膝关节X线透视图像和CT数据的2D/3D配准及其应用研究
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摘要
研究背景
膝关节在体运动和假体稳定性研究是运动医学及临床医学研究中的难点问题。由于组成膝关节的骨骼及植入假体位置深在,因此冀望从体表研究骨骼运动及植入体稳定性的方法都不适当。X射线具有很强穿透性,且医用放射剂量不断减小,因此各种基于X线的成像设备逐渐成为疾病诊断和研究人体内部信息的主要工具,对膝关节的研究也完全可以利用X线图像来进行。
X线透视能够观察人体内部信息,但其图像是体内结构的二维叠加投影图,缺乏三维信息。CT设备利用X线穿透原理成像,其图像数据能够完整记录体内结构的三维信息,但却只是某静止状态下,无法体现实时情况。将这两种数据优势结合起来的2D／3D配准成为近年来医学图像处理领域的热门,其应用范围包括了运动医学、定位放射、手术导航、术后评估等等。
基于图像内容的2D／3D配准是指利用计算机图像技术模拟X射线透视原理,对前期获得的研究对象体数据如CT或MR等进行虚拟放射投影,生成数字影像重建图像(DRR),然后通过变换体数据的空间位置及角度,对新生成的DRR图像及研究对象真实X线图像的相似性测度求极值,确定体数据对应X线图像所处的空间位置。近年来,随着X线摄影技术及CT等大型设备性能的不断提升,以及医学图像处理领域软硬件的高速发展,2D／3D配准的效果也越来越好。
在综合国内外研究方法和成果的基础上,结合自身研究目标,我们采用GPGPU处理器,基于CUDA构架,开发了处理单幅X线图像和螺旋CT体数据的2D／3D配准系统。主要过程为：首先通过张正友标定法计算X线图像的成像条件(即DR拍摄条件),并将其设置为配准程序的参数；然后在硬件GPGPU支持下,基于CUDA构架,利用光线跟踪原理生成DRR图像,以SSD(Sum-of-Squares difference)作为DRR与X线图像的相似性测度对象,求得研究对象的空间定位；通过整合研究对象的空间位置变换,完成对其运动过程的三维描述；最后利用三维激光扫描仪和测量软件Raindrop Geomagic8.0对结果进行验证。结果显示,第一组将标本作为整体移动,进行2D／3D配准后,6个自由度中平移误差分别为(x,y,z轴平均值,单位：mm,下同)：0.84,0.33,0.62；旋转误差分别为(x,y,z轴平均值,单位：。,下同)：0.32,0.53,0.80；第二组对标本进行模拟弯曲运动,配准分两部分进行。结果显示,配准后股骨部分6自由度中平移误差分别为：1.55,1.25,0.98,旋转误差分别为：0.99,1.08,1.16；胫骨部分6自由度中平移误差为：1.65,1.27,0.89,旋转误差为：0.86,1.30,0.83。我们认为,本研究开发的2D／3D医学图像配准系统达到了预期目标,可为下一步的实验工作提供良好的数据处理平台,本实验中利用膝关节标本模拟运动并进行配准计算的方法可作为膝关节在体运动检测的实验路线。
目的
1.建立基于张正友标定法原理的X线图像拍摄标定系统；
2.建立基于CUDA构架的2D／3D医学图像配准系统；
3.研究以三维激光扫描仪和测量软件相配合验证2D／3D配准结果的方法；
4.以膝关节标本为实验对象,建立应用此配准系统对膝关节在体运动进行分析研究的技术路线。
材料与方法
1.X线拍摄标定系统的建立：硬件设备为平面标定板,其核心是14×14cm印刷电路板,参数如下：PCB板厚度0.4mm,铜线宽度0.254mm、间距10mm,铜线11排11列正交分布。电路板由两块有机玻璃板夹持,保证其始终为一平面。使用时,拍摄多幅不同角度下标定板的X线图像,通过基于张正友标定法原理的程序计算X线拍摄空间条件,即为2D／3D配准程序中虚拟光源及影像接收屏相对位置关系参数。
2.建立基于GPGPU的2D／3D配准系统：基于GPGPU硬件设备及CUDA构架建立2D／3D配准系统,利用光线追踪算法对CT数据进行数字影像重建(DRR),与真实X线图像进行相似性比较,以SSD作为相似性测度,变换CT体数据空间位置及角度,当SSD获得极值时,得到对应X线图像的CT体数据位置参数,完成2D／3D配准。
3.研究以三维激光扫描仪和测量软件相配合验证2D／3D配准结果的方法：硬件设备为三维激光扫描仪,型号3DD RealScan USB 200,点云密度512×1000,测量软件为Raindrop Geomagic8.0。在对研究对象进行X线拍摄的同时,利用三维激光扫描仪记录每种状态下研究对象的三维点云信息。统一坐标系后,在Geomagic8.0中利用3D／3D配准功能对不同位置点云进行配准,得到研究对象空间位置变换参数,以此为金标准验证本研究开发的2D／3D配准系统的计算结果。
4.整体配准实验：冰冻状态下人体膝关节标本进行CT扫描,获得原始DICOM格式数据集,图像参数：层厚0.75mm,像素512×512矩阵,像素大小0.3515625mm×0.3515625mm,共582幅。继续在冰冻状态下(保证其整体可视为刚体状态)拍摄膝关节标本X线图像14幅,图像格式为DICOM,其中前6幅内容为标定板,后8幅为标本透视图像,拍摄时对标本整体进行了随机的位置改变。拍摄每张X线图像的同时进行三维激光扫描,保存对应点云文件。将X线图像、CT数据输入2D／3D配准系统中进行整体配准,最后以激光点云数据配准结果对其进行验证,分析误差大小及产生原因。
5.模拟运动配准实验：CT数据同整体配准组,相同条件X线图像连续拍摄16幅,前8幅为标定板图像,后8幅为解冻后标本透视图像,拍摄时人为弯曲不同角度以模拟膝关节运动,同时进行激光三维扫描,记录对应点云数据。将CT数据分割为两部分：股骨部分和胫骨部分,分别与处理后X线图像进行配准。整合空间变换参数,求得膝关节标本“运动”参数,最后以点云配准结果对其进行验证,分析误差大小及原因,探讨此方法的可行性。
结果与讨论
1.开发了基于GPGPU处理的2D／3D医学图像配准程序,以及X线图像拍摄标定系统,同时建立了利用三维激光扫描仪与测量软件相结合对2D／3D配准结果进行验证的方法。
1.1基于张正友标定法原理,结合X线穿透特性设计制作平面标定板,改进了标定程序,实验结果显示其精度较高,可用来进行X线图像拍摄空间位置的标定。
1.2开发了以激光三维扫描仪为硬件基础,Raindrop Geomagic8.0为软件支持验证配准结果的技术路线。从软硬件设备自身精度入手,分析其作为金标准的误差范围。结果显示,本研究可在20-30cm距离内完成扫描,此距离内三维激光扫描仪精度为0.01mm；Geomagic8.0软件中,三维点云配准误差最大平均值为0.08mm,最小值可达0.02mm。
1.3基于硬件设备GPGPU及CUDA构架,完成了2D／3D医学图像配准系统的编程与调试。与传统算法相比,利用此硬件显卡加速,DRR图像可实时更新,配准速度大大加快。
2.利用人体膝关节标本进行实验,获得一套CT图像数据。第一组将标本整体进行移动,共拍摄X线图像14幅,其中前6幅内容为标定板；第二组对标本进行弯曲模拟运动,共拍摄X线图像16幅,前8幅内容为标定板。两组X图像分别与CT数据搭配进行处理,计算2D／3D配准参数。
2.1整体配准组：将6幅图像分为3组(可复用)对DR拍摄参数进行了标定计算,三次结果取均值设置为2D／3D配准程序的源屏相对位置关系值；导入CT体数据及X线图像进行配准计算,获得8个位置6自由度参数,对应每一幅图像中标本的空间位置。以第一幅图像中标本位置为基准,计算后续图像中标本位置变换参数,以对应的三维点云配准结果对其验证。结果显示,6个自由度中平移误差分别为(x,y,z轴平均值,单位：mm)：0.84,0.33,0.62；旋转误差分别为(x,y,z轴平均值,单位：°)：0.32,0.53,0.80,误差最大出现在X轴平移及Y轴旋转,分别为1.25mm和1.54°。我们认为主要误差来源在于DRR的产生及其与X线图像的比较。首先,DRR的产生是模拟真实X线成像过程,由于CT体数据与真实物体相差甚多,且光线跟踪算法与X线穿透物体过程也有较大差异,因此DRR图像不可能与真实X线图像完全一致。此外,DRR与X线图像在细节纹理部分相差较大,进行相似性测度计算时,由此产生的误差无法避免；其次,DRR图像与X线图像比较时,“景深”方向的微小数值变化对DRR图像产生的影响很小,造成配准时虽然空间位置有变化,但相似性测度值出现钝化,仅依靠求函数极值难以消除这种误差。
2.2模拟运动配准组：CT数据分为两部分进行分段配准,上半部分以股骨和髌骨为主干(包括软组织),下半部分以胫骨和腓骨为主干(包含软组织)。两部分CT数据分别与X线图像进行了配准,利用三维点云进行精度验证。结果显示,股骨部分6自由度中平移误差为(x,y,z轴平均值,单位：mm,下同)：1.55,1.25,0.98,旋转误差为(x,y,z轴平均值,单位：°,下同)：0.99,1.08,1.16；胫骨部分6自由度中平移误差为：1.65,1.27,0.89,旋转误差为：0.86,1.30,0.83。对误差进行分析：首先,整体配准实验中的误差因素依然存在；其次,膝关节弯曲角度变化时,关节周围软组织形态发生改变,而CT数据相应部分仍维持原状,导致DRR与X线图像进行相似性测度计算时,软组织部分信息差别增大从而影响了精度。第三,分段配准导致体数据可用信息减少,对配准结果也有一定的影响。
结论
1.本研究开发的2D／3D医学图像配准系统达到了实用的要求,可以用来检测膝关节及内置假体的三维运动情况。
2.以三维激光扫描仪及Raindrop Geomagic8.0软件支持的配准系统精度检验方法不仅能够检测研究对象整体运动情况,还可以对其内部不同刚性部分之间(如骨骼)相对运动的情况做高精度测定,此方法可成为今后此类系统精度检验更理想的选择。
3.本研究中所采用的对膝关节标本模拟运动进行配准的技术方法,可推广到关节在体运动检测应用中。
Background
Knee motion in vivo and prosthesis stability study are difficult topics in sports medicine and clinical research, for the bones of knee and implanted prosthesis are in the deeper structure, so it is not appropriate and realistic to substitute the information of the surface movement for the bones motion and analyze the stability of the prosthesis by surface information. Since X-ray are highly penetrating, and with its medical radiation dosage decreasing constantly, a variety of imaging equipments have become the mainstream tools to diagnose and study the internal human body, and it's absolutely a good way to utilize X-ray images in knee motion study.
