A novel system for thE 3-D reconstruction of the human spine and rib cage from biplanar X-ray images

The main objective of this study was to develop a 3-D X-ray reconstruction system of the spine and rib cage for an accurate 3-D clinical assessment of spinal deformities. The system currently used at Sainte-Justine Hospital in Montreal is based on an implicit calibration technique based on a direct linear transform (DLT), using a sufficiently large rigid object incorporated in the positioning apparatus to locate any anatomical structure to be reconstructed within its bounds. During the time lapse between the two successive X-ray acquisitions required for the 3-D reconstruction, involuntary patient motion introduce errors due to the incorrect epipolar geometry inferred from the stationary object. An approach using a new calibration jacket and explicit calibration algorithm is proposed in this paper. This approach yields accurate results and compensates for involuntary motion occurring between X-ray exposures.     

Motion correction for coronary stent reconstruction from rotational X-ray projection sequences

This paper presents a new method for 3-D tomographic reconstruction of stent in X-ray cardiac rotational angiography. The method relies on 2-D motion correction from two radiopaque markerballs located on each side of the stent. The two markerballs are on a guidewire and linked to the balloon, which is introduced into the artery. Once the balloon has been inflated, deflated, and the stent deployed, a rotational sequence around the patient is acquired. Under the assumption that the guidewire and the stent have the same 3-D motion during rotational acquisition, we developed an algorithm to correct cardiac stent motion on the 2-D X-ray projection images. The 3-D image of the deployed stent is then reconstructed with the Feldkamp algorithm using all the available projections. Although the correction is an approximation, we show that the intrinsic geometrical error of our method has no visual impact on the reconstruction when the 2-D markerball centers are exactly detected and the markerballs have the same 3-D motion as the stent. Qualitative and quantitative results on simulated sequences under different realistic conditions demonstrate the robustness of the method. Finally, results from animal data acquired on a rotational angiography device are presented.     

基于刚体几何不变性的雷达目标运动路径拟合和三维优化重建方法

对于飞机、船舰等刚体雷达目标,其在运动过程中具有空间几何不变性。利用这一约束条件,可以通过雷达回波中提取出的目标散射点的一维距离史重建出目标的三维形状和运动路径。鉴于现有的基于几何不变性的雷达目标三维重建算法存在鲁棒性差的问题,本文利用雷达目标的运动惰性,对初步重建后得到的目标运动路径进行了拟合,并利用拟合后的运动路径对目标散射点的三维坐标进行了优化重建。文中对重建的误差进行了分析,提出了仿射扰动和欧式重建误差的误差模型。仿真实验证明,经仿射匹配校正后的拟合路径与真实路径基本吻合,从而可以有效获得目标的运动特征;同时,利用本文提出的优化重建方法能够有效抑制目标的欧式重建误差,提高了重建算法的准确性。      

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.     

Three-dimensional motion tracking of coronary arteries in biplane cineangiograms

A three-dimensional (3-D) method for tracking the coronary arteries through a temporal sequence of biplane X-ray angiography images is presented. A 3-D centerline model of the coronary vasculature is reconstructed from a biplane image pair at one time frame, and its motion is tracked using a coarse-to-fine hierarchy of motion models. Three-dimensional constraints on the length of the arteries and on the spatial regularity of the motion field are used to overcome limitations of classical two-dimensional vessel tracking methods, such as tracking vessels through projective occlusions. This algorithm was clinically validated in five patients by tracking the motion of the left coronary tree over one cardiac cycle. The root mean square reprojection errors were found to be submillimeter in 93% (54/58) of the image pairs. The performance of the tracking algorithm was quantified in three dimensions using a deforming vascular phantom. RMS 3-D distance errors were computed between centerline models tracked in the X-ray images and gold-standard centerline models of the phantom generated from a gated 3-D magnetic resonance image acquisition. The mean error was 0.69 (+/- 0.06) mm over eight temporal phases and four different biplane orientations.     

