A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction

We analyze a variational approach to image segmentation that is based on a strictly convex non-quadratic cost functional. The smoothness term combines a standard first-order measure for image regions with a total-variation based measure for signal transitions. Accordingly, the costs associated with discontinuities are given by the length of level lines and local image contrast. For real images, this provides a reasonable approximation of the variational model of Mumford and Shah that has been suggested as a generic approach to image segmentation.The global properties of the convex variational model are favorable to applications: Uniqueness of the solution, continuous dependence of the solution on both data and parameters, consistent and efficient numerical approximation of the solution with the FEM-method.Various global and local properties of the convex variational model are analyzed and illustrated with numerical examples. Apart from the favorable global properties, the approach is shown to provide a sound mathematical model of a useful locally adaptive smoothing process. A comparison is carried out with results of a region-growing technique related to the Mumford-Shah model.     

局部熵驱动的模糊区域竞争图像分割

针对现有图像分割模型对光照敏感,提出一种新的基于区域的主动轮廓线模型。该模型能量泛函包含一个惩罚区域弧长的几何正则项和一个区域数据拟合项,特别的是数据拟合项采用局部熵来区分不同的区域。首先,根据图像像素空间排列之间的相关性,采用一个滑动窗函数提取图像局部熵特征,将图像从灰度空间转化到相应局部熵特征空间;然后,在局部熵空间计算最大后验分割概率得出两相区域竞争模型,为了能够快速求解该模型,采用隶属度函数替换特征函数得到了凸的模糊区域竞争模型。最后,采用快速的Chambolle对偶方法得到全局最小解。实验结果表明,该算法可以得到令人满意的分割效果且收敛速度快和对光照稳定。     

多帧图像的Tikhonov正则化重建算法研究*

介绍了Tikhonov正则化超分辨率重建算法的基本原理和特点,在原有正则化空域图像复原方法的基础上,根据多帧序列图像之间的互补信息,提出一种改进的正则化空域图像复原的新方法,该算法直接将正则化函数作用于图像超分辨率重建算法的条件概率项内,提高了正则化项的校正效率,并用共轭梯度运算来改善算法的收敛性,节省了图像重建所需的时间。实验和仿真结果表明,与传统方法相比,该算法不仅减轻了图像边缘纹理的模糊性,提高了图像的清晰度,而且收敛速度快。     

Robust reconstruction of low-resolution document images by exploiting repetitive character behaviour

In this paper, we present a new approach for reconstructing low-resolution document images. Unlike other conventional reconstruction methods, the unknown pixel values are not estimated based on their local surrounding neighbourhood, but on the whole image. In particular, we exploit the multiple occurrence of characters in the scanned document. In order to take advantage of this repetitive behaviour, we divide the image into character segments and match similar character segments to filter relevant information before the reconstruction. A great advantage of our proposed approach over conventional approaches is that we have more information at our disposal, which leads to a better reconstruction of the high-resolution (HR) image. Experimental results confirm the effectiveness of our proposed method, which is expressed in a better optical character recognition (OCR) accuracy and visual superiority to other traditional interpolation and restoration methods.     

Image Sequence Analysis via Partial Differential Equations

This article deals with the problem of restoring and motion segmenting noisy image sequences with a static background. Usually, motion segmentation and image restoration are considered separately in image sequence restoration. Moreover, motion segmentation is often noise sensitive. In this article, the motion segmentation and the image restoration parts are performed in a coupled way, allowing the motion segmentation part to positively influence the restoration part and vice-versa. This is the key of our approach that allows to deal simultaneously with the problem of restoration and motion segmentation. To this end, we propose a theoretically justified optimization problem that permits to take into account both requirements. The model is theoretically justified. Existence and unicity are proved in the space of bounded variations. A suitable numerical scheme based on half quadratic minimization is then proposed and its convergence and stability demonstrated. Experimental results obtained on noisy synthetic data and real images will illustrate the capabilities of this original and promising approach.     

脑部MRI图像头皮三维提取及重建

开颅手术中,为了满足手术导航系统进行快速、准确定位的要求,提出一种脑部核磁共振成像(MRI)图像三维头皮轮廓提取方法。首先采用各向异性扩散滤波方法对图像滤波,借助BrainSuite3医学软件获取脑标记图像;然后将图像中脑实质部分剔除,根据非脑组织图像计算头皮组织的分割阈值;再利用数学形态学处理二值图像获取头皮轮廓;最后结合目标灰度信息,用移动立方体(MC)算法进行三维重建。实验结果表明,该方法结合阈值、数学形态学和MC算法,能连续、光滑地提取出头皮外轮廓,并使精度达到亚像素级别。     