The internal structure of the human body can be observed by X-ray equipment, but it only shows two-dimension superimposed projection image, not three-dimension. While CT volume data can completely record all structural three-dimension information in vivo, but it is some kind of static situation, unable to display motion state. Therefore,2D/3D medical image registration which can combine the advantages of above two has become a popular research in recent years, and is widely applied in the fields as sports medicine, location radio surgery, surgical navigation, postoperative evaluation, and so on.
2D/3D registration refers to a method that can obtain registration parameters of 2D and 3D data by comparing of DRR and real X-ray images. First, generate DRR images by simulating X-ray fluoroscopy in computer with the research objects CT or MR data acquired before; second, with the translation and rotation of the CT data, different DRR and X-ray images are compared to get maximum similarity, and obtain the location parameters of the 3D data in this state. Due to the improvement of the X-ray and CT equipment, and developing of medical image processing hardware and software,2D/3D registration results are more and more accuracy.
Based on the research methods and outcomes internal and abroad, and aimed at own objectives, we developed a 2D/3D registration system for single X-ray image to spiral CT data with the hardware GPGPU and framework CUDA. Main process is as follows:first, obtain the condition of X-ray image-shooting by Zhang Zhengyou calibration method (DR shooting conditions), and set the parameters in the registration procedure. Second, with the support of the hardware GPGPU, generate different DRR images by translating and rotating CT data. Compare DRR and X-ray images using SSD(Sum-of-Squares difference) as the similarity measure object and locate the CT data when SSD is minimum. Complete description of the three-dimensional motion is outlined through the transform of the coordinate system. Third,2D/3D registration results are validated with the 3D laser scanning systems and software Raindrop Geomagic8.0. In the experiment as knee an integer, in 6 degrees of freedom the average translation errors were as follows (x,y,z axis,unit:mm, the same below):0.84,0.33,0.62; the average rotation errors were (x,y,z axis, unit: degree, the same below):0.32,0.53,0.80. In the experiment simulating knee motion, for the femur part, average translation errors were:1.55,1.25,0.98, and average rotation errors were:0.99,1.08,1.16; and for the tibia part, average translation errors were:1.65,1.27,0.89, and average rotation errors were:0.86,1.30,0.83. The results showed that the 2D/3D registration system achieved our goal, and it could be a good platform for future experiments.
Objectives
1. To establish X-ray image-shooting calibration system based on the Zhang Zhengyou method.
2. To establish 2D/3D medical image registration system based on GPGPU and CUDA framework.
3. To develop a method of checking 2D/3D registration results by using 3D laser scanner and software.
4. To establish methods to study knee motion with this system.
Materials and methods
1. Establishment of the X-ray image-shooting calibration system. The hardware was a calibration plane with a printed circuit board as core part. We printed 0.254mm wide bronze lines with spacing of 10mm on a 0.4mm thickness PCB board, and lines were 11×11 arraying on direct cross and composed 10×10mm square grids. The printed circuit board was retained by two pieces of plexiglass boards, so it could be a standard plane. When used, Take some X-ray images of the calibration plane in different views, and carry out procedure based on Zhang Zhengyou calibration principle with the images to get the condition of the X-ray image-shooting, that is the location parameters of the light source and image receiver in the procedure.
2. Establishment of the 2D/3D registration system based on GPGPU. We established a 2D/3D registration system based on GPGPU and CUDA framework. The procedure can build DRR images with CT data by the method of ray-tracing, then compare DRR and true X-ray images with SSD, by transforming the location and posture of the CT data, position parameters of CT data were obtained when SSD reached to extreme.
