Reconstruction of 3-D left ventricular motion from planar tagged cardiac MR images: an estimation theoretic approach

Magnetic resonance (MR) tagging has shown great potential for noninvasive measurement of the motion of a beating heart. In MR tagged images, the heart appears with a spatially encoded pattern that moves with the tissue. The position of the tag pattern in each frame of the image sequence can be used to obtain a measurement of the 3-D displacement field of the myocardium. The measurements are sparse, however, and interpolation is required to reconstruct a dense displacement field from which measures of local contractile performance such as strain can be computed. Here, the authors propose a method for estimating a dense displacement field from sparse displacement measurements. Their approach is based on a multidimensional stochastic model for the smoothness and divergence of the displacement field and the Fisher estimation framework. The main feature of this method is that both the displacement field model and the resulting estimate equation are defined only on the irregular domain of the myocardium. The authors' methods are validated on both simulated and in vivo heart data.     

Noise characteristics of 3-D and 2-D PET images

The authors analyzed the noise characteristics of two-dimensional (2-D) and three-dimensional (3-D) images obtained from the GE Advance positron emission tomography (PET) scanner. Three phantoms were used: a uniform 20-cm phantom, a 3-D Hoffman brain phantom, and a chest phantom with heart and lung inserts. Using gated acquisition, the authors acquired 20 statistically equivalent scans of each phantom in 2-D and 3-D modes at several activity levels. From these data, they calculated pixel normalized standard deviations (NSD's), scaled to phantom mean, across the replicate scans, which allowed them to characterize the radial and axial distributions of pixel noise. The authors also performed sequential measurements of the phantoms in 2-D and 3-D modes to measure noise (from interpixel standard deviations) as a function of activity. To compensate for the difference in axial slice width between 2-D and 3-D images (due to the septa and reconstruction effects), they developed a smoothing kernel to apply to the 2-D data. After matching the resolution, the ratio of image-derived NSD values (NSD_2D/NSD_3D)² averaged throughout the uniform phantom was in good agreement with the noise equivalent count (NEC) ratio (NEC_3D/NEC_2D). By comparing different phantoms, the authors showed that the attenuation and emission distributions influence the spatial noise distribution. The estimates of pixel noise for 2-D and 3-D images produced here can be applied in the weighting of PET kinetic data and may be useful in the design of optimal dose and scanning requirements for PET studies. The accuracy of these phantom-based noise formulas should be validated for any given imaging situation, particularly in 3-D, if there is significant activity outside the scanner field of view     

3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization.

This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.     

Nonrigid registration of 3-D free-hand ultrasound images of the breast

Three-dimensional (3-D) ultrasound imaging of the breast enables better assessment of diseases than conventional two-dimensional (2-D) imaging. Free-hand techniques are often used for generating 3-D data from a sequence of 2-D slice images. However, the breast deforms substantially during scanning because it is composed primarily of soft tissue. This often causes tissue mis-registration in spatial compounding of multiple scan sweeps. To overcome this problem, in this paper, instead of introducing additional constraints on scanning conditions, we use image processing techniques. We present a fully automatic algorithm for 3-D nonlinear registration of free-hand ultrasound data. It uses a block matching scheme and local statistics to estimate local tissue deformation. A Bayesian regularization method is applied to the sample displacement field. The final deformation field is obtained by fitting a B-spline approximating mesh to the sample displacement field. Registration accuracy is evaluated using phantom data and similar registration errors are achieved with (0.19 mm) and without (0.16 mm) gaps in the data. Experimental results show that registration is crucial in spatial compounding of different sweeps. The execution time of the method on moderate hardware is sufficiently fast for fairly large research studies.     

Estimation of 3-D left ventricular deformation from medical images using biomechanical models

The quantitative estimation of regional cardiac deformation from three-dimensional (3-D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image-derived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic, linear-elastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3-D estimates of heart deformation.     

