基于顺序形态学的医学图像插值算法的研究

医学图像插值方法是医学图像三维重建的关键技术,插值的结果直接决定了三维重建的效果.本文在深入研究了顺序形态学理论的基础上,提出了一种基于顺序形态学的插值算法,该算法采用百分位膨胀和腐蚀算子,解决了线性插值和形状插值等算法产生的边界模糊的问题.仿真实验表明该算法产生的断层图像和原有断层图像过渡自然,为后续的医学图像三维重建奠定了基础.     

基于改进三维后向投影的多圈圆迹SAR相干三维成像方法

圆迹SAR(CSAR)因其特殊曲线运动轨迹而具备3维成像能力。单圈CSAR理论上可以获得距离方位平面亚波长级的分辨率,但是高程向分辨率却很低。同时,利用后向投影(BP)算法进行CSAR 3维成像的算法复杂度高,成像效率低。该文提出一种基于改进3维后向投影的多圈CSAR相干3维成像方法,针对现有成像算法时间复杂度高的问题,提出一种构造几何插值核的CSAR改进3维后向投影算法,可将3维插值操作转化为1维插值操作和距离向量搜索操作,通过多圈CSAR改进3维后向投影成像结果相干积累的方式得到最终3维图像。该文所提方法可有效解决单圈CSAR 3维成像高程向分辨率低的问题,改善3维成像细节,同时能够大幅降低CSAR 3维成像时间。仿真圆锥目标和美国空军实验室GOTCHA数据3维成像结果验证了该文所提方法的有效性。     

Interpolation of 3-D binary images based on morphological skeletonization

In this paper, the morphological skeleton interpolation (MSI) algorithm is presented. It is an efficient, shape-based interpolation method used for interpolating slices in a three-dimensional (3-D) binary object. It is based on morphological skeletonization, which is used for two-dimensional (2-D) slice representation. The proposed morphological skeleton matching process provides translation, rotation, and scaling information at the same time. The interpolated slices preserve the shape of the original object slices, when the slices have similar shapes. It can also modify the shape of an object when the successive slices do not have similar shapes. Applications on artificial and real data are also presented.     

基于三维递归搜索的多级运动估计视频帧率上转换算法

运动补偿插帧是目前主要的帧率上转换方法。为减小内插帧中的块效应,并降低运算量以满足实时高清视频应用,该文提出了一种基于3维递归搜索(3-D Recursive Search, 3-D RS)的多级块匹配运动估计视频帧率上转换算法。该算法将3-D RS与双向运动估计相结合,首先对序列中相邻帧进行由粗到精的三级运动估计,再利用简化的中值滤波器平滑运动矢量场,最后通过线性插值补偿得到内插帧。实验结果表明,与现有的运动补偿插帧算法相比,该算法内插帧的主、客观质量都有所提高,且算法复杂度低,有很强的实用性。     

Development of a vertebral endplate 3-D reconstruction technique

The increase of low back problems has stimulated the development of different analysis and evaluation techniques. Among these methods, the direct linear transformation (DLT) technique is commonly used to reconstruct the spine in three dimensions by means of its known image coordinates on radiographs. Despite its efficiency and precision, general reconstruction of some standard anatomical landmarks does not give all the necessary data for a detailed analysis of the intrinsic geometrical characteristics of lumbar vertebrae. Thus, in order to obtain such geometrical information a three-dimensional (3-D) reconstruction vertebral endplate contour technique has been developed. This technique involves: (1) iterative optimization and reconstruction processes of the vertebral endplate centroid; and (2) 3-D reconstruction of vertebral endplate contour. Validation based on mathematical simulations demonstrated that two or three iterations are necessary to correct (within 2 mm) the endplate centroid position for simulated error higher than 10 mm. Other validations based on 3-D reconstructions of a chamfered tube and a dry vertebra contours of known dimensions have given mean errors of 2 mm. Application on a healthy subject demonstrated the potential of this 3-D reconstruction technique. Finally, 3-D data obtained on vertebral endplates would allow the development of new clinical measurements that could be used to evaluate the lumbar spine geometrical behavior and orthoses biomechanical effects     

Enhanced spatial network method for the analysis of open microstripdiscontinuities

In this paper, a new technique is presented for the numerical analysis of open boundary three-dimensional (3-D) vias embedded in multilayered strata. This approach is based on an enhanced spatial network method (SNM) algorithm, and leads to speed-up factors of 10-12 over the standard SNM implementation. Absorbing boundary conditions, based on the perfect matching layer (PML) concept, are implemented for open boundary truncation. Unlike the standard PML's, the proposed absorbing boundary conditions (ABC's) do not require introduction of additional variables     