图像光流联合驱动的变分光流计算新方法

提出一种基于图像光流联合驱动的变分光流计算方法。数据项采用灰度守恒和梯度守恒相结合、局部约束与全局约束结合的思想,并引入正则化因子提高计算精度。平滑项采用图像与光流联合驱动的各向异性平滑策略,将数据项与平滑项紧密地联系起来,并通过设计扩散张量的两个本征值来控制光流扩散速度。最后采用多分辨率分层细化策略解决大位移问题。实验结果证明,该计算模型在背景复杂、光照变化、运动边界等情况的光流计算具有很好的效果。     

结合区域生长与灰度重建的CT图像肺气管树分割

目的 CT图像中肺气管树分割对肺部疾病的精确定位与量化评估具有重要意义。针对不同气管分枝在大小、形状和密度分布方面的差异,提出一种区域生长与形态学灰度重建相结合的3维肺气管树分割流程,重点解决气管提取过程中的局部泄漏问题。方法 首先,采用阈值分割和形态学闭运算提取肺实质以定义感兴趣区域;然后,通过改进迟滞阈值区域生长法分割较粗气管,结合局部体积突变指标抑制侧向泄漏;接着,利用3维形态学灰度重建算法分割较细气管,并采用形状约束连接元分析和管形描述子剔除伪气管区域;最后,将上述两步分割结果融合成完整气管树。结果 采用EXACT’09竞赛提供的公开数据,选取20例测试图像及手工标记结果作为参考,分别从分杈点、分支数量和分支数比率等方面进行量化评估。实验结果表明,本文方法能在较低泄漏前提下成功检测出参考标准中一半以上的分支、平均分支数比率达到55.5%。结论 与竞赛网站公布的其他方法相比,本文方法结果评价指标处于中上水平,但算法简单、计算复杂度低、易于实现,在泄漏检测方面有一定优势。     

Unsupervised segmentation of noisy and inhomogeneous images using global region statistics with non-convex regularization

Improving the segmentation of magnetic resonance (MR) images remains challenging because of the presence of noise and inhomogeneous intensity. In this paper, we present an unsupervised, multiphase segmentation model based on a Bayesian framework for both MR image segmentation and bias field correction in the presence of noise. In our model, global region statistics are utilized as segmentation criteria in order to classify regions with similar mean intensities but different variances. Additionally, we propose an edge indicator function based on a guided filter (instead of a Gaussian filter) that can preserve the underlying edges of the image obscured by noise. The proposed edge indicator function is integrated with non-convex regularization to overcome the influence of noise, resulting in more accurate segmentation. Furthermore, the proposed model utilizes a Markov random field to model the spatial correlation between neighboring pixels, which increases the robustness of the model under high-noise conditions. Experimental results demonstrate significant advantages in terms of both segmentation accuracy and bias field correction for inhomogeneous images in the presence of noise.     

Perceptual grouping of segmented regions in color images

Image segmentation is often the first yet important step of an image understanding system. However, general-purpose image segmentation algorithms that do not rely on specific object models still cannot produce perceptually coherent segmentation of regions at a level comparable to humans. Over-segmentation and under-segmentation have plagued the research community in spite of many significant advances in the field. Therefore, grouping of segmented region plays a significant role in bridging image segmentation and high-level image understanding. In this paper, we focused on non-purposive grouping (NPG), which is built on general expectations of a perceptually desirable segmentation as opposed to any object specific models, such that the grouping algorithm is applicable to any image understanding application. We propose a probabilistic model for the NPG problem by defining the regions as a Markov random field (MRF). A collection of energy functions is used to characterize desired single-region properties and pair-wise region properties. The single-region properties include region area, region convexity, region compactness, and color variances in one region. The pair-wise properties include color mean differences between two regions; edge strength along the shared boundary; color variance of the cross-boundary area; and contour continuity between two regions. The grouping process is implemented by a greedy method using a highest confidence first (HCF) principle. Experiments have been performed on hundreds of color photographic images to show the effectiveness of the grouping algorithm using a set of fixed parameters.     

Optimal design of 2D conducting graded materials by minimizing quadratic functionals in the field

We explore a typical optimal design problem in 2D conductivity: given fixed amounts of two isotropic dielectric materials, decide how we are to mix them in a 2D domain so as to minimize a certain cost functional depending on the underlying electric field. We rely on a reformulation of the optimal design problem as a vector variational problem and examine its relaxation, taking advantage of the explicit formulae for the relaxed integrands recently computed in Pedregal (2003). We provide numerical evidence, based on our relaxation, that Tartar’s result Tartar (1994) is verified when the target field is zero (also for divergence-free fields) and optimal solutions are given by first-order laminates. This same evidence also holds for a general quadratic functional in the field.     

