Characterization of pinhole SPECT acquisition geometry

A method is presented to estimate the acquisition geometry of a pinhole single photon emission computed tomography (SPECT) camera with a circular detector orbit. This information is needed for the reconstruction of tomographic images. The calibration uses the point source projection locations of a tomographic acquisition of three point sources located at known distances from each other. It is shown that this simple phantom provides the necessary and sufficient information for the proposed calibration method. The knowledge of two of the distances between the point sources proves to be essential. The geometry is estimated by fitting analytically calculated projections to the measured ones, using a simple least squares Powell algorithm. Some mild a priori knowledge is used to constrain the solutions of the fit. Several of the geometrical parameters are however highly correlated. The effect of these correlations on the reconstructed images is evaluated in simulation studies and related to the estimation accuracy. The highly correlated detector tilt and electrical shift are shown to be the critical parameters for accurate image reconstruction. The performance of the algorithm is finally demonstrated by phantom measurements. The method is based on a single SPECT scan of a simple calibration phantom, executed immediately after the actual SPECT acquisition. The method is also applicable to cone-beam SPECT and X-ray CT.     

Multi-pinhole SPECT calibration: influence of data noise and systematic orbit deviations

The geometry of a single pinhole SPECT system with circular orbit can be uniquely determined from a measurement of three point sources, provided that at least two inter-point distances are known. In contrast, it has been shown mathematically that, for a multi-pinhole SPECT system with circular orbit, only two point sources are needed, and the knowledge of the distance between them is not required. In this paper, we report that this conclusion only holds if the motion of the camera is perfectly circular. In reality, the detector heads systematically slightly deviate from the circular orbit, which may introduce non-negligible bias in the estimated parameters and degrade the reconstructed image. An analytical linear model was extended to estimate the influence of both data noise and systematic deviations on the accuracy of the calibration and on the image quality of the reconstruction. It turns out that applying the knowledge of the distances greatly reduces the reconstruction error, especially in the presence of systematic deviations. In addition, we propose that instead of using the information about the distances between the point sources, it is more straightforward to use the knowledge about the distances between the pinhole apertures during multi-pinhole calibration. The two distance-fixing approaches yield similar reconstruction accuracy. Our theoretical results are supported by reconstruction images of a Jaszczak-type phantom scan.     

视场网状分区域建模的星敏感器标定方法

星敏感器标定是基于更高精度的测量基准对光学系统内方位元素进行建模与最优化解算的过程。针对大视场星敏感器光学系统误差分布非理想轴对称的实际情况,提出了一种采用视场网状分区域建模的内方位元素最优化解算方法。首先,在补偿了星敏感器与标定系统初始对准误差后,基于针孔模型计算主点和焦距;然后,在视场分区域建模思想的指导下,采用多项式拟合结合双线性插值的方法修正畸变;最后,提出了基于测角误差的标定精度评价准则。经实验室标定与外场观星验证,x轴与y轴标定残差较全局建模法分别降低了35%和20%,证明了该方法的有效性。     

Pinhole SPECT imaging: compact projection/backprojection operator for efficient algebraic reconstruction

We describe the efficient algebraic reconstruction (EAR) method, which applies to cone-beam tomographic reconstruction problems with a circular symmetry. Three independant steps/stages are presented, which use two symmetries and a factorization of the point spread functions (PSFs), each reducing computing times and eventually storage in memory or hard drive. In the case of pinhole single photon emission computed tomography (SPECT), we show how the EAR method can incorporate most of the physical and geometrical effects which change the PSF compared to the Dirac function assumed in analytical methods, thus showing improvements on reconstructed images. We also compare results obtained by the EAR method with a cubic grid implementation of an algebraic method and modeling of the PSF and we show that there is no significant loss of quality, despite the use of a noncubic grid for voxels in the EAR method. Data from a phantom, reconstructed with the EAR method, demonstrate 1.08-mm spatial tomographic resolution despite the use of a 1.5-mm pinhole SPECT device and several applications in rat and mouse imaging are shown. Finally, we discuss the conditions of application of the method when symmetries are broken, by considering the different parameters of the calibration and nonsymmetric physical effects such as attenuation.     

