Effective fuzzy c-means based kernel function in segmenting medical images

The objective of this paper is to develop an effective robust fuzzy c-means for a segmentation of breast and brain magnetic resonance images. The widely used conventional fuzzy c-means for medical image segmentations has limitations because of its squared-norm distance measure to measure the similarity between centers and data objects of medical images which are corrupted by heavy noise, outliers, and other imaging artifacts. To overcome the limitations this paper develops a novel objective function based standard objective function of fuzzy c-means that incorporates the robust kernel-induced distance for clustering the corrupted dataset of breast and brain medical images. By minimizing the novel objective function this paper obtains effective equation for optimal cluster centers and equation to achieve optimal membership grades for partitioning the given dataset. In order to solve the problems of clustering performance affected by initial centers of clusters, this paper introduces a specialized center initialization method for executing the proposed algorithm in segmenting medical images. Experiments are performed with synthetic, real breast and brain images to assess the performance of the proposed method. Further the validity of clustering results is obtained using silhouette method and this paper compares the results with the results of other recent reported fuzzy c-means methods. The experimental results show the superiority of the proposed clustering results.     

Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization

An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.     

A novel kernelized fuzzy C-means algorithm with application in medical image segmentation

Image segmentation plays a crucial role in many medical imaging applications. In this paper, we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data. The algorithm is realized by modifying the objective function in the conventional fuzzy C-means (FCM) algorithm using a kernel-induced distance metric and a spatial penalty on the membership functions. Firstly, the original Euclidean distance in the FCM is replaced by a kernel-induced distance, and thus the corresponding algorithm is derived and called as the kernelized fuzzy C-means (KFCM) algorithm, which is shown to be more robust than FCM. Then a spatial penalty is added to the objective function in KFCM to compensate for the intensity inhomogeneities of MR image and to allow the labeling of a pixel to be influenced by its neighbors in the image. The penalty term acts as a regularizer and has a coefficient ranging from zero to one. Experimental results on both synthetic and real MR images show that the proposed algorithms have better performance when noise and other artifacts are present than the standard algorithms.     

磁共振成像PROPELLER采样数据重建中的运动估计新算法

PROPELLER（推进器）采样技术能够利用K空间中心重叠采样区域的数据来估计采集过程中受检查者的运动进而加以补偿,对运动伪影的消除效果非常显著。然而,由于其重建时的运动估计是基于最大化频域空间上相关系数的配准算法,该算法为了实现旋转估计与平移估计的分离,在进行旋转估计时,仅仅采用K空间数据的模,在数据量有限的情况下造成估计精度较低,在重建图像上表现为模糊及星条状伪影。本研究基于最大化图像空间上的互信息提出一种PROPELLER采样数据的运动估计新算法,首先由每个K空间带进行傅立叶逆变换后取模重建出系列临时图像,对这些图像进行模糊增强后以互信息作为相似性测度迭代搜索最优的运动参数。实验证明,该方法能显著提高PROPELLER采样数据重建中运动估计与补偿的精度,从而更好地消除伪影,特别是用于有运动时T1加权头部成像时。     

Motion correction for three-dimensional chemical exchange saturation transfer imaging without direct water saturation artifacts

In chemical exchange saturation transfer (CEST) MRI, motion correction is compromised by the drastically changing image contrast at different frequency offsets, particularly at the direct water saturation. In this study, a simple extension for conventional image registration algorithms is proposed, enabling robust and accurate motion correction of CEST-MRI data. The proposed method uses weighted averaging of motion parameters from a conventional rigid image registration to identify and mitigate erroneously misaligned images. Functionality of the proposed method was verified by ground truth datasets generated from 10 three-dimensional in vivo measurements at 3 T with simulated realistic random rigid motion patterns and noise. Performance was assessed using two different criteria: the maximum image misalignment as a measure for the robustness against direct water saturation artifacts, and the spectral error as a measure of the overall accuracy. For both criteria, the proposed method achieved the best scores compared with two motion-correction algorithms specifically developed to handle the varying contrasts in CEST-MRI. Compared with a straightforward linear interpolation of the motion parameters at frequency offsets close to the direct water saturation, the proposed method offers better performance in the absence of artifacts. The proposed method for motion correction in CEST-MRI allows identification and mitigation of direct water saturation artifacts that occur with conventional image registration algorithms. The resulting improved robustness and accuracy enable reliable motion correction, which is particularly crucial for an automated and carefree evaluation of spectral CEST-MRI data, e.g., for large patient cohorts or in clinical routines.     