3-D tracking and motion estimation using hierarchical Kalman filter

The authors present a novel approach to the problem of tracking and reconstructing articulated objects in 3-D space. The newly conceived computational process and its supporting data structure, the hierarchical Kalman filter (HKF) and the adaptive hierarchical structure (AHS). Allow the problem to be treated in a singlet unified framework. There are three novelties in the authors' formulation: reducing the 3-D tracking problem to 2-D tracking; incorporating the kinematic and the dynamic properties of object; and tracking nonrigid objects. To demonstrate the appropriateness of the proposed method, the authors present some of the experimental results on both synthetic and real images     

Automated Motion Estimation for 2-D Cine DENSE MRI

Cine displacement encoding with stimulated echoes (DENSE) is a magnetic resonance (MR) method that directly encodes tissue displacement into MR phase images. This technique has successfully interrogated many forms of tissue motion, but is most commonly used to evaluate cardiac mechanics. Currently, motion analysis from cine DENSE images requires manually delineated anatomical structures. An automated analysis would improve measurement throughput, simplify data interpretation, and potentially access important physiological information during the MR exam. In this paper, we present the first fully automated solution for the estimation of tissue motion and strain from 2-D cine DENSE data. Results using both simulated and human cardiac cine DENSE data indicate good agreement between the automated algorithm and the standard semi-manual analysis method.     

三维目标曲线SAR成像的降维搜索算法

曲线合成孔径雷达(CurviLinear Synthetic Aperture Radar,CLSAR)利用雷达平台的单条曲线轨迹就可形成三维成像所需的曲线合成孔径。由于CLSAR采集的数据在三维频率空间是稀疏的,简单地采用非参数化方法所获得的图像几乎无法使用,所以有价值的目标三维像必须采用参数化方法来获得。该文提出一种新的适用于CLSAR的目标三维成像算法。该算法巧妙地利用了接收数据中距离方向与垂直距离方向参数间的弱耦合性,将高维优化问题解耦为低维优化问题,并顺序地估计出相应参数,最后采用一个迭代过程进行参数求精。仿真实验表明,新算法是一种适用于CLSAR的有效的目标三维成像算法。     

Hierarchical 3-D Floorplanning Algorithm for Wirelength Optimization

Three-dimensional (3-D) IC physical design problems are usually of higher complexity, with a greatly enlarged solution space due to multiple device structure. In this paper, a new 3-D floorplanning algorithm is proposed for wirelength optimization. Our main contributions and results can be summarized as follows. First, a new hierarchical flow of 3-D floorplanning with a new inter-layer partitioning method. The blocks are partitioned into different layers before floorplanning. A simulated annealing (SA) engine is used to partition blocks with the objective of minimizing the statistical wirelength estimation results. The solution quality is not degraded by the hierarchical flow. Second, floorplans of all the layers are generated in a SA process. Original 3-D floorplanning problem is transformed into solving several 2-D floorplanning problems simultaneously. The solution space is scaled down to maintain a low design complexity. Finally, Experimental results show that our algorithm improves wirelength by 14%-51% compared with previous 3-D floorplanning algorithms. The hierarchical approach is proven to be very efficient and offers a potential way for high-performance 3-D design     

Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography

This paper presents a method to reconstruct moving objects from cone beam X-ray projections acquired during a single rotational run using a given motion vector field. The method is applicable to voxel driven cone-beam filtered back-projection reconstruction approaches. Here, a formulation based on the algorithm of Feldkamp, Davis, and Kress (FDK) is presented. The motion correction is applied during the back-projection step by shifting the voxel to be reconstructed according to the motion vector field. The method is applied to three-dimensional (3-D) rotational X-ray angiography. Projections from a beating coronary heart phantom are simulated. Motion-compensated reconstructions with varying accuracy of the applied motion field are carried out for a late diastolic heart phase and compared to the reconstruction obtained with the standard FDK-method from projections of the corresponding motion-free model in the same heart phase. Furthermore, gated reconstructions are calculated by weighting the projections according to their cardiac phase without using a motion vector field. Different gating window widths are applied, and the reconstructions are compared. Using the correct motion field with the motion-compensated reconstruction, the image quality of the standard reconstruction from the corresponding motion-free coronary model can almost be recovered. The reconstructed image quality stays acceptable if the accuracy of the motion field sampling points is better than 1 mm. The gated reconstructions with a window width of 15%-20% of the cardiac cycle lead to superior results compared to nearest neighbor gating, especially for histogram based visualization and analysis. The motion-compensated reconstructions provide sharp images of the coronaries far surpassing the image quality of gated reconstructions.     