采用高频能量的CT几何参数自标定方法

针对锥束CT系统中几何参数失配引起几何伪影的问题,提出了一种采用空域高频能量的几何伪影自校正算法。该算法以重建图像的空域高频能量为目标函数建立优化模型,通过单纯形法迭代求解使空域高频能量最大的几何参数最优解。利用投影图像的特性提取部分参数作为输入初值,减小算法搜索范围。并采用图形处理器（Graphic Processing Unit,GPU）对自校正过程中的图像重建并行加速,减少重建时间,提高校正速度。实验结果表明:该算法具有较高的求解精度,最大相对误差不超过5%,对重建图像中的几何伪影有较好的校正效果。同时,在不影响精度的情况下减少了迭代次数,算法执行效率提高了18.8%。     

Novel Approach for 3-D Reconstruction of Coronary Arteries From Two Uncalibrated Angiographic Images

Three-dimensional reconstruction of vessels from digital X-ray angiographic images is a powerful technique that compensates for limitations in angiography. It can provide physicians with the ability to accurately inspect the complex arterial network and to quantitatively assess disease induced vascular alterations in three dimensions. In this paper, both the projection principle of single view angiography and mathematical modeling of two view angiographies are studied in detail. The movement of the table, which commonly occurs during clinical practice, complicates the reconstruction process. On the basis of the pinhole camera model and existing optimization methods, an algorithm is developed for 3-D reconstruction of coronary arteries from two uncalibrated monoplane angiographic images. A simple and effective perspective projection model is proposed for the 3-D reconstruction of coronary arteries. A nonlinear optimization method is employed for refinement of the 3-D structure of the vessel skeletons, which takes the influence of table movement into consideration. An accurate model is suggested for the calculation of contour points of the vascular surface, which fully utilizes the information in the two projections. In our experiments with phantom and patient angiograms, the vessel centerlines are reconstructed in 3-D space with a mean positional accuracy of 0.665 mm and with a mean back projection error of 0.259 mm. This shows that the algorithm put forward in this paper is very effective and robust.     

光场相机建模与畸变校正改进方法

光场相机作为一种新型的成像系统,可以直接从一次曝光的图像中得到三维信息。为了能够更充分有效地利用光场数据包含的角度和位置信息,完成更加精准的场景深度计算,从而提升光场相机的三维重建的精度,需要实现精确的几何建模,并精确标定其模型参数。该方法从薄透镜模型和小孔成像模型出发,将主透镜建模为薄透镜模型,将微透镜建模为小孔成像模型,结合光场相机双平面模型,将每个提取到的特征点与其在三维空间中的射线建立联系,详细解释了内参矩阵中每个参数的物理意义,以及标定过程中初值确定的过程,并在镜头径向畸变模型的基础上进一步应用了相机镜头的切向畸变模型以及基于射线重投影误差的非线性优化方法,改进了光场相机的标定方法。实验显示,该方法的RMS射线重投影误差为0.332 mm,与经典的Dansereau标定方法相比,进行非线性优化后得到的射线重投影误差精度提升了8%。该方法详细分析的场景点与特定像素索引的推导过程对光场相机的标定具有重要的研究意义,为光场相机光学模型的建立与初始化标定奠定了基础。     

Heart-surface reconstruction and ECG electrodes localization using fluoroscopy, epipolar geometry and stereovision: application to noninvasive imaging of cardiac electrical activity