基于调幅-调频与熵图多模态医学图像的配准

背景：基于传统互信息量的多模态医学图像配准方法配准时需要利用二维直方图或者Parzen窗函数的方法估计概率密度分布,进而计算互信息量,这种方式计算速度慢,而且只考虑了图像的灰度信息,容易出现误配。 目的：针对目前主流的配准方法鲁棒性差、耗时的缺点,提出了一种新的基于调幅-调频(AM-FM)特征互信息量的快速配准方法。 方法：该方法考虑了图像的空间和结构信息;首先通过AM-FM模型对图像进行分解,得到图像的AM-FM特征,与图像的灰度特征一起组成高维特征;然后利用熵图和最小生成树加快AM-FM特征互信息量的计算,从而实现了医学图像的快速配准。 结果与结论：对20组磁共振T1-T2加权图像、CT/正电子发射计算机断层成像图像进行了实验,结果表明该方法在图像空间分辨率较低,有噪声影响等情况下均可以达到较好的结果,且配准精度优于国际上的主流方法,具有计算速度快,精度高,鲁棒性强的特点,适于临床应用。     

Robust surface registration using salient anatomical features for image-guided liver surgery: algorithm and validation

A successful surface-based image-to-physical space registration in image-guided liver surgery (IGLS) is critical to provide reliable guidance information to surgeons and pertinent surface displacement data for use in deformation correction algorithms. The current protocol used to perform the image-to-physical space registration involves an initial pose estimation provided by a point based registration of anatomical landmarks identifiable in both the preoperative tomograms and the intraoperative presentation. The surface based registration is then performed via a traditional iterative closest point (ICP) algorithm between the preoperative liver surface, segmented from the tomographic image set, and an intraoperatively acquired point cloud of the liver surface provided by a laser range scanner. Using this more conventional method, the registration accuracy can be compromised by poor initial pose estimation as well as tissue deformation due to the laparotomy and liver mobilization performed prior to tumor resection. In order to increase the robustness of the current surface-based registration method used in IGLS, we propose the incorporation of salient anatomical features, identifiable in both the preoperative image sets and intraoperative liver surface data, to aid in the initial pose estimation and play a more significant role in the surface-based registration via a novel weighting scheme. Examples of such salient anatomical features are the falciform groove region as well as the inferior ridge of the liver surface. In order to validate the proposed weighted patch registration method, the alignment results provided by the proposed algorithm using both single and multiple patch regions were compared with the traditional ICP method using six clinical datasets. Robustness studies were also performed using both phantom and clinical data to compare the resulting registrations provided by the proposed algorithm and the traditional method under conditions of varying initial pose. The results provided by the robustness trials and clinical registration comparisons suggest that the proposed weighted patch registration algorithm provides a more robust method with which to perform the image-to-physical space registration in IGLS. Furthermore, the implementation of the proposed algorithm during surgical procedures does not impose significant increases in computation or data acquisition times.     

Robust edge-directed interpolation of magnetic resonance images

Image interpolation is intrinsically a severely under-determined inverse problem. Traditional non-adaptive interpolation methods do not account for local image statistics around the edges of image structures. In practice, this results in artifacts such as jagged edges, blurring and/or edge halos. To overcome this shortcoming, edge-directed interpolation has been introduced in different forms. One variant, new edge-directed interpolation (NEDI), has successfully exploited the 'geometric duality' that links the low-resolution image to its corresponding high-resolution image. It has been demonstrated that for scalar images, NEDI is able to produce better results than non-adaptive traditional methods, both visually and quantitatively. In this work, we return to the root of NEDI as a least-squares estimation method of neighborhood patterns and propose a robust scheme to improve it. The improvement is twofold: firstly, a robust least-squares technique is used to improve NEDI's performance to outliers and noise; secondly, the NEDI algorithm is extended with the recently proposed non-local mean estimation scheme. Moreover, the edge-directed concept is applied to the interpolation of multi-valued diffusion-weighted images. The framework is tested on phantom scalar images and real diffusion images, and is shown to achieve better results than the non-adaptive methods as well as NEDI, in terms of visual quality as well as quantitative measures.     