Optimal CT scanning plan for long-bone 3-D reconstruction

Digital computed tomographic (CT) data are widely used in three-dimensional (3-D) construction of bone geometry and density features for 3-D modelling purposes. During in vivo CT data acquisition the number of scans must be limited in order to protect patients from the risks related to X-ray absorption. The aim of this work is to automatically define, given a finite number of CT slices, the scanning plan which returns the optimal 3-D reconstruction of a bone segment from in vivo acquired CT images. An optimization algorithm based on a Discard-Insert-Exchange technique has been developed. In the proposed method the optimal scanning sequence is searched by minimizing the overall reconstruction error of a two-dimensional (2-D) prescanning image: an anterior-posterior (AP) X-ray projection of the bone segment. This approach has been validated in vitro on 3 different femurs. The 3-D reconstruction errors obtained through the optimization of the scanning plan on the 3-D prescanning images and on the corresponding 3-D data sets have been compared. 2-D and 3-D data sets have been reconstructed by linear interpolation along the longitudinal axis. Results show that direct 3-D optimization yields root mean square reconstruction errors which are only 4%-7% lower than the 2-D-optimized plan, thus proving that 2-D-optimization provides a good suboptimal scanning plan for 3-D reconstruction. Further on, 3-D reconstruction errors given by the optimized scanning plan and a standard radiological protocol for long bones have been compared. Results show that the optimized plan yields 20%-50% lower 3-D reconstruction errors     

Three-dimensional surface reconstruction using optical flow formedical imaging

The recovery of a three-dimensional (3-D) model from a sequence of two-dimensional (2-D) images is very useful in medical image analysis. Image sequences obtained from the relative motion between the object and the camera or the scanner contain more 3-D information than a single image. Methods to visualize the computed tomograms can be divided into two approaches: the surface rendering approach and the volume rendering approach. In this paper, a new surface rendering method using optical flow is proposed. Optical flow is the apparent motion in the image plane produced by the projection of real 3-D motion onto the 2-D image. The 3-D motion of an object can be recovered from the optical-flow field using additional constraints. By extracting the surface information from 3-D motion, it is possible to obtain an accurate 3-D model of the object. Both synthetic and real image sequences have been used to illustrate the feasibility of the proposed method. The experimental results suggest that the proposed method is suitable for the reconstruction of 3-D models from ultrasound medical images as well as other computed tomograms     

Constrained registration for motion compensation in atrial fibrillation ablation procedures

Fluoroscopic overlay images rendered from preoperative volumetric data can provide additional anatomical details to guide physicians during catheter ablation procedures for treatment of atrial fibrillation (AFib). As these overlay images are often compromised by cardiac and respiratory motion, motion compensation methods are needed to keep the overlay images in sync with the fluoroscopic images. So far, these approaches have either required simultaneous biplane imaging for 3-D motion compensation, or in case of monoplane X-ray imaging, provided only a limited 2-D functionality. To overcome the downsides of the previously suggested methods, we propose an approach that facilitates a full 3-D motion compensation even if only monoplane X-ray images are available. To this end, we use a training phase that employs a biplane sequence to establish a patient specific motion model. Afterwards, a constrained model-based 2-D/3-D registration method is used to track a circumferential mapping catheter. This device is commonly used for AFib catheter ablation procedures. Based on the experiments on real patient data, we found that our constrained monoplane 2-D/3-D registration outperformed the unconstrained counterpart and yielded an average 2-D tracking error of 0.6 mm and an average 3-D tracking error of 1.6 mm. The unconstrained 2-D/3-D registration technique yielded a similar 2-D performance, but the 3-D tracking error increased to 3.2 mm mostly due to wrongly estimated 3-D motion components in X-ray view direction. Compared to the conventional 2-D monoplane method, the proposed method provides a more seamless workflow by removing the need for catheter model re-initialization otherwise required when the C-arm view orientation changes. In addition, the proposed method can be straightforwardly combined with the previously introduced biplane motion compensation technique to obtain a good trade-off between accuracy and radiation dose reduction.     