To date there is no imaging modality for cardiac arrhythmias which remain the leading cause of sudden death in the United States (> 300000/yr.). Electrocardiographic imaging (ECGI), a noninvasive modality that images cardiac arrhythmias from body surface potentials, requires the geometrical relationship between the heart surface and the positions of body surface ECG electrodes. A photographic method was validated in a mannequin and used to determine the three-dimensional coordinates of body surface ECG electrodes to within 1 mm of their actual positions. Since fluoroscopy is available in the cardiac electrophysiology (EP) laboratory where diagnosis and treatment of cardiac arrhythmias is conducted, a fluoroscopic method to determine the heart surface geometry was developed based on projective geometry, epipolar geometry, point reconstruction, b-spline interpolation and visualization. Fluoroscopy-reconstructed hearts in a phantom and a human subject were validated using high-resolution computed tomography (CT) imaging. The mean absolute distance error for the fluoroscopy-reconstructed heart relative to the CT heart was 4 mm (phantom) and 10 mm (human). In the human, ECGI images of normal cardiac electrical activity on the fluoroscopy-reconstructed heart showed close correlation with those obtained on the CT heart. Results demonstrate the feasibility of this approach for clinical noninvasive imaging of cardiac arrhythmias in the interventional EP laboratory.     

A graphical method for determining the in-plane rotation angle in geometric calibration of circular cone-beam CT systems

It is well known that seven parameters completely describe a circular cone-beam geometry in either flat-panel X-ray computed tomography (CT) or single pinhole SPECT imaging. This paper considers the problem of determining one of the seven parameters only, the detector in-plane rotation or twist angle η. We describe a graphical procedure that can determine η independently of all other six parameters from a geometric calibration scan of point objects. Our method is exact in the ideal noise-free case and is general in that the other two out-of-plane detector rotation angles θ and φ can be nonzero. The calibration scan typically needs at least two point objects and an even number of projection views over a full 360° data acquisition. Under certain conditions, projection data truncation or a short scan acquisition of 180° + fan angle can be accommodated without affecting the accuracy of the calibration result. The graphical method is equally applicable to rotational multipinhole SPECT geometry. In this case, the final result is averaged from the individual estimates considering each pinhole separately. We use computer simulations and a multipinhole SPECT experiment to demonstrate the accuracy and precision of the proposed method.     

3-D reconstruction of microcalcification clusters using stereo imaging: algorithm and mammographic unit calibration

The three-dimensional (3-D) shape of microcalcification clusters is an important indicator in early breast cancer detection. In fact, there is a relationship between the cluster topology and the type of lesion (malignant or benign). This paper presents a 3-D reconstruction method for such clusters using two 2-D views acquired during standard mammographic examinations. For this purpose, the mammographic unit was modeled using a camera with virtual optics. This model was used to calibrate the acquisition unit and then to reconstruct the clusters in the 3-D space after microcalcification segmentation and matching. The proposed model is hardware independent since it is suitable for digital mammographic units with different geometries and with various physical acquisition principles. Three-dimensional reconstruction results are presented here to prove the validity of the method. Tests were first performed using a phantom with a well-known geometry. The latter contained X-ray opaque glass balls representing microcalcifications. The positions of these balls were reconstructed with a 16.25-microm mean accuracy. This very high inherent algorithm accuracy is more than enough for a precise 3-D cluster representation. Further validation tests were carried out using a second phantom including a spherical cluster. This phantom was built with materials simulating the behavior of both mammary tissue and microcalcifications toward Xrays. The reconstructed shape was effectively spherical. Finally, reconstructions were carried out for real clusters and their results are also presented.     

Motion Capture of the Human Body Using Multiple Depth Sensors

The movements of the human body are difficult to capture owing to the complexity of the three‐dimensional skeleton model and occlusion problems. In this paper, we propose a motion capture system that tracks dynamic human motions in real time. Without using external markers, the proposed system adopts multiple depth sensors (Microsoft Kinect) to overcome the occlusion and body rotation problems. To combine the joint data retrieved from the multiple sensors, our calibration process samples a point cloud from depth images and unifies the coordinate systems in point clouds into a single coordinate system via the iterative closest point method. Using noisy skeletal data from sensors, a posture reconstruction method is introduced to estimate the optimal joint positions for consistent motion generation. Based on the high tracking accuracy of the proposed system, we demonstrate that our system is applicable to various motion‐based training programs in dance and Taekwondo.     