基于压缩感知的自适应正则化磁共振图像重构

当前基于压缩传感理论的正则化磁共振(CS-MR)图像重构算法普遍采用全局正则化参数,不能很好地在保持边缘和平滑噪声方面做出平衡。为此,提出一种自适应的正则化CS-MRI重构算法。结合图像稀疏性和其局部光滑性的先验知识,采用非线性共轭梯度下降算法求取最优化问题,并在迭代过程中自适应地改变局部正则化参数。新的正则化参数可以更好地恢复图像边缘,并且有利于平滑噪声,使代价函数在定义域内具有凸性;同时先验信息包含于正则化参数中,以提高图像的高频成分。实验结果表明该算法能有效权衡恢复图像边缘和平滑噪声两者的关系。     

Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering

We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimized. The new method is applicable to any images where the noise to be removed is uncorrelated with the signal, under the assumptions that the filter used is suitable for the given type of data, and that neither the additive noise nor the filtering procedure alter the average gray value; no other knowledge (e.g. the noise variance, training data etc.) is needed.We analyse the theoretical properties of the method, then test the performance of our time estimation procedure experimentally, and demonstrate that it yields near-optimal results for a wide range of noise levels and for various filtering methods.     

基于CT序列图像的活体距骨分割及三维重建

了解距骨的解剖结构及空间关系,可为对其进行非侵入式运动学研究打下基础,对后足的疾病诊断具有重要意义。本文基于活体后足的CT序列图像,采用阈值、数学形态学和交互式操作相结合的手段从图像中分割出距骨,并用体绘制方法对距骨进行三维重建。实验表明,本文提出的分割方法简单且自动化程度较高。     

On the Incorporation of Time-delay Regularization into Curvature-based Diffusion

A new anisotropic nonlinear diffusion model incorporating time-delay regularization into curvature-based diffusion is proposed for image restoration and edge detection. A detailed mathematical analysis of the proposed model in the form of the proof of existence, uniqueness and stability of the viscosity solution of the model is presented. Furthermore, implementation issues and computational methods for the proposed model are also discussed in detail. The results obtained from testing our denoising and edge detection algorithm on several synthetic and real images showed the effectiveness of the proposed model in prserving sharp edges and fine structures while removing noise.     

An iterative Gibbsian technique for reconstruction of m-ary images

The reconstruction of m-ary images corrupted by independent noise is treated. The original image is modeled by a Markov Random Field (MRF) whose parameters are unknown. Likewise, the probabilistic structure of the noise is unknown. This paper presents an iterative procedure which performs the parameter estimation and image reconstruction tasks at the same time. The procedure that we call Gibbsian EM algorithm, is a generalization to the MRF context of a general algorithm, known as the EM algorithm, used to approximate maximum-likelihood estimates for incomplete data problems. A number of experiments are presented in the case of Gaussian noise and binary noise, showing that the Gibbsian EM algorithm is useful and effective for image reconstruction and segmentation.     

GASepo-a software solution for quantitative analysis of digital images in Epo doping control

A software has been developed that is aimed at quantitative analysis of images acquired by isoelectric focusing and double blotting procedures used for recombinant erythropoietin doping control. It represents a unified and easy-to-use tool for Epo doping experts in WADA accredited laboratories. It is based on image segmentation philosophy that enables identification of individual bands whose characteristics are needed for evaluation of the Epo doping positivity criteria. Several modules implemented in the GASepo software include an original know how, in particular, the method of robust calculation of the cut-off line, band segmentation and classification algorithms. GASepo is being used in several doping control laboratories worldwide.     

Unsupervised segmentation of ultrasonic liver images by multiresolution fractal feature vector

The feasibility of selecting fractal feature vector based on multiresolution analysis to segment suspicious abnormal regions of ultrasonic liver images is described in this paper. The proposed feature extraction algorithm is based on the spatial-frequency decomposition and fractal geometry. Segmentation of various liver diseases reveals that the fractal feature vector based on multiresolution analysis is trustworthy. A quantitative characterization based on the proposed unsupervised segmentation algorithm can be utilized to establish an automatic computer-aided diagnostic system. As well, to increase the visual interpretation capability of ultrasonic liver image for junior physicians, off-line learning software is developed to investigate the visual criteria.     

自适应滤波结合改进T-snake模型的甲状腺超声图自动分割方法

提出一种基于T-snake模型的甲状腺超声波图像分割的新方法。首先,结合基于窗口的各向异性扩散滤波方法与自适应加权中值滤波算法有效地消除甲状腺超声波图像斑点噪声;其次,以传统T-snake模型为基础,增加自适应区域能量和膨胀力对非连续边界与弱边界进行有效提取,实现甲状腺超声波图像的自动分割;最后设定模型参数,使用临床数据进行实验。结果证明,应用该方法得到自动分割结果的平均相对差异度小于5%,平均相对重叠度大于91%,验证了其可行性。