3. The study of the method of checking 2D/3D registration results with 3D laser scanner and software. The hardware is a 3D laser scanner (type:3DD RealScan USB 200), and its point cloud density is 512x1000. The software is Raindrop Geomagic8.0. At the moment of taking X-ray images of research objects, we recorded their 3D point clouds and saved them corresponding to X-ray images. In the software Geomagic, carried out 3D/3D registration for the point clouds after they were imported and transformed to a new coordinate system, and finally obtained the location transform parameters of the whole objects or some parts of them. As gold standards, point cloud registration parameters were used to check the 2D/3D registration procedure results.
4. The experiment as knee an integer. A human knee specimen was scanned in CT equipment, and got 582 images which the parameters is:DICOM format、512×512pixel size、0.3515625^2mm/pixle and 0.75mm thickness. Kept the knee specimen frozen, and took 14 X-ray images, in which the former 6 pieces were calibration board images, while the latter 8 ones were frozen knee images, and all files were saved as DICOM format. The specimen had different position and posture in the X-ray images, and it was scanned by 3D laser scanner at the moment of image-shooting. X-ray images and CT data were imported into the 2D/3D images registration procedure and calculated. Finally, the laser point cloud data registration results were obtained in software and used to validate the 2D/3D registration results, and errors and causes were analyzed.
5. Experiment of motion simulation registration. CT data is the same one. The defrosted specimen was bent to different angles to simulate the knee motion, and 16 X-ray images were taken at the same time. The former 8 images were for calibration board, while the latter 8 ones were for specimen.3D laser point cloud was captured at the moment of taking X-ray images. CT data was segmented to two parts:femur part and tibia part, and they were registered to X-ray images separately. The results were dealt to calculate the parameters of knee motion, and were validated by the method of point cloud registration. Finally, we analyzed the errors and probed the feasibility of this method.
Results and discussion
1. Developed a 2D/3D image registration procedure based on hardware GPGPU, and an X-ray image-shooting calibration procedure, and developed a method that could validate the results of 2D/3D registration by the 3D laser scanner and software.
1.1 Calibration procedure for X-ray image-shooting. We designed and made a calibration board fitting the X-ray and Zhang Zhengyou calibration method, then improved the procedure to fit the board. Accuracy results could be calculated and the procedure was suitable for the X-ray image-shooting calibration.
1.2 Developed a method which could validate the accuracy of the 2D/3D registration results by making use of the 3D laser scanner and Raindrop Geomagic8.0. We analyzed the errors of this method based on the accuracy of the hardware and software. The accuracy of the 3D laser scanner could be 0.01mm at the maximum distance of 20-30cm, while the errors of the point cloud registration could be 0.08mm as a maximum.
1.3 Developed a 2D/3D registration system based on the GPGPU and CUDA framework. Compared with the traditional method, DRR images can be updated in real time, and the registration process can be great accelerated.
2. Two experiments with a human knee specimen were done separately. Obtained CT data and two series of X-ray images, one was for the movement as knee specimen integer, and the other was for simulation of knee motion. The former were 14 images in which 6 images were for the calibration board, and the latter were 16 images in which 8 were for the calibration board.2D/3D registration of the two groups images to CT data were carried out separately.
2.1 Experiment as knee a integer.6 calibration board images were divided to 3 groups to calculate the parameters of the X-ray shooting conditions, and the average value of the 3 group results was set in the procedure as the parameters of the source and image receiver. CT data and X-ray images were imported into the procedure and got 8 groups of registration parameters including 6 degrees of freedom, responded to the absolute locations of the knee in the images. Refer to the first image, the follow-up images were calculated to get the location transform parameters, and the results were valuated by the method of the point cloud registration. As knee a integrated body, the registration errors of the 6 degree of freedom were as follows:the average translation errors were(x,y,z axis, unit:mm): 0.84,0.33,0.62; the rotation errors were(x,y,z axis, unit:degree):0.32,0.53,0.80, and the maximum was 1.25mm(translation) along x-axis and 1.54 degree(rotation) by y-axis. We believed that the main error were from the processes of DRR generation and comparison of two kinds of images. First, DRR generation process was a virtual X-ray image shooting, but CT data was different with the real object and the ray-tracing algorithm was also quite different with the process of X-ray penetrating, so DRR images were not possible same as real X-ray images. What's more, the detail texture difference of the two kinds of images would cause unavoidable errors in the similarity measurement calculation. Second, when DRR and X-ray images were compared, small changes in the depth of field had little impact on the DRR images. Although the location parameters were changed, the similarity measurement might has no change, and the error was hard to remove.
2.2 Motion simulation registration. CT data was segmented to two parts, one was the upper part of the knee (including the soft tissue) that the main bones were femur and patella, the other was the lower part that the main bones were tibia and fibula. The two parts of CT data were registered to X-ray images separately, and the results were valuated with the method of point cloud registration. The results showed that the femur part errors of 6 degrees of freedom of were as follows: the average translation errors (x,y,z axis, unit:mm, same below):1.55,1.25,0.98; the average rotation errors (x,y,z axis, unit:degree, same below):0.99,1.08,1.16; and as part of the tibia, the average translation errors were:1.65,1.27,0.89; and the average rotation errors were:0.86,1.30,0.83. Finally, the errors were analyzed. First, the error factors appeared in earlier experiment still existed. Second, when knee flexion was changed, the soft tissue around the joints had some deformation, but CT data remained the same state, so the soft tissue information caused more interference when DRR and X-ray images were compared. Third, the segment of the CT data reduced the information and affected the results to some extent.
Conclusion
1.2D/3D image registration system has achieved the practical requirement and it can be used to test the knee motion and prosthesis location.
2. The method based on the 3D laser scanner and Raindrop Geomagic8.0 can be used to detect the whole objects movement, and also calculate the relative movement of the different parts (such as bones), so it could be a better choice to valuate the accuracy of such systems.
3. The method used in the registration study of the knee motion simulation can be extended to test the joint motion in vivo.