基于同心圆光栅和契形光栅的摄像机自标定方法

提出一种利用同心圆光栅和契形光栅作为标定模板,基于正交方向消失点摄像机自标定的新方法。新方法利用相移条纹相位提取精度高的特性来求零相位特征点,避免了传统标记点提取误差给标定结果带来的影响。要求摄像机至少从6个方位拍摄标靶,采用四步相移得到光栅的截断相位并求解零相位交点,计算消失点从而解算出摄像机的内参数。根据模拟实验得到影响消失点标定精度因素的分析结果,制作了含有7个周期的同心圆光栅和4个周期的契形光栅。实际测量实验中分别用光栅靶标和灰度同心圆靶标进行相机标定,对比重投影误差,结果证明新方法提高了基于消失点标定算法的精度和稳健性。     

航空多光谱相机三坐标无源定位技术

航空多光谱相机采用焦平面探测成像系统，可在全天时、准全天候作业的条件下对机下进行大幅宽高分辨率成像探测。针对航空多光谱相机的三坐标无源定位问题，简介了相机组成及无测距信息辅助情况下的三坐标无源定位原理，梳理了航空多光谱相机的三坐标无源定位关键技术。通过载体的位置姿态精确测量，测角电路设计、测角误差标定与补偿，多传感器安装姿态标定，时间同步设计四大关键技术保证相机的定位精度。飞行试验结果表明，图像拼接精度优于10″，验证了技术方法有效。     

Implementation of uniform and simultaneous ART for 3-D reconstruction in an X-ray imaging system

The authors propose a 3-D volume reconstruction method using X-ray images with a calibration method to implement it in an X-ray imaging system. Previously the authors have proposed an advanced 3-D reconstruction algorithm based on an algebraic reconstruction technique (ART), called a uniform and simultaneous ART (USART). In practice, however, there are two main issues in implementing it in a realised X-ray imaging system. The first one is the huge computation time and memory required in achieving 3-D volume, which is a common limitation in most ART methods. The second issue is the system calibration for determining the geometry of the X-ray imaging conditions needed for the ART method. These two critical problems are addressed. A fast computing model of USART is proposed, where spherical voxel elements are employed in computation to reduce the computation time and memory. Then, a calibration method is proposed to identify the X-ray imaging geometry based on a cone beam projection model. For this purpose, a set of X-ray images of a reference grid pattern is used and the X-ray source positions are determined from the analysis of the image features, the centres of the grid points in the X-ray images. The validity of the proposed 3-D reconstruction method is investigated using a series of experiments.     

结构光场光束直线跟踪的两步标定方法

为了实现结构光系统的三维重建,针对传统标定方 法结构复杂、标定过程繁琐等问题,提出一种基于光束直线跟踪 的两步标定方法。本文方法首先在前后两个平面上分别对投射侧模式上的每个检测点进行 标定,建立投射侧光线方程;然后在 前后两个平面上分别对平面上的每个目标点建立接收侧CCD的光线方程。在三维测量时,光 场中的一个点分别映射为投射 侧和接收侧前后平面上的两个点,连接前后平面上的两个点各得到一条空间直线,通过求解 两条空间直线的交点即可求得三 维空间点的坐标。分析了系统结构在标定时可能产生的误差,系统误差主要来自角度偏移和 水平偏移,并提出了误差解决方 案。实验结果表明,与传统的基于针孔模型的标定方法相比,本文方法无须考虑系统的成像 模型及其参数求解,简洁、高效。标定产生的景深相对误差小于0.2% ,能够改善结构光系统的几何标定精度。     