Estimation of the heart respiratory motion with applications for cone beam computed tomography imaging: a simulation study

Computed tomography (CT) reconstruction methods assume imaging of static objects; object movement during projection data acquisition causes tomogram artifacts. The continuously moving heart, therefore, represents a complicated imaging case. The associated problems due to the heart beating can be overcome either by using very short projection acquisition times, during which the heart may be considered static, or by ECG-gated acquisition. In the latter case, however, the acquisition of a large number of projections may not be completed in a single breath hold, thus heart displacement occurs as an additional problem. This problem has been addressed by applying heart motion models in various respiratory motion compensation algorithms. Our paper focuses on cone beam computed tomography (CBCT), performed in conjunction with isocentric, fluoroscopic equipment, and continuous ECG and respiratory monitoring. Such equipment is used primarily for in-theater three-dimensional (3-D) imaging and benefits particularly from the recent developments in flat panel detector technologies. The objectives of this paper are: (i) to develop a model for the motion of the heart due to respiration during the respiratory cycle; (ii) to apply this model to the tomographic reconstruction algorithm, in order to account for heart movement due to respiration in the reconstruction; and (iii) to initially evaluate this method by means of simulation studies. Based on simulation studies, we were able to demonstrate that heart displacement due to respiration can be estimated from the same projection data, required for a CBCT reconstruction. Our paper includes semiautomatic segmentation of the heart on the X-ray projections and reconstruction of a convex 3-D-heart object that performs the same motion as the heart during respiration, and use of this information into the CBCT reconstruction algorithm. The results reveal significant image quality improvements in cardiac image reconstruction.     

基于改进核范数的2DPCA人脸识别算法研究

传统的二维主成分分析法广泛应用于图像特征提取,为了使此算法更加有效,提出了一种结构化二维算法,即核范数2DPCA算法(N-2-DPCA).该算法基于核范数重构误差准则,将核范数最优化问题转化为基于F范数的最优化问题,然后通过采用迭代方法寻找到最佳投影矩阵,最后运用最小欧氏距离规则识别出待识别人脸的身份.在此基础之上,将N-2-DPCA扩展到基于双边投影的算法(N-B2-DPCA),采用曲线搜索算法寻找到双边投影矩阵,继而进行识别.最后将提出的算法在FERET和Yale B人脸数据库中进行人脸识别评估,实验结果表明所提出的算法与L1-2DPCA相比,重建误差降低了2.19％,识别率提高了2.03％,性能更好.     

Reconstruction of coronary arteries from a single rotational X-ray projection sequence

Cardiovascular diseases remain the primary cause of death in developed countries. In most cases, exploration of possibly underlying coronary artery pathologies is performed using X-ray coronary angiography. Current clinical routine in coronary angiography is directly conducted in two-dimensional projection images from several static viewing angles. However, for diagnosis and treatment purposes, coronary artery reconstruction is highly suitable. The purpose of this study is to provide physicians with a three-dimensional (3-D) model of coronary arteries, e.g., for absolute 3-D measures for lesion assessment, instead of direct projective measures deduced from the images, which are highly dependent on the viewing angle. In this paper, we propose a novel method to reconstruct coronary arteries from one single rotational X-ray projection sequence. As a side result, we also obtain an estimation of the coronary artery motion. Our method consists of three main consecutive steps: 1) 3-D reconstruction of coronary artery centerlines, including respiratory motion compensation; 2) coronary artery four-dimensional motion computation; 3) 3-D tomographic reconstruction of coronary arteries, involving compensation for respiratory and cardiac motions. We present some experiments on clinical datasets, and the feasibility of a true 3-D Quantitative Coronary Analysis is demonstrated.     

网格运动分析与形态学滤波相结合的视频对象分割

提出了一种基于二维网格运动分析与改进形态学滤波空域自动分割策略相结合的视频对象时空分割算法。该算法首先利用高阶统计方法对视频图像的二维网格表示进行运动分析，快速得到前景对象区域，通过后处理有效获得前景对象运动检测掩膜。然后，用一种结合交变序列重建滤波算法和自适应阈值判别算法的改进分水岭分割策略有效获得前景对象的精确边缘。最后，用区域基时空融合算法将时域分割结果和空域分割结果结合起来提取出边缘精细的视频对象。实验结果表明，本算法综合了多种算法的优点，主客观分割效果理想。     

Statistical bias in 3-D reconstruction from a monocular video.