膝关节在体运动和假体稳定性研究是运动医学及临床医学研究中的难点问题。由于组成膝关节的骨骼及植入假体位置深在,因此冀望从体表研究骨骼运动及植入体稳定性的方法都不适当。X射线具有很强穿透性,且医用放射剂量不断减小,因此各种基于X线的成像设备逐渐成为疾病诊断和研究人体内部信息的主要工具,对膝关节的研究也完全可以利用X线图像来进行。
X线透视能够观察人体内部信息,但其图像是体内结构的二维叠加投影图,缺乏三维信息。CT设备利用X线穿透原理成像,其图像数据能够完整记录体内结构的三维信息,但却只是某静止状态下,无法体现实时情况。将这两种数据优势结合起来的2D／3D配准成为近年来医学图像处理领域的热门,其应用范围包括了运动医学、定位放射、手术导航、术后评估等等。
基于图像内容的2D／3D配准是指利用计算机图像技术模拟X射线透视原理,对前期获得的研究对象体数据如CT或MR等进行虚拟放射投影,生成数字影像重建图像(DRR),然后通过变换体数据的空间位置及角度,对新生成的DRR图像及研究对象真实X线图像的相似性测度求极值,确定体数据对应X线图像所处的空间位置。近年来,随着X线摄影技术及CT等大型设备性能的不断提升,以及医学图像处理领域软硬件的高速发展,2D／3D配准的效果也越来越好。
在综合国内外研究方法和成果的基础上,结合自身研究目标,我们采用GPGPU处理器,基于CUDA构架,开发了处理单幅X线图像和螺旋CT体数据的2D／3D配准系统。主要过程为：首先通过张正友标定法计算X线图像的成像条件(即DR拍摄条件),并将其设置为配准程序的参数；然后在硬件GPGPU支持下,基于CUDA构架,利用光线跟踪原理生成DRR图像,以SSD(Sum-of-Squares difference)作为DRR与X线图像的相似性测度对象,求得研究对象的空间定位；通过整合研究对象的空间位置变换,完成对其运动过程的三维描述；最后利用三维激光扫描仪和测量软件Raindrop Geomagic8.0对结果进行验证。结果显示,第一组将标本作为整体移动,进行2D／3D配准后,6个自由度中平移误差分别为(x,y,z轴平均值,单位：mm,下同)：0.84,0.33,0.62；旋转误差分别为(x,y,z轴平均值,单位：。,下同)：0.32,0.53,0.80；第二组对标本进行模拟弯曲运动,配准分两部分进行。结果显示,配准后股骨部分6自由度中平移误差分别为：1.55,1.25,0.98,旋转误差分别为：0.99,1.08,1.16；胫骨部分6自由度中平移误差为：1.65,1.27,0.89,旋转误差为：0.86,1.30,0.83。我们认为,本研究开发的2D／3D医学图像配准系统达到了预期目标,可为下一步的实验工作提供良好的数据处理平台,本实验中利用膝关节标本模拟运动并进行配准计算的方法可作为膝关节在体运动检测的实验路线。
目的
1.建立基于张正友标定法原理的X线图像拍摄标定系统；
2.建立基于CUDA构架的2D／3D医学图像配准系统；
3.研究以三维激光扫描仪和测量软件相配合验证2D／3D配准结果的方法；
4.以膝关节标本为实验对象,建立应用此配准系统对膝关节在体运动进行分析研究的技术路线。
材料与方法
1.X线拍摄标定系统的建立：硬件设备为平面标定板,其核心是14×14cm印刷电路板,参数如下：PCB板厚度0.4mm,铜线宽度0.254mm、间距10mm,铜线11排11列正交分布。电路板由两块有机玻璃板夹持,保证其始终为一平面。使用时,拍摄多幅不同角度下标定板的X线图像,通过基于张正友标定法原理的程序计算X线拍摄空间条件,即为2D／3D配准程序中虚拟光源及影像接收屏相对位置关系参数。
2.建立基于GPGPU的2D／3D配准系统：基于GPGPU硬件设备及CUDA构架建立2D／3D配准系统,利用光线追踪算法对CT数据进行数字影像重建(DRR),与真实X线图像进行相似性比较,以SSD作为相似性测度,变换CT体数据空间位置及角度,当SSD获得极值时,得到对应X线图像的CT体数据位置参数,完成2D／3D配准。
3.研究以三维激光扫描仪和测量软件相配合验证2D／3D配准结果的方法：硬件设备为三维激光扫描仪,型号3DD RealScan USB 200,点云密度512×1000,测量软件为Raindrop Geomagic8.0。在对研究对象进行X线拍摄的同时,利用三维激光扫描仪记录每种状态下研究对象的三维点云信息。统一坐标系后,在Geomagic8.0中利用3D／3D配准功能对不同位置点云进行配准,得到研究对象空间位置变换参数,以此为金标准验证本研究开发的2D／3D配准系统的计算结果。
4.整体配准实验：冰冻状态下人体膝关节标本进行CT扫描,获得原始DICOM格式数据集,图像参数：层厚0.75mm,像素512×512矩阵,像素大小0.3515625mm×0.3515625mm,共582幅。继续在冰冻状态下(保证其整体可视为刚体状态)拍摄膝关节标本X线图像14幅,图像格式为DICOM,其中前6幅内容为标定板,后8幅为标本透视图像,拍摄时对标本整体进行了随机的位置改变。拍摄每张X线图像的同时进行三维激光扫描,保存对应点云文件。将X线图像、CT数据输入2D／3D配准系统中进行整体配准,最后以激光点云数据配准结果对其进行验证,分析误差大小及产生原因。
5.模拟运动配准实验：CT数据同整体配准组,相同条件X线图像连续拍摄16幅,前8幅为标定板图像,后8幅为解冻后标本透视图像,拍摄时人为弯曲不同角度以模拟膝关节运动,同时进行激光三维扫描,记录对应点云数据。将CT数据分割为两部分：股骨部分和胫骨部分,分别与处理后X线图像进行配准。整合空间变换参数,求得膝关节标本“运动”参数,最后以点云配准结果对其进行验证,分析误差大小及原因,探讨此方法的可行性。
结果与讨论
1.开发了基于GPGPU处理的2D／3D医学图像配准程序,以及X线图像拍摄标定系统,同时建立了利用三维激光扫描仪与测量软件相结合对2D／3D配准结果进行验证的方法。
1.1基于张正友标定法原理,结合X线穿透特性设计制作平面标定板,改进了标定程序,实验结果显示其精度较高,可用来进行X线图像拍摄空间位置的标定。
1.2开发了以激光三维扫描仪为硬件基础,Raindrop Geomagic8.0为软件支持验证配准结果的技术路线。从软硬件设备自身精度入手,分析其作为金标准的误差范围。结果显示,本研究可在20-30cm距离内完成扫描,此距离内三维激光扫描仪精度为0.01mm；Geomagic8.0软件中,三维点云配准误差最大平均值为0.08mm,最小值可达0.02mm。
1.3基于硬件设备GPGPU及CUDA构架,完成了2D／3D医学图像配准系统的编程与调试。与传统算法相比,利用此硬件显卡加速,DRR图像可实时更新,配准速度大大加快。
2.利用人体膝关节标本进行实验,获得一套CT图像数据。第一组将标本整体进行移动,共拍摄X线图像14幅,其中前6幅内容为标定板；第二组对标本进行弯曲模拟运动,共拍摄X线图像16幅,前8幅内容为标定板。两组X图像分别与CT数据搭配进行处理,计算2D／3D配准参数。
2.1整体配准组：将6幅图像分为3组(可复用)对DR拍摄参数进行了标定计算,三次结果取均值设置为2D／3D配准程序的源屏相对位置关系值；导入CT体数据及X线图像进行配准计算,获得8个位置6自由度参数,对应每一幅图像中标本的空间位置。以第一幅图像中标本位置为基准,计算后续图像中标本位置变换参数,以对应的三维点云配准结果对其验证。结果显示,6个自由度中平移误差分别为(x,y,z轴平均值,单位：mm)：0.84,0.33,0.62；旋转误差分别为(x,y,z轴平均值,单位：°)：0.32,0.53,0.80,误差最大出现在X轴平移及Y轴旋转,分别为1.25mm和1.54°。我们认为主要误差来源在于DRR的产生及其与X线图像的比较。首先,DRR的产生是模拟真实X线成像过程,由于CT体数据与真实物体相差甚多,且光线跟踪算法与X线穿透物体过程也有较大差异,因此DRR图像不可能与真实X线图像完全一致。此外,DRR与X线图像在细节纹理部分相差较大,进行相似性测度计算时,由此产生的误差无法避免；其次,DRR图像与X线图像比较时,“景深”方向的微小数值变化对DRR图像产生的影响很小,造成配准时虽然空间位置有变化,但相似性测度值出现钝化,仅依靠求函数极值难以消除这种误差。
2.2模拟运动配准组：CT数据分为两部分进行分段配准,上半部分以股骨和髌骨为主干(包括软组织),下半部分以胫骨和腓骨为主干(包含软组织)。两部分CT数据分别与X线图像进行了配准,利用三维点云进行精度验证。结果显示,股骨部分6自由度中平移误差为(x,y,z轴平均值,单位：mm,下同)：1.55,1.25,0.98,旋转误差为(x,y,z轴平均值,单位：°,下同)：0.99,1.08,1.16；胫骨部分6自由度中平移误差为：1.65,1.27,0.89,旋转误差为：0.86,1.30,0.83。对误差进行分析：首先,整体配准实验中的误差因素依然存在；其次,膝关节弯曲角度变化时,关节周围软组织形态发生改变,而CT数据相应部分仍维持原状,导致DRR与X线图像进行相似性测度计算时,软组织部分信息差别增大从而影响了精度。第三,分段配准导致体数据可用信息减少,对配准结果也有一定的影响。
结论
1.本研究开发的2D／3D医学图像配准系统达到了实用的要求,可以用来检测膝关节及内置假体的三维运动情况。
2.以三维激光扫描仪及Raindrop Geomagic8.0软件支持的配准系统精度检验方法不仅能够检测研究对象整体运动情况,还可以对其内部不同刚性部分之间(如骨骼)相对运动的情况做高精度测定,此方法可成为今后此类系统精度检验更理想的选择。
3.本研究中所采用的对膝关节标本模拟运动进行配准的技术方法,可推广到关节在体运动检测应用中。
Background
Knee motion in vivo and prosthesis stability study are difficult topics in sports medicine and clinical research, for the bones of knee and implanted prosthesis are in the deeper structure, so it is not appropriate and realistic to substitute the information of the surface movement for the bones motion and analyze the stability of the prosthesis by surface information. Since X-ray are highly penetrating, and with its medical radiation dosage decreasing constantly, a variety of imaging equipments have become the mainstream tools to diagnose and study the internal human body, and it's absolutely a good way to utilize X-ray images in knee motion study.
The internal structure of the human body can be observed by X-ray equipment, but it only shows two-dimension superimposed projection image, not three-dimension. While CT volume data can completely record all structural three-dimension information in vivo, but it is some kind of static situation, unable to display motion state. Therefore,2D/3D medical image registration which can combine the advantages of above two has become a popular research in recent years, and is widely applied in the fields as sports medicine, location radio surgery, surgical navigation, postoperative evaluation, and so on.