低信噪比的接收通道阵列幅相误差校正方法

针对低信噪比情况,建立了新的接收阵列误差模型,提出了一种改进单辅助源通道阵列幅相误差校正算法.该算法利用自相关矩阵对角线部分求解通道幅度误差,用最小二乘法对上三角部分求解通道相位误差.仿真结果表明:在低信噪比时,改进校正算法性能明显优于传统校正算法,在高信噪比时,2种算法残差均非常小.实验结果表明:利用改进的校正算法对综合孔径辐射计进行校正后所得的图像边界清晰、干扰较少,与实际亮温对应较好,明显优于采用传统校正算法进行校正后所得的图像.     

基于CCD标定的微像素精度图像定位技术

基于光电成像器件CCD的点目标定位技术被广泛运用于天文定位、侦察等民用及军用方面。传统点目标定位精度一般为亚像素级,受CCD自身成像误差限制,目标定位精度难以大幅提高。提出通过干涉条纹对CCD进行标定,从而得到CCD频域像素响应函数的精确表达式,由此重构高质量的目标入射光场图像,进而提高光电成像系统对点目标定位的精度。首先建立了干涉条纹标定CCD及目标光场图像重构的理想模型,并通过仿真验证了点目标图像重构效果以及最终点目标的定位精度。仿真结果表明,经干涉条纹标定CCD后,重构的目标光场图像质量得到大幅度的提升,接近于CCD像面前入射光场图像,通过高斯曲面拟合得到点目标形心坐标及其微位移的提取精度均达微像素级别,相比于传统的亚像素定位,定位精度得到了大幅度的提高。     

Automatic Contour Detection Using a "Fixed-Point Hachimura-Kuwahara Filter" for SPECT Attenuation Correction

Attenuation correction for single-photon emission computed tomography (SPECT) usually assumes a uniform attenuation distribution within the body surface contour. Previous methods to estimate this contour have used thresholding of a reconstructed section image. This method is often very sensitive to the selection of a threshold value, especially for nonuniform activity distributions within the body. We have proposed the "fixed-point Hachimura-Kuwahara filter" to extract contour primitives from SPECT images. The Hachimura-Kuwahara filter, which preserves edges but smoothes nonedge regions, is applied repeatedly to identify the invariant set-the fixed-point image-which is unchanged by this nonlinear, two-dimensional filtering operation. This image usually becomes a piecewise constant array. In order to detect the contour, the tracing algorithm based on the minimum distance connection criterion is applied to the extracted contour primitives. This procedure does not require choice of a threshold value in determining the contour. SPECT data from a water-filled elliptical phantom containing three sources was obtained and scattered projections were reconstructed. The automatic edge detection procedure was applied to the scattered window reconstruction, resulting in a reasonable outline of the phantom.     

Young's Modulus Reconstruction for Radio-Frequency Ablation Electrode-Induced Displacement Fields: A Feasibility Study

Radio-frequency (RF) ablation is a minimally invasive treatment for tumors in various abdominal organs. It is effective if good tumor localization and intraprocedural monitoring can be done. In this paper, we investigate the feasibility of using an ultrasound-based Young's modulus reconstruction algorithm to image an ablated region whose stiffness is elevated due to tissue coagulation. To obtain controllable tissue deformations for abdominal organs during and/or intermediately after the RF ablation, the proposed modulus imaging method is specifically designed for using tissue deformation fields induced by the RF electrode. We have developed a new scheme under which the reconstruction problem is simplified to a 2-D problem. Based on this scheme, an iterative Young's modulus reconstruction technique with edge-preserving regularization was developed to estimate the Young's modulus distribution. The method was tested in experiments using a tissue-mimicking phantom and on ex vivo bovine liver tissues. Our preliminary results suggest that high contrast modulus images can be successfully reconstructed. In both experiments, the geometries of the reconstructed modulus images of thermal ablation zones match well with the phantom design and the gross pathology image, respectively.