Nonlinear filtering approach to 3-D gray-scale image interpolation

Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image. The authors propose a nonlinear-filter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. The authors also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effective than traditional gray-scale interpolation techniques.     

Matching 3-D prone and supine CT colonography scans using graphs

In this paper, we propose a new registration method for prone and supine computed tomographic colonography scans using graph matching. We formulate 3-D colon registration as a graph matching problem and propose a new graph matching algorithm based on mean field theory. In the proposed algorithm, we solve the matching problem in an iterative way. In each step, we use mean field theory to find the matched pair of nodes with highest probability. During iterative optimization, one-to-one matching constraints are added to the system in a step-by-step approach. Prominent matching pairs found in previous iterations are used to guide subsequent mean field calculations. The proposed method was found to have the best performance with smallest standard deviation compared with two other baseline algorithms called the normalized distance along the colon centerline (NDACC) ( p = 0.17) with manual colon centerline correction and spectral matching ( p < 1e-5). A major advantage of the proposed method is that it is fully automatic and does not require defining a colon centerline for registration. For the latter NDACC method, user interaction is almost always needed for identifying the colon centerlines.     

3-D/2-D registration by integrating 2-D information in 3-D

In image-guided therapy, high-quality preoperative images serve for planning and simulation, and intraoperatively as "background", onto which models of surgical instruments or radiation beams are projected. The link between a preoperative image and intraoperative physical space of the patient is established by image-to-patient registration. In this paper, we present a novel 3-D/2-D registration method. First, a 3-D image is reconstructed from a few 2-D X-ray images and next, the preoperative 3-D image is brought into the best possible spatial correspondence with the reconstructed image by optimizing a similarity measure (SM). Because the quality of the reconstructed image is generally low, we introduce a novel SM, which is able to cope with low image quality as well as with different imaging modalities. The novel 3-D/2-D registration method has been evaluated and compared to the gradient-based method (GBM) using standardized evaluation methodology and publicly available 3-D computed tomography (CT), 3-D rotational X-ray (3DRX), and magnetic resonance (MR) and 2-D X-ray images of two spine phantoms, for which gold standard registrations were known. For each of the 3DRX, CT, or MR images and each set of X-ray images, 1600 registrations were performed from starting positions, defined as the mean target registration error (mTRE), randomly generated and uniformly distributed in the interval of 0-20 mm around the gold standard. The capture range was defined as the distance from gold standard for which the final TRE was less than 2 mm in at least 95% of all cases. In terms of success rate, as the function of initial misalignment and capture range the proposed method outperformed the GBM. TREs of the novel method and the GBM were approximately the same. For the registration of 3DRX and CT images to X-ray images as few as 2-3 X-ray views were sufficient to obtain approximately 0.4 mm TREs, 7-9 mm capture range, and 80%-90% of successful registrations. To obtain similar results for MR to X-ray registrations, an image, reconstructed from at least 11 X-ray images was required. Reconstructions from more than 11 images had no effect on the registration results.     

一种高分辨率3维图像的自适应降噪算法

为了获得高保真3维图像,采用了一种针对高分辨率3维图像的自适应均值降噪算法。首先使用一种由激光器、高分辨率3维相机、直线电机和计算机等设备组成的线激光高精度3维测量实验系统对自然纹理皮革进行测量。然后针对系统测量所得的高分辨率3维自然纹理图像(每英寸点数大于1000),进行了理论分析和实验验证,取得了降噪后的高保真3维图像数据,并与传统的均值滤波、小波变换滤波的降噪效果进行对比。结果表明,该算法能自动选取最优的降噪窗口,有效地去除3维图像的噪声信息,并保留高分辨率图像丰富的边缘、细节信息,最终得到高保真的高分辨率3维自然纹理图像。该实验结果对于高分辨率图像的降噪问题是十分有帮助的。     

Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation

An efficient Gauss-Newton iterative imaging technique utilizing a three-dimensional (3-D) field solution coupled to a two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is presented for microwave tomographic imaging in medical applications. While electromagnetic wave propagation is described fully by a 3-D vector field, a 3-D scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy. In addition, the image recovery has been restricted to 2-D but is generalizable to three dimensions. Image artifacts related primarily to 3-D effects are reduced when compared with results from an entirely two-dimensional inversion (2-D/2-D). Important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for Jacobian construction. Methods which enhance the image quality such as the log-magnitude/unwrapped phase minimization were also applied. Results obtained from synthetic measurement data show that the new 3-D/2-D algorithm consistently outperforms its 2-D/2-D counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts.     