2D/3D registration refers to a method that can obtain registration parameters of 2D and 3D data by comparing of DRR and real X-ray images. First, generate DRR images by simulating X-ray fluoroscopy in computer with the research objects CT or MR data acquired before; second, with the translation and rotation of the CT data, different DRR and X-ray images are compared to get maximum similarity, and obtain the location parameters of the 3D data in this state. Due to the improvement of the X-ray and CT equipment, and developing of medical image processing hardware and software,2D/3D registration results are more and more accuracy.
Based on the research methods and outcomes internal and abroad, and aimed at own objectives, we developed a 2D/3D registration system for single X-ray image to spiral CT data with the hardware GPGPU and framework CUDA. Main process is as follows:first, obtain the condition of X-ray image-shooting by Zhang Zhengyou calibration method (DR shooting conditions), and set the parameters in the registration procedure. Second, with the support of the hardware GPGPU, generate different DRR images by translating and rotating CT data. Compare DRR and X-ray images using SSD(Sum-of-Squares difference) as the similarity measure object and locate the CT data when SSD is minimum. Complete description of the three-dimensional motion is outlined through the transform of the coordinate system. Third,2D/3D registration results are validated with the 3D laser scanning systems and software Raindrop Geomagic8.0. In the experiment as knee an integer, in 6 degrees of freedom the average translation errors were as follows (x,y,z axis,unit:mm, the same below):0.84,0.33,0.62; the average rotation errors were (x,y,z axis, unit: degree, the same below):0.32,0.53,0.80. In the experiment simulating knee motion, for the femur part, average translation errors were:1.55,1.25,0.98, and average rotation errors were:0.99,1.08,1.16; and for the tibia part, average translation errors were:1.65,1.27,0.89, and average rotation errors were:0.86,1.30,0.83. The results showed that the 2D/3D registration system achieved our goal, and it could be a good platform for future experiments.
Objectives
1. To establish X-ray image-shooting calibration system based on the Zhang Zhengyou method.
2. To establish 2D/3D medical image registration system based on GPGPU and CUDA framework.
3. To develop a method of checking 2D/3D registration results by using 3D laser scanner and software.
4. To establish methods to study knee motion with this system.
Materials and methods
1. Establishment of the X-ray image-shooting calibration system. The hardware was a calibration plane with a printed circuit board as core part. We printed 0.254mm wide bronze lines with spacing of 10mm on a 0.4mm thickness PCB board, and lines were 11×11 arraying on direct cross and composed 10×10mm square grids. The printed circuit board was retained by two pieces of plexiglass boards, so it could be a standard plane. When used, Take some X-ray images of the calibration plane in different views, and carry out procedure based on Zhang Zhengyou calibration principle with the images to get the condition of the X-ray image-shooting, that is the location parameters of the light source and image receiver in the procedure.
2. Establishment of the 2D/3D registration system based on GPGPU. We established a 2D/3D registration system based on GPGPU and CUDA framework. The procedure can build DRR images with CT data by the method of ray-tracing, then compare DRR and true X-ray images with SSD, by transforming the location and posture of the CT data, position parameters of CT data were obtained when SSD reached to extreme.
3. The study of the method of checking 2D/3D registration results with 3D laser scanner and software. The hardware is a 3D laser scanner (type:3DD RealScan USB 200), and its point cloud density is 512x1000. The software is Raindrop Geomagic8.0. At the moment of taking X-ray images of research objects, we recorded their 3D point clouds and saved them corresponding to X-ray images. In the software Geomagic, carried out 3D/3D registration for the point clouds after they were imported and transformed to a new coordinate system, and finally obtained the location transform parameters of the whole objects or some parts of them. As gold standards, point cloud registration parameters were used to check the 2D/3D registration procedure results.
4. The experiment as knee an integer. A human knee specimen was scanned in CT equipment, and got 582 images which the parameters is:DICOM format、512×512pixel size、0.3515625^2mm/pixle and 0.75mm thickness. Kept the knee specimen frozen, and took 14 X-ray images, in which the former 6 pieces were calibration board images, while the latter 8 ones were frozen knee images, and all files were saved as DICOM format. The specimen had different position and posture in the X-ray images, and it was scanned by 3D laser scanner at the moment of image-shooting. X-ray images and CT data were imported into the 2D/3D images registration procedure and calculated. Finally, the laser point cloud data registration results were obtained in software and used to validate the 2D/3D registration results, and errors and causes were analyzed.