Automatic registration of the prostate for computed-tomography-guided radiotherapy

The recent development of integrated computed tomography (CT)/linear accelerator (LINAC) combinations, where the CT scanner and the LINAC use the same patient couch, and of kilovoltage cone-beam CT systems attached to the LINAC gantry, means that suitable hardware is now available for CT-guided localization of the prostate. Clinical implementation is, however, currently impeded by the lack of robust and accurate software tools to compare the position of the prostate in the CT images used for the treatment plan with its position in the daily CT images. Manual registration of the planning CT images with the daily CT images can be slow and can introduce significant inter-user variations. We have developed an automatic registration technique that is not adversely influenced by changes in prostate shape, size or orientation, presence of rectal gas, or bladder filling. The cost function used in the registration is the mean absolute difference in CT numbers voxel-by-voxel between the daily CT image and the planning CT image for a volume extracted from the planning CT images using the original physician-drawn gross tumor volume contours. To enhance soft tissue contrast in the prostate region and to reduce the impact of rectal gas calcifications and bone on the registration, voxels with CT numbers that represent gas or bone are filtered out from the calculation. The results of the automatic registration agreed with the mean results of seven human observers, with standard deviations of 0.5 mm, 0.5 mm, and 1.0 mm in the left/right (RL), anterior/posterior (AP), and superior/inferior (SI) directions, respectively, for a patient that was relatively easy to localize. Agreement (one standard deviation) for a patient that was difficult to localize was 0.6 mm, 1.4 mm, and 1.9 mm in the RL, AP, and SI directions, respectively. These results are better than the interuser uncertainties reported for a manual alignment technique and are close to the reported intrauser uncertainties. The results are independent of the shape of contours in the original treatment plan, reducing the impact of interobserver variations in contouring the prostate. The algorithm is fast and reliable, allowing the entire CT localization process to take place in 5-9 minutes. In 120 CT image sets from seven patients, the failure rate was found to be less than 1%. The use of this algorithm will facilitate the clinical implementation of CT-guided localization of the prostate.     

Use of simulated annealing for optimization of alignment parameters in limited MRI acquisition volumes of the brain

Studies suggest that clinical outcomes are improved in repeat trigeminal neuralgia (TN) Gamma Knife radiosurgery if a different part of the nerve from the previous radiosurgery is treated. The MR images taken in the first and repeat radiosurgery need to be coregistered to map the first radiosurgery volume onto the second treatment planning image. We propose a fully automatic and robust three-dimensional (3-D) mutual information- (MI-) based registration method engineered by a simulated annealing (SA) optimization technique. Commonly, Powell's method and Downhill simplex (DS) method are most popular in optimizing the MI objective function in medical image registration applications. However, due to the nonconvex property of the MI function, robustness of those two methods is questionable, especially for our cases, where only 28 slices of MR T1 images were utilized. Our SA method obtained successful registration results for all the 41 patients recruited in this study. On the other hand, Powell's method and the DS method failed to provide satisfactory registration for 11 patients and 9 patients, respectively. The overlapping volume ratio (OVR) is defined to quantify the degree of the partial volume overlap between the first and second MR scan. Statistical results from a logistic regression procedure demonstrated that the probability of a success of Powell's method tends to decrease as OVR decreases. The rigid registration with Powell's or the DS method is not suitable for the TN radiosurgery application, where OVR is likely to be low. In summary, our experimental results demonstrated that the MI-based registration method with the SA optimization technique is a robust and reliable option when the number of slices in the imaging study is limited.     