The present state-of-the-art in computing the error statistics in three-dimensional (3-D) reconstruction from video concentrates on estimating the error covariance. A different source of error which has not received much attention is the fact that the reconstruction estimates are often significantly statistically biased. In this paper, we derive a precise expression for the bias in the depth estimate, based on the continuous (differentiable) version of structure from motion (SfM). Many SfM algorithms, or certain portions of them, can be posed in a linear least-squares (LS) framework Ax = b. Examples include initialization procedures for bundle adjustment or algorithms that alternately estimate depth and camera motion. It is a well-known fact that the LS estimate is biased if the system matrix A is noisy. In SfM, the matrix A contains point correspondences, which are always difficult to obtain precisely; thus, it is expected that the structure and motion estimates in such a formulation of the problem would be biased. Existing results on the minimum achievable variance of the SfM estimator are extended by deriving a generalized Cramer-Rao lower bound. A detailed analysis of the effect of various camera motion parameters on the bias is presented. We conclude by presenting the effect of bias compensation on reconstructing 3-D face models from rendered images.     

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.     

Reconstruction of 3-D geometry using 2-D profiles and a geometric prior model

A method has been developed to reconstruct three-dimensional (3-D) surfaces from two-dimensional (2-D) projection data. It is used to produce individualized boundary element models, consisting of thorax and lung surfaces, for electro- and magnetocardiographic inverse problems. Two orthogonal projections are utilized. A geometrical prior model, built using segmented magnetic resonance images, is deformed according to profiles segmented from projection images. In the authors' method, virtual X-ray images of the prior model are first constructed by simulating real X-ray imaging. The 2-D profiles of the model are segmented from the projections and elastically matched with the profiles segmented from patient data. The displacement vectors produced by the elastic 2-D matching are back projected onto the 3-D surface of the prior model. Finally, the model is deformed, using the back-projected vectors. Two different deformation methods are proposed. The accuracy of the method is validated by a simulation. The average reconstruction error of a thorax and lungs was 1.22 voxels, corresponding to about 5 mm     

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.     

A novel temporal calibration method for 3-D ultrasound

This paper examines a novel approach for temporal calibration of a three-dimensional (3-D) freehand ultrasound system. A localization system fixed on the probe gives the position and orientation of the probe. For quantitative use, calibration is needed to correctly localize a B-scan in four-dimensional (4-D) (3-D+t) space. Temporal latency estimation is defined in a general robust formulation using no specific probe motion constraints. Experiments were performed on synthetic and real data using a 3-D freehand ultrasound system. The achieved precision is lower than the image acquisition rate (40 ms). A validation study using a calibration phantom has been performed to evaluate the influence of incorrect latency estimation on the 3-D reconstruction procedure. We showed that for latency estimation errors less than 40 ms, the 3-D reconstruction errors are negligible for volume estimation.     

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

Three-dimensional biplanar reconstruction of scoliotic rib cage using the estimation of a mixture of probabilistic prior models

In this paper, we present an original method for the three-dimensional (3-D) reconstruction of the scoliotic rib cage from a planar and a conventional pair of calibrated radiographic images (postero-anterior with normal incidence and lateral). To this end, we first present a robust method for estimating the model parameters in a mixture of probabilistic principal component analyzers (PPCA). This method is based on the stochastic expectation maximization (SEM) algorithm. Parameters of this mixture model are used to constrain the 3-D biplanar reconstruction problem of scoliotic rib cage. More precisely, the proposed PPCA mixture model is exploited for dimensionality reduction and to obtain a set of probabilistic prior models associated with each detected class of pathological deformations observed on a representative training scoliotic rib cage population. By using an appropriate likelihood, for each considered class-conditional prior model, the proposed 3-D reconstruction is stated as an energy function minimization problem, which is solved with an exploration/selection algorithm. The optimal 3-D reconstruction then corresponds to the class of deformation and parameters leading to the minimal energy. This 3-D method of reconstruction has been successfully tested and validated on a database of 20 pairs of biplanar radiographic images of scoliotic patients, yielding very promising results. As an alternative to computed tomography-scan 3-D reconstruction this scheme has the advantage of low radiation for the patient, and may also be used for diagnosis and evaluation of deformity of a scoliotic rib cage. The proposed method remains sufficiently general to be applied to other reconstruction problems for which a database of objects to be reconstructed is available (with two or more radiographic views).