5. Experiment of motion simulation registration. CT data is the same one. The defrosted specimen was bent to different angles to simulate the knee motion, and 16 X-ray images were taken at the same time. The former 8 images were for calibration board, while the latter 8 ones were for specimen.3D laser point cloud was captured at the moment of taking X-ray images. CT data was segmented to two parts:femur part and tibia part, and they were registered to X-ray images separately. The results were dealt to calculate the parameters of knee motion, and were validated by the method of point cloud registration. Finally, we analyzed the errors and probed the feasibility of this method.
Results and discussion
1. Developed a 2D/3D image registration procedure based on hardware GPGPU, and an X-ray image-shooting calibration procedure, and developed a method that could validate the results of 2D/3D registration by the 3D laser scanner and software.
1.1 Calibration procedure for X-ray image-shooting. We designed and made a calibration board fitting the X-ray and Zhang Zhengyou calibration method, then improved the procedure to fit the board. Accuracy results could be calculated and the procedure was suitable for the X-ray image-shooting calibration.
1.2 Developed a method which could validate the accuracy of the 2D/3D registration results by making use of the 3D laser scanner and Raindrop Geomagic8.0. We analyzed the errors of this method based on the accuracy of the hardware and software. The accuracy of the 3D laser scanner could be 0.01mm at the maximum distance of 20-30cm, while the errors of the point cloud registration could be 0.08mm as a maximum.
1.3 Developed a 2D/3D registration system based on the GPGPU and CUDA framework. Compared with the traditional method, DRR images can be updated in real time, and the registration process can be great accelerated.
2. Two experiments with a human knee specimen were done separately. Obtained CT data and two series of X-ray images, one was for the movement as knee specimen integer, and the other was for simulation of knee motion. The former were 14 images in which 6 images were for the calibration board, and the latter were 16 images in which 8 were for the calibration board.2D/3D registration of the two groups images to CT data were carried out separately.
2.1 Experiment as knee a integer.6 calibration board images were divided to 3 groups to calculate the parameters of the X-ray shooting conditions, and the average value of the 3 group results was set in the procedure as the parameters of the source and image receiver. CT data and X-ray images were imported into the procedure and got 8 groups of registration parameters including 6 degrees of freedom, responded to the absolute locations of the knee in the images. Refer to the first image, the follow-up images were calculated to get the location transform parameters, and the results were valuated by the method of the point cloud registration. As knee a integrated body, the registration errors of the 6 degree of freedom were as follows:the average translation errors were(x,y,z axis, unit:mm): 0.84,0.33,0.62; the rotation errors were(x,y,z axis, unit:degree):0.32,0.53,0.80, and the maximum was 1.25mm(translation) along x-axis and 1.54 degree(rotation) by y-axis. We believed that the main error were from the processes of DRR generation and comparison of two kinds of images. First, DRR generation process was a virtual X-ray image shooting, but CT data was different with the real object and the ray-tracing algorithm was also quite different with the process of X-ray penetrating, so DRR images were not possible same as real X-ray images. What's more, the detail texture difference of the two kinds of images would cause unavoidable errors in the similarity measurement calculation. Second, when DRR and X-ray images were compared, small changes in the depth of field had little impact on the DRR images. Although the location parameters were changed, the similarity measurement might has no change, and the error was hard to remove.
2.2 Motion simulation registration. CT data was segmented to two parts, one was the upper part of the knee (including the soft tissue) that the main bones were femur and patella, the other was the lower part that the main bones were tibia and fibula. The two parts of CT data were registered to X-ray images separately, and the results were valuated with the method of point cloud registration. The results showed that the femur part errors of 6 degrees of freedom of were as follows: the average translation errors (x,y,z axis, unit:mm, same below):1.55,1.25,0.98; the average rotation errors (x,y,z axis, unit:degree, same below):0.99,1.08,1.16; and as part of the tibia, the average translation errors were:1.65,1.27,0.89; and the average rotation errors were:0.86,1.30,0.83. Finally, the errors were analyzed. First, the error factors appeared in earlier experiment still existed. Second, when knee flexion was changed, the soft tissue around the joints had some deformation, but CT data remained the same state, so the soft tissue information caused more interference when DRR and X-ray images were compared. Third, the segment of the CT data reduced the information and affected the results to some extent.
Conclusion
1.2D/3D image registration system has achieved the practical requirement and it can be used to test the knee motion and prosthesis location.
2. The method based on the 3D laser scanner and Raindrop Geomagic8.0 can be used to detect the whole objects movement, and also calculate the relative movement of the different parts (such as bones), so it could be a better choice to valuate the accuracy of such systems.
3. The method used in the registration study of the knee motion simulation can be extended to test the joint motion in vivo.
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[3] 欧阳钧，朱青安，瞿文亮，等．胸腰段脊柱纵向撞击伤后稳定性评价方法的比较[J]．医用生物力学，1997,12(4)：201-204．
[4] 刘印凡，李元敬．我国优秀女子铁饼运动员最后用力阶段膝关节急性损伤的生物力学分析[J]．天津体育学院学报，2005,20(2)：72-73．
[5] 李鉴轶，焦培峰，张美超，等．膝关节在体稳定性评价系统的建立．中国骨与关节损伤杂志[J]．2007，22(6)：471-473．
[6] Tomazevic D. 3-D/2-D registration of CT and MR to X-ray images[J]. IEEE transactions on medical imaging, 2003,22(11):1407-1416.
[7] Yamazaki T, Watanabe T, Nakajima Y, et al. Improvement of depth position in 2-D/3-D registration of knee implants using single-plane fluoroscopy[J]. IEEE transactions on medical imaging. 2004,23(5):602-612.
[8] 王骏．我国医学影像技术近十年发展概述[J]．影像技术，2004(3)：6-11．
[9] 吴春禹．DR胸部摄影图像质量影响因素的分析．南华大学学报(医学版),2009，37(5)：598-599．
[10] Guoyan Zheng. Unifying Energy Minimization and Mutual Information Maximization for Robust 2D/3D Registration of X-Ray and CT Images[C]. DAGM 2007, LNCS 4713:547-557.
[11] Guoyan Zheng, Xiao Dong, Lutz-Peter Nolte. Robust and Accurate Reconstruction of Patient-Specific 3D Surface Models from Sparse Point Sets: A Sequential Three-Stage Trimmed Optimization Approach[C], MIAR 2006, LNCS 4091:68-75.
[12] Gongli Wang, Guoyan Zheng, Paul Alfred Grutzner, et al. A CT-Free Intraoperative Planning and Navigation System for High Tibial DomeOsteotomy[C]. MICCAI 2004, LNCS 3217:610-620.
[13] Jeffrey Bingham, Guoan Li. An Optimized Image Matching Method for Determining In-Vivo TKA Kinematics with a Dual-Orthogonal Fluoroscopic Imaging System[J]. Journal of Biomechanical Engineering. 2006,(128):588-595.