基于特征提取的脑部医学图像配准研究

目的 基于特征的配准算法具有鲁棒性强、针对性好等显著优势,在图像配准领域被广泛应用,但是该类方法的精度受图像间特征构建和环境噪声影响大,该研究旨在对其缺点进行改进。方法 该研究基于SURF和ORB两种算法,提出了SURF-ORB算法,将参考图像与待配准图像分成上下两部分分别配准。在配准过程中,首先对SURF提取的图像特征点的Harris响应值进行优化,并使用灰度质心法确定特征点主方向。然后计算rBRIEF（旋转BRIEF）描述子,并使用汉明距离进行特征点匹配。最后加入RANSAC精匹配算法,剔除误匹配点。结果和结论 该研究通过对比分析SURF、ORB、SURF-ORB这3种算法的配准结果、抗噪声能力及多模态配准能力,验证了SURF-ORB算法具有较高的配准精度、配准速度和抗噪声能力。文章的创新之处该研究首次将SURF和ORB两种算法进行结合并应用于脑部横断面图像。     

Image registration with auto-mapped control volumes

Many image registration algorithms rely on the use of homologous control points on the two input image sets to be registered. In reality, the interactive identification of the control points on both images is tedious, difficult, and often a source of error. We propose a two-step algorithm to automatically identify homologous regions that are used as a priori information during the image registration procedure. First, a number of small control volumes having distinct anatomical features are identified on the model image in a somewhat arbitrary fashion. Instead of attempting to find their correspondences in the reference image through user interaction, in the proposed method, each of the control regions is mapped to the corresponding part of the reference image by using an automated image registration algorithm. A normalized cross-correlation (NCC) function or mutual information was used as the auto-mapping metric and a limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) was employed to optimize the function to find the optimal mapping. For rigid registration, the transformation parameters of the system are obtained by averaging that derived from the individual control volumes. In our deformable calculation, the mapped control volumes are treated as the nodes or control points with known positions on the two images. If the number of control volumes is not enough to cover the whole image to be registered, additional nodes are placed on the model image and then located on the reference image in a manner similar to the conventional BSpline deformable calculation. For deformable registration, the established correspondence by the auto-mapped control volumes provides valuable guidance for the registration calculation and greatly reduces the dimensionality of the problem. The performance of the two-step registrations was applied to three rigid registration cases (two PET-CT registrations and a brain MRI-CT registration) and one deformable registration of inhale and exhale phases of a lung 4D CT. Algorithm convergence was confirmed by starting the registration calculations from a large number of initial transformation parameters. An accuracy of approximately 2 mm was achieved for both deformable and rigid registration. The proposed image registration method greatly reduces the complexity involved in the determination of homologous control points and allows us to minimize the subjectivity and uncertainty associated with the current manual interactive approach. Patient studies have indicated that the two-step registration technique is fast, reliable, and provides a valuable tool to facilitate both rigid and nonrigid image registrations.     

Robust and fast shell registration in PET and MR/CT brain images

A robust and fast hybrid method using a shell volume that consists of high contrast voxels with their neighbors is proposed for registering PET and MR/CT brain images. Whereas conventional hybrid methods find the best matched pairs from several manually selected or automatically extracted local regions, our method automatically selects a shell volume in the PET image, and finds the best matched corresponding volume using normalized mutual information (NMI) in overlapping volumes while transforming the shell volume into an MR or CT image. A shell volume not only can reduce irrelevant corresponding voxels between two images during optimization of transformation parameters, but also brings a more robust registration with less computational cost. Experimental results on clinical data sets showed that our method successfully aligned all PET and MR/CT image pairs without losing any diagnostic information, while the conventional registration methods failed in some cases.     

Biomechanical Model as a Registration Tool for Image-Guided Neurosurgery: Evaluation Against BSpline Registration

In this paper we evaluate the accuracy of warping of neuro-images using brain deformation predicted by means of a patient-specific biomechanical model against registration using a BSpline-based free form deformation algorithm. Unlike the BSpline algorithm, biomechanics-based registration does not require an intra-operative MR image which is very expensive and cumbersome to acquire. Only sparse intra-operative data on the brain surface is sufficient to compute deformation for the whole brain. In this contribution the deformation fields obtained from both methods are qualitatively compared and overlaps of Canny edges extracted from the images are examined. We define an edge based Hausdorff distance metric to quantitatively evaluate the accuracy of registration for these two algorithms. The qualitative and quantitative evaluations indicate that our biomechanics-based registration algorithm, despite using much less input data, has at least as high registration accuracy as that of the BSpline algorithm.     

