,并通过引入辅助变量和Bregman迭代参数设计了相应的快速Split Bregman算法。实验表明,所提出的非局部TV模型在纹理、边缘、光滑度等特征保持方面具有良好特性,且差异不大,但不同模型的计算效率存在较大差异。     

Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection

In this work, we are trying to propose fast algorithms for Mumford-Shah image segmentation using some recently proposed piecewise constant level set methods (PCLSM). Two variants of the PCLSM will be considered in this work. The first variant, which we call the binary level set method, needs a level set function which only takes values ±1 to identify the regions. The second variant only needs to use one piecewise constant level set function to identify arbitrary number of regions. For the Mumford-Shah image segmentation model with these new level set methods, one needs to minimize some smooth energy functionals under some constrains. A penalty method will be used to deal with the constraint. AOS (additive operator splitting) and MOS (multiplicative operator splitting) schemes will be used to solve the Euler-Lagrange equations for the minimization problems. By doing this, we obtain some algorithms which are essentially applying the MBO scheme for our segmentation models. Advantages and disadvantages are discussed for the proposed schemes. We acknowledge support from the Norwegian Research Council and IMS of the National University of Singapore.     

一种新变分方法在图像分割中的应用

针对传统的水平集方法用于图像分割时速度较慢的现象,提出一种新的变分方法(PDE)。首先修改了CV模型的能量函数,然后用凸松弛方法将其转化为凸优化问题,并引入一个辅助变量,再采用高效和无条件稳定的AOS算法,测试实验获得了较好的分割效果。实验结果表明,所提出的变分方法(PDE)是可行有效的。     

Error estimation for Bregman iterations and inverse scale space methods in image restoration

Summary In this paper, we consider error estimation for image restoration problems based on generalized Bregman distances. This error estimation technique has been used to derive convergence rates of variational regularization schemes for linear and nonlinear inverse problems by the authors before (cf. Burger in Inverse Prob 20: 1411–1421, 2004; Resmerita in Inverse Prob 21: 1303–1314, 2005; Inverse Prob 22: 801–814, 2006), but so far it was not applied to image restoration in a systematic way. Due to the flexibility of the Bregman distances, this approach is particularly attractive for imaging tasks, where often singular energies (non-differentiable, not strictly convex) are used to achieve certain tasks such as preservation of edges. Besides the discussion of the variational image restoration schemes, our main goal in this paper is to extend the error estimation approach to iterative regularization schemes (and time-continuous flows) that have emerged recently as multiscale restoration techniques and could improve some shortcomings of the variational schemes. We derive error estimates between the iterates and the exact image both in the case of clean and noisy data, the latter also giving indications on the choice of termination criteria. The error estimates are applied to various image restoration approaches such as denoising and decomposition by total variation and wavelet methods. We shall see that interesting results for various restoration approaches can be deduced from our general results by just exploring the structure of subgradients.      

Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective

We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By duality, we establish an information-theoretic interpretation using Bregman divergences. We demonstrate how this formulation couples in a principled way image restoration tasks such as denoising, deblurring (deconvolution), and inpainting with segmentation. We present an alternating minimization algorithm to solve the resulting composite photometric/geometric inverse problem. We use Fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates. We derive the shape gradient of our data-fitting energy and investigate convex relaxation for the geometric problem. We introduce a new alternating split-Bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real-world images.     

Bregmanized Domain Decomposition for Image Restoration

Computational problems of large-scale data are gaining attention recently due to better hardware and hence, higher dimensionality of images and data sets acquired in applications. In the last couple of years non-smooth minimization problems such as total variation minimization became increasingly important for the solution of these tasks. While being favorable due to the improved enhancement of images compared to smooth imaging approaches, non-smooth minimization problems typically scale badly with the dimension of the data. Hence, for large imaging problems solved by total variation minimization domain decomposition algorithms have been proposed, aiming to split one large problem into N>1 smaller problems which can be solved on parallel CPUs. The N subproblems constitute constrained minimization problems, where the constraint enforces the support of the minimizer to be the respective subdomain. In this paper we discuss a fast computational algorithm to solve domain decomposition for total variation minimization. In particular, we accelerate the computation of the subproblems by nested Bregman iterations. We propose a Bregmanized Operator Splitting–Split Bregman (BOS-SB) algorithm, which enforces the restriction onto the respective subdomain by a Bregman iteration that is subsequently solved by a Split Bregman strategy. The computational performance of this new approach is discussed for its application to image inpainting and image deblurring. It turns out that the proposed new solution technique is up to three times faster than the iterative algorithm currently used in domain decomposition methods for total variation minimization.     