[14] Shirley A M Baert, Graeme P Penney, Theo van Walsum, et al. Precalibration Versus 2D-3D Registration for 3D Guide Wire Display in Endovascular Interventions[C]. MICCAI 2004, LNCS 3217:577-584.
[15] E. Freund, F, Heinze, J, Rossmann. Robotic Simulation System for Precise Positioning in Medical Applications. Perspective in Image-Guided Surgery[C]. MRNV 2004:270-277.
[16] Christof Hurschler, Frank Seehaus, Dipl-Sportwiss,et al. Accuracy of Model-based RSA Contour Reduction in a Typical Clinical Application [J].Clin Orthop Relat Res. 2008 (466): 1978-1986.
[17]梁玮，鲍旭东，罗立民．基于互信息的2D-3D医学图像配准[J]．生物医学工程研究,2004,23(1)：14-16．
[18]张薇，黄毓瑜，栾胜，等．基于灰度的二维、三维图像配准方法及其在骨科导航手术中的实现[J]．中国医学影像技术,20072，3(7)：145-149．
[19]戴君益．C-arm影像与电脑断层影像之方位校准方法[D]：[硕士论文]．台湾：国立中央大学．2008．
[1]Maintz J B A, Viercever M A. A survey of medical image registration [J]. Medical Image Alysis,1998(2):1-36.
[2]Ardekani B A, Braun M, Hutton M et al. A fully automatic multimodality image Registration algorithm[J]. Journal of Computer Assisted Tomography, 1995,19(4):615-623.
[3]Maintz J B A, Vanden Elsen P A, Viergever M A. Comparison of feature-based matching of CT and MR brain image [J]. Computer Vision, Virtual Reality, and Robotics in Medicine,1995,905:219-228.
[4]Garling EH, Kaptein BL, Geleijns K, et al. Marker configuration model Based Roentgen Fluoroscopics Analysis[J]. J Biomech,2005,38(4):893-901.
[5]S.Schreiner, Funda J, Barnes A C,et al.Accuracy assessment of a clinical biplane fluoroscope for three-dimensional measurements and targeting [J]. Proceedings of SPIE 3031,160(1997).
[6]D. P. Chakraborty. Image intensifier distortion correction[J]. Med Phys,1987; 14:249-252.
[7]I.Sobel. On Calibrating Computer Controlled Cameras for Perceiving 3D Scenes [J]. Artificial Intelligence,1974;5:185-198.
[8]W Faig. Calibration of close-range photogrammetry systems:Mathematical formulation [J]. Photogrammetric Eng. Remote Sensing,1975;41:1479-1486.
[9]H.M.Karara. Handbook of Non-Topographic Photogrammetry[M]. Amer Soc of Photogrammetry,1979.
[10]Zhang Z. Flexible camera calibration by viewing a plane from unknown orientations [J]. Proceedings of the 7th International Conference on Computer Vision. Greece, Corfu,1999.666～673.
[11]崔智,张良震,朱淼良.基于光线跟踪的数字影像重建技术[J].小型微型计算机系统,2001,22(10)：1259-1261.
[12]汪俊,吴章文,张从华,等.基于射线追踪的数字重建影像增强技术[J].生物医学工程学杂志.2005,22(1)：125-128.
[13]Levoy, M. Display of surface from volume data [J].Computer Graphics and Application,1988,8(3):29-37.
[14]陆态.X线透视图像(2D)与CT体积图像(3D)配准方法研究及其应用[D]:[硕 士论文].南京：东南大学,2008.
[15]NVIDIA CUD A Computational Unified Device Architecture Programming Guide Version 2.0[M]. NVIDIA Corporation,2008.
[16]Sanjiv S Samant, Junyi Xia, et al. High performance computing for deformable image registration:Towards a new paradigm in adaptive radiotherapy[J]. Medical Physics.2008,Vol 35(8):3546-3553.
[17]Bo Li, Alistair A Young, Brett R Cowan. GPU Accelerated Non-rigid Registration for the Evaluation of Cardiac Function[C]. MICCAI 2008,880-887.
[18]张加万,杨甲东,孙济洲.基于GPU的弹性图像配准方法[J].天津大学学报,2008,41(8)：946-950.
[19]Andre Gueziec, Kenong Wu, Bill Williamson, et al. Exploiting 2-D to 3-D Intra-Operative Image Registration for Qualitative Evaluations and Post-Operative Simulations. MICCAI'99, LNCS 1679,820-833.
[20]Dejan Tomazevic, Bostjan Likar, Franjo Pernus. "Gold standard" data for evaluation and comparison of 3D/2D registration methods[J]. Computer Aided Surgery.2004; 9(4):137-144.
[1]Zhang Z. Flexible camera calibration by viewing a plane from unknown orientations [J]. Proceedings of the 7th International Conference on Computer Vision. Greece, Corfu,1999.666～673.
[2]刘金颂,原思聪,张庆阳,等.双目立体视觉中的摄像机标定技术研究[J].计算机工程与应用.2008,44(6)：237-239.
[3]Scaramuzza D, Martinelli A, Siegwart R. A Flexible Technique for Accurate Omnidirectional Camera Calibration and Structure from Motion. Proceedings of IEEE International Conference of Vision Systems (ICVS'06), New York, January 5-7,2006.
[4]张惠,Pascal Haigron,舒华中,等.X射线图像和CT图像的多维配准[J].电子学报.2002,30(10)：1573-1576.
[5]黄永锋,李彬,赵俊.基于外标记点的2D／3D图像配准方法[J].上海交通大学学报.2006,40(7)：1108-1111.
[6]贾富仓,李修往,陈恩平.CT图像引导脊柱外科配准方法研究[J].深圳大学学报理工版.2007,24(4)：406-409.
[7]张翼,王满宁,宋志坚.脊柱手术导航中分布式2D／3D图像配准方法[J].计算机辅助设计与图像学学报.2007,19(9)：1154-1158.
[8]戴君益.C-arm影像与电脑断层影像之方位校准方法[D][硕士论文].台湾：国立中央大学,2008.
[2] Michelle RD, Linda SP, Pouran F, et al. A Prospective Study of Overuse Knee Injuries Among Female Athletes With Muscle Imbalances and Structural Abnonnalities[J]. Journal of Athletic Training, 2004,39(3):263-267.
[3] 欧阳钧，朱青安，瞿文亮，等．胸腰段脊柱纵向撞击伤后稳定性评价方法的比较[J]．医用生物力学，1997,12(4)：201-204．
[4] 刘印凡，李元敬．我国优秀女子铁饼运动员最后用力阶段膝关节急性损伤的生物力学分析[J]．天津体育学院学报，2005,20(2)：72-73．
[5] 李鉴轶，焦培峰，张美超，等．膝关节在体稳定性评价系统的建立．中国骨与关节损伤杂志[J]．2007，22(6)：471-473．
[6] Tomazevic D. 3-D/2-D registration of CT and MR to X-ray images[J]. IEEE transactions on medical imaging, 2003,22(11):1407-1416.
[7] Yamazaki T, Watanabe T, Nakajima Y, et al. Improvement of depth position in 2-D/3-D registration of knee implants using single-plane fluoroscopy[J]. IEEE transactions on medical imaging. 2004,23(5):602-612.