Direct cone-beam cardiac reconstruction algorithm with cardiac banding artifact correction

Multislice helical computed tomography (CT) is a promising noninvasive technique for coronary artery imaging. Various factors can cause inconsistencies in cardiac CT data, which can result in degraded image quality. These inconsistencies may be the result of the patient physiology (e.g., heart rate variations), the nature of the data (e.g., cone-angle), or the reconstruction algorithm itself. An algorithm which provides the best temporal resolution for each slice, for example, often provides suboptimal image quality for the entire volume since the cardiac temporal resolution (TRc) changes from slice to slice. Such variations in TRc can generate strong banding artifacts in multiplanar reconstruction images or three-dimensional images. Discontinuous heart walls and coronary arteries may compromise the accuracy of the diagnosis. A beta-blocker is often used to reduce and stabilize patients' heart rate but cannot eliminate the variation. In order to obtain robust and optimal image quality, a software solution that increases the temporal resolution and decreases the effect of heart rate is highly desirable. This paper proposes an ECG-correlated direct cone-beam reconstruction algorithm (TCOT-EGR) with cardiac banding artifact correction (CBC) and disconnected projections redundancy compensation technique (DIRECT). First the theory and analytical model of the cardiac temporal resolution is outlined. Next, the performance of the proposed algorithms is evaluated by using computer simulations as well as patient data. It will be shown that the proposed algorithms enhance the robustness of the image quality against inconsistencies by guaranteeing smooth transition of heart cycles used in reconstruction.     

Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET

Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm3 and 64 mm3). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The analysis of both simulated and acquired datasets led to similar results and conclusions as far as the performance of segmentation algorithms under evaluation is concerned.     

High-quality 3D correction of ring and radiant artifacts in flat panel detector-based cone beam volume CT imaging

The use of an x-ray flat panel detector is increasingly becoming popular in 3D cone beam volume CT machines. Due to the deficient semiconductor array manufacturing process, the cone beam projection data are often corrupted by different types of abnormalities, which cause severe ring and radiant artifacts in a cone beam reconstruction image, and as a result, the diagnostic image quality is degraded. In this paper, a novel technique is presented for the correction of error in the 2D cone beam projections due to abnormalities often observed in 2D x-ray flat panel detectors. Template images are derived from the responses of the detector pixels using their statistical properties and then an effective non-causal derivative-based detection algorithm in 2D space is presented for the detection of defective and mis-calibrated detector elements separately. An image inpainting-based 3D correction scheme is proposed for the estimation of responses of defective detector elements, and the responses of the mis-calibrated detector elements are corrected using the normalization technique. For real-time implementation, a simplification of the proposed off-line method is also suggested. Finally, the proposed algorithms are tested using different real cone beam volume CT images and the experimental results demonstrate that the proposed methods can effectively remove ring and radiant artifacts from cone beam volume CT images compared to other reported techniques in the literature.     

利用边缘和表面特征实现脑图像的自动配准

本文中我们使用基于CT、MR和PET图像等值特征表面的配准算法对多模医学图像进行了配准研究，在CT、MR和PET的原始图像中提取等值特征表面，进行图像的几何对准，并对结果进行初步评估，同时对该算法的稳健性，搜索最近点策略和采样策略进行了研究，结果表明；这种方法能够达到亚像素级的配准精度，是一种稳健、高精度、全自动的配准方法。     

一种基于稀疏分解去除EEG信号中MRI伪迹的新方法

在脑电图(Electroencephalography,EEG)和功能磁共振成像(Functional magnetic resonance imaging, FMRI)同时记录时,如何有效的去除混入EEG信号中的强磁共振(Magnetic resonance imaging,MRI)伪迹干扰信号是当前在EEG和FMRI的联合研究中面临的一个信号前期处理难点。主要从MRI干扰信号和EEG信号在时空上的差别出发,提出了一种基于混合过完备库的稀疏成分分析的分解方法,实现了强MRI干扰下的EEG信号的估计。在方法实现中,首先利用小波和离散余弦构造能体现MRI干扰和EEG时空特性差别的混合过完备库,然后通过匹配追踪(Matching pursuit,MP)方法在混合过完备库中的学习,实现MRI伪迹的消除。对模拟数据以及真实记录的混入了MRI干扰的EEG信号的估计实验结果,证实了该方法的有效性。