融合区域和边缘特征的水平集水下图像分割

目的 水平集模型是图像分割中的一种先进方法,在陆地环境图像分割中展现出较好效果。特征融合策略被广泛引入到该模型框架,以拉伸目标-背景对比度,进而提高对高噪声、杂乱纹理等多类复杂图像的处理性能。然而,在水下环境中,由于水体高散射、强衰减等多因素的共同作用,使得现有图像特征及水平集模型难以适用于对水下图像的分割任务,分割结果与目标形态间存在较大差异。鉴于此,提出一种适用于水下图像分割的区域-边缘水平集模型,以提高水下图像目标分割的准确性。方法 综合应用图像的区域特征及边缘特征对水下目标进行辨识。对于区域特征,引入水下图像显著性特征;对于边缘特征,创新性地提出了一种基于深度信息的边缘特征提取方法。所提方法在融合区域级和边缘级特征的基础上,引入距离正则项对水平集函数进行规范,以增强水平集函数演化的稳定性。结果 基于YouTube和Bubblevision的水下数据集的实验结果表明,所提方法不仅对高散射强衰减的低对比度水下图像实现较好的分割效果,同时对处理强背景噪声图像也有较好的鲁棒性,与水平集分割方法（local pre-fitting,LPF）相比,分割精确度至少提高11.5%,与显著性检测方法（hierarchical co-salient detection via color names,HCN）相比,精确度提高6.7%左右。结论 实验表明区域-边缘特征融合以及其基础上的水平集模型能够较好地克服水下图像分割中的部分难点,所提方法能够较好分割水下目标区域并拟合目标轮廓,与现有方法对比获得了较好的分割结果。     

基于GFO模型的水平集分割算法

众所周知,水平集分割方法由于能克服Snake分割中所要求的初始轮廓必须与目标轮廓相近以及图像结构不应发生拓扑改变这两大难题而深受青睐。然而,其在图像分割遇到的最大困难是解决边界泄漏问题。虽然有许多研究工作均试图解决这一难题,但收获甚微,究其原因主要是：图像的梯度信息不仅被作为轮廓线运动的停止策略,同时也将为零水平集向目标轮廓运动提供吸引力。因此,其不可避免将产生边界泄漏现象。针对这一难题,本文通过采用GFO模型以提供更鲁棒的边界信息和更可靠的停止策略来构造运动驱动力,从而较好地解决传统水平集分割算法所不能解决的大部分边界泄漏难题。     

基于变分水平集的图像分割模型

基于传统的变分水平集方法的图像分割,水平集函数必须周期性地重新初始化使之保持为符号距离函数,这存在如何选择重新初始化的时间和方式的难题.Li模型通过在能量泛函中引入一个内部约束能量,去除了水平集函数在演化过程中需重新初始化的难题.通过对Li模型的分析,提出了一个新的变分水平集的分割模型.该模型通过在能量泛函中加入一个较简单的内部约束能量,同样可以实现水平集演化过程中的无需重新初始化.并且通过对边缘停止函数的重新定义,引入了新的外部能量,使得本文模型对噪声图像的分割更具鲁棒性.实验表明无论是在收敛速度上,还是在对噪声图像的分割质量上,本文模型和Li模型相比都具有一定的优势.     

基于声纳图像的水平集分割算法研究

针对现有的图像分割方法无法准确地分割声纳图像的问题,提出了一种改进的水平集声纳图像分割方法。介绍了LBF能量模型,借鉴其无重初始化的水平集演化思想。为克服声纳图像中复杂背景带来的负面效应,利用形态学顶帽—底帽变换对声纳图像进行预处理,并在此基础上进行无需初始化的水平集分割。进行仿真对比实验,实验结果显示:与LBF能量模型相比,改进的水平集分割方法更加适应于背景不均匀的声纳图像分割。     

Mumford–Shah and Potts Regularization for Manifold-Valued Data

Mumford–Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford–Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan–Hadamard manifolds (which includes the data space in diffusion tensor imaging (DTI)), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford–Shah and Potts problems (for image regularization), we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to DTI as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum on real data.     

A novel multi-scale level set method for SAR image segmentation based on a statistical model

To overcome the problems of large data volumes and strong speckle noise in synthetic aperture radar (SAR) images, a multi-scale level set approach for SAR image segmentation is proposed in this article. Because the multi-scale analysis of SAR images preserves their highest resolution features while additionally making use of sets of images at lower resolutions to improve specific functions, the proposed method is useful for removing the influence of speckle and, at the same time, preserving important structural information. The Gamma distribution is one of the most commonly used models employed to represent the statistical characteristics of speckle noise in a SAR image and it is introduced to define the energy functional. Moreover, based on the multi-scale level set framework, an improved multi-layer approach is introduced for multi-region segmentation. To obtain a fast and more accurate result, a novel threshold segmentation result is used to represent the initial segmentation curve. The experiments with synthetic and real SAR images demonstrate the effectiveness of the new method.