[8] 王骏．我国医学影像技术近十年发展概述[J]．影像技术，2004(3)：6-11．
[9] 吴春禹．DR胸部摄影图像质量影响因素的分析．南华大学学报(医学版),2009，37(5)：598-599．
[10] Guoyan Zheng. Unifying Energy Minimization and Mutual Information Maximization for Robust 2D/3D Registration of X-Ray and CT Images[C]. DAGM 2007, LNCS 4713:547-557.
[11] Guoyan Zheng, Xiao Dong, Lutz-Peter Nolte. Robust and Accurate Reconstruction of Patient-Specific 3D Surface Models from Sparse Point Sets: A Sequential Three-Stage Trimmed Optimization Approach[C], MIAR 2006, LNCS 4091:68-75.
[12] Gongli Wang, Guoyan Zheng, Paul Alfred Grutzner, et al. A CT-Free Intraoperative Planning and Navigation System for High Tibial DomeOsteotomy[C]. MICCAI 2004, LNCS 3217:610-620.
[13] Jeffrey Bingham, Guoan Li. An Optimized Image Matching Method for Determining In-Vivo TKA Kinematics with a Dual-Orthogonal Fluoroscopic Imaging System[J]. Journal of Biomechanical Engineering. 2006,(128):588-595.
[14] Shirley A M Baert, Graeme P Penney, Theo van Walsum, et al. Precalibration Versus 2D-3D Registration for 3D Guide Wire Display in Endovascular Interventions[C]. MICCAI 2004, LNCS 3217:577-584.
[15] E. Freund, F, Heinze, J, Rossmann. Robotic Simulation System for Precise Positioning in Medical Applications. Perspective in Image-Guided Surgery[C]. MRNV 2004:270-277.
[16] Christof Hurschler, Frank Seehaus, Dipl-Sportwiss,et al. Accuracy of Model-based RSA Contour Reduction in a Typical Clinical Application [J].Clin Orthop Relat Res. 2008 (466): 1978-1986.
[17]梁玮，鲍旭东，罗立民．基于互信息的2D-3D医学图像配准[J]．生物医学工程研究,2004,23(1)：14-16．
[18]张薇，黄毓瑜，栾胜，等．基于灰度的二维、三维图像配准方法及其在骨科导航手术中的实现[J]．中国医学影像技术,20072，3(7)：145-149．
[19]戴君益．C-arm影像与电脑断层影像之方位校准方法[D]：[硕士论文]．台湾：国立中央大学．2008．
[1]Maintz J B A, Viercever M A. A survey of medical image registration [J]. Medical Image Alysis,1998(2):1-36.
[2]Ardekani B A, Braun M, Hutton M et al. A fully automatic multimodality image Registration algorithm[J]. Journal of Computer Assisted Tomography, 1995,19(4):615-623.
[3]Maintz J B A, Vanden Elsen P A, Viergever M A. Comparison of feature-based matching of CT and MR brain image [J]. Computer Vision, Virtual Reality, and Robotics in Medicine,1995,905:219-228.
[4]Garling EH, Kaptein BL, Geleijns K, et al. Marker configuration model Based Roentgen Fluoroscopics Analysis[J]. J Biomech,2005,38(4):893-901.
[5]S.Schreiner, Funda J, Barnes A C,et al.Accuracy assessment of a clinical biplane fluoroscope for three-dimensional measurements and targeting [J]. Proceedings of SPIE 3031,160(1997).
[6]D. P. Chakraborty. Image intensifier distortion correction[J]. Med Phys,1987; 14:249-252.
[7]I.Sobel. On Calibrating Computer Controlled Cameras for Perceiving 3D Scenes [J]. Artificial Intelligence,1974;5:185-198.
[8]W Faig. Calibration of close-range photogrammetry systems:Mathematical formulation [J]. Photogrammetric Eng. Remote Sensing,1975;41:1479-1486.
[9]H.M.Karara. Handbook of Non-Topographic Photogrammetry[M]. Amer Soc of Photogrammetry,1979.
[10]Zhang Z. Flexible camera calibration by viewing a plane from unknown orientations [J]. Proceedings of the 7th International Conference on Computer Vision. Greece, Corfu,1999.666～673.
[11]崔智,张良震,朱淼良.基于光线跟踪的数字影像重建技术[J].小型微型计算机系统,2001,22(10)：1259-1261.
[12]汪俊,吴章文,张从华,等.基于射线追踪的数字重建影像增强技术[J].生物医学工程学杂志.2005,22(1)：125-128.
[13]Levoy, M. Display of surface from volume data [J].Computer Graphics and Application,1988,8(3):29-37.
[14]陆态.X线透视图像(2D)与CT体积图像(3D)配准方法研究及其应用[D]:[硕 士论文].南京：东南大学,2008.
[15]NVIDIA CUD A Computational Unified Device Architecture Programming Guide Version 2.0[M]. NVIDIA Corporation,2008.
[16]Sanjiv S Samant, Junyi Xia, et al. High performance computing for deformable image registration:Towards a new paradigm in adaptive radiotherapy[J]. Medical Physics.2008,Vol 35(8):3546-3553.
[17]Bo Li, Alistair A Young, Brett R Cowan. GPU Accelerated Non-rigid Registration for the Evaluation of Cardiac Function[C]. MICCAI 2008,880-887.
[18]张加万,杨甲东,孙济洲.基于GPU的弹性图像配准方法[J].天津大学学报,2008,41(8)：946-950.
[19]Andre Gueziec, Kenong Wu, Bill Williamson, et al. Exploiting 2-D to 3-D Intra-Operative Image Registration for Qualitative Evaluations and Post-Operative Simulations. MICCAI'99, LNCS 1679,820-833.
[20]Dejan Tomazevic, Bostjan Likar, Franjo Pernus. "Gold standard" data for evaluation and comparison of 3D/2D registration methods[J]. Computer Aided Surgery.2004; 9(4):137-144.
[1]Zhang Z. Flexible camera calibration by viewing a plane from unknown orientations [J]. Proceedings of the 7th International Conference on Computer Vision. Greece, Corfu,1999.666～673.
[2]刘金颂,原思聪,张庆阳,等.双目立体视觉中的摄像机标定技术研究[J].计算机工程与应用.2008,44(6)：237-239.
[3]Scaramuzza D, Martinelli A, Siegwart R. A Flexible Technique for Accurate Omnidirectional Camera Calibration and Structure from Motion. Proceedings of IEEE International Conference of Vision Systems (ICVS'06), New York, January 5-7,2006.
[4]张惠,Pascal Haigron,舒华中,等.X射线图像和CT图像的多维配准[J].电子学报.2002,30(10)：1573-1576.
[5]黄永锋,李彬,赵俊.基于外标记点的2D／3D图像配准方法[J].上海交通大学学报.2006,40(7)：1108-1111.
[6]贾富仓,李修往,陈恩平.CT图像引导脊柱外科配准方法研究[J].深圳大学学报理工版.2007,24(4)：406-409.
[7]张翼,王满宁,宋志坚.脊柱手术导航中分布式2D／3D图像配准方法[J].计算机辅助设计与图像学学报.2007,19(9)：1154-1158.
[8]戴君益.C-arm影像与电脑断层影像之方位校准方法[D][硕士论文].台湾：国立中央大学,2008.