3-D segmentation of MR images of the head for 3-D display

Algorithms for 3-D segmentation and reconstruction of anatomical surfaces from magnetic resonance imaging (MRI) data are presented. The 3-D extension of the Marr-Hildreth operator is described, and it is shown that its zero crossings are related to anatomical surfaces. For an improved surface definition, morphological filters-dilation and erosion-are applied. From these contours, 3-D reconstructions of skin, bone, brain, and the ventricular system can be generated. Results obtained with different segmentation parameters and surface rendering methods are presented. The fidelity of the generated images comes close to anatomical reality. It is noted that both the convolution and the morphological filtering are computationally expensive, and thus take a long time on a general-purpose computer. Another problem is assigning labels to the constituents of the head; in the current implementation, this is done interactively.     

基于最大功率传输效率法的近场三维方向图赋形

讨论如何利用带约束的最大功率传输效率(CMMPTE)法通过阵列天线来综合三维方向图.通过引入测试接收阵列天线,待设计的阵列天线与之构成无线功率传输(WPT)系统,从而将方向图的综合问题转换成WPT系统功率传输效率(PTE)的优化问题.通过调整约束条件,在保证PTE最大化的条件下可获得阵列天线的激励分布,根据激励分布设计...     

A computer-vision technique for the acquisition and processing of 3-D profiles of dental imprints: an application in orthodontics

The authors present a computer vision technique for the acquisition and processing of 3-D images of the profile of wax dental imprints in the automation of diagnosis in orthodontics. The acquisition of the 3-D images is based on the absorption of light by a dispersive medium and uses standard CCD (charge coupled device) cameras. The profiles of both sides of the imprint are acquired simultaneously. The 3-D image of each side of the imprint is segmented by nonlinear filtering of the 3-D data, and the interstices between the teeth are detected. Two operators are presented: one for the detection of the interstices between the teeth for incisors, canines, and premolars, and one for those between molars. A method for deciding the optimal neighborhood of application of each operator is also presented. Experimental results show that the two operators are very effective at detecting the interstices.     

基于靶标的三目视觉3维坐标测量系统

为了解决复杂环境中大视场、高精度、非接触3维测量问题,采用三目摄像机结构,通过靶标成像来测量被测点3维坐标的测量系统。测量时摄像机采集测量靶标的图像,计算机通过图像处理的方法获取测量靶标上标志点的3维坐标,并提出基于被测点与标志点间距离方程与直线约束的被测点求解优化方法。测量系统通过高精度光栅位移平台带动测量靶标移动来完成测试。结果表明,测量系统在视场范围、测量精度、使用灵活性等方面有较大的改进,能够测量视场深度从2m~5m范围内的视场,测量精度优于0.2mm。     

Flat Projection for 3-D

The two challenges for three-dimensional (3-D) display are designing the optics for wide fields of view, and delivering pixels at the rates needed to support this. Getting such pixel rates at low cost is merely an extension of the key challenge for two-dimensional (2-D) displays,and the cost advantage of projection in this respect over alternatives increases considerably at the data rates needed for 3-D. Both 2-D and 3-D projection concepts are bulky, so the authors describe how to project images within a flat panel. Flat projection is not only inexpensive: it can generate virtual as well as real images, and allows the screen to take images and input from the viewer as well as vice versa. Real images are created by pointing a projector into a wedge-shaped light guide, and either the projector or the screen can be shuttered in order to time-multiplex a 3-D image on a large screen. Virtual images are created by pointing a projector into a slab embossed with a grating and can deliver the collimated illumination needed if a liquid crystal display is to time-multiplex a 3-D image with the high off-screen resolution provided by holograms.