Invertible temporal subband/wavelet filter banks with half-pixel-accurate motion compensation

Three-dimensional (3-D) subband/wavelet coding with motion compensation has been demonstrated to be an efficient technique for video coding applications in some recent research works. When motion compensation is performed with half-pixel accuracy, images need to be interpolated in both temporal subband analysis and synthesis stages. The resulting subband filter banks developed in these former algorithms were not invertible due to image interpolation. In this paper, an invertible temporal analysis/synthesis system with half-pixel-accurate motion compensation is presented. We look at temporal decomposition of image sequences as a kind of down-conversion of the sampling lattices. The earlier motion-compensated (MC) interlaced/progressive scan conversion scheme is extended for temporal subband analysis/synthesis. The proposed subband/wavelet filter banks allow perfect reconstruction of the decomposed video signal while retaining high energy compaction of subband transforms. The invertible filter banks are then utilized in our 3-D subband video coder. This video coding system does not contain the temporal DPCM loop employed in the conventional hybrid coder and the earlier MC 3-D subband coders. The experimental results show a significant PSNR improvement by the proposed method. The generalization of our algorithm for MC temporal filtering at arbitrary subpixel accuracy is also discussed.     

基于优先度排序的3维数据缺失快速插补法

为了快速准确地对3维光学测量的缺失数据进行插值,以利于后期对比研究,提出了基于优先度排序的3维数据缺失快速插补估算方法,并把该算法用于插补模拟实验数据以及20帧振动扬声器测试数据的验证。结果表明,与其它常用缺失数据插补方法相比,该方法运算速度快、插补效果好,有利于处理3维测量结果的多帧和大量的数据。     

Local hull-based surface construction of volumetric data from silhouettes

The marching cubes (MC) is a general method which can construct a surface of an object from its volumetric data generated using a shape from silhouette method. Although MC is efficient and straightforward to implement, a MC surface may have discontinuity even though the volumetric data is continuous. This is because surface construction is more sensitive to image noise than the construction of volumetric data. To address this problem, we propose a surface construction algorithm which aggregates local surfaces constructed by the 3-D convex hull algorithm. Thus, the proposed method initially classifies local convexities from imperfect MC vertices based on sliced volumetric data. Experimental results show that continuous surfaces are obtained from imperfect silhouette images of both convex and nonconvex objects.     

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.     

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     

Exact rebinning methods for three-dimensional PET

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.     

Morphology-based three-dimensional interpolation

In many medical applications, the number of available two-dimensional (2-D) images is always insufficient. Therefore, the three-dimensional (3-D) reconstruction must be accomplished by appropriate interpolation methods to fill gaps between available image slices. In this paper, we propose a morphology-based algorithm to interpolate the missing data. The proposed algorithm consists of several steps. First, the object or hole contours are extracted using conventional image-processing techniques. Second, the object or hole matching issue is evaluated. Prior to interpolation, the centroids of the objects are aligned. Next, we employ a dilation operator to transform digital images into distance maps and we correct the distance maps if required. Finally, we utilize an erosion operator to accomplish the interpolation. Furthermore, if multiple objects or holes are interpolated, we blend them together to complete the algorithm. We experimentally evaluate the proposed method against various synthesized cases reported in the literature. Experimental results show that the proposed method is able to handle general object interpolation effectively.     

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.     

兼容多标准的高效运动补偿新结构

为有效解决运动补偿的多标准兼容问题,该文提出了一种改进的适用于多标准运动补偿的新插值算法结构,新插值算法基于文中提出的RL(Rounding Last)策略和DTS(Diagonal Two Step)策略,其采用一种统一的两步插值结构有效地兼容了各标准中亮度分量和色度分量的插值。基于新算法,设计实现了一种可重构的多标准运动补偿硬件电路,该电路采用了基于可变块大小的运动补偿结构。实现结果表明,与JM8.4中基于44固定块大小的运动补偿结构相比,所设计的电路使得带宽需求降低了27%~50%,平均单次访问外部存储器的突发长度提高了1.22~2.25倍;电路在125 MHz工作频率下可满足全高清1080 p (19201080) 30帧/s的实时解码需求。     

A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry

In cone-beam computerized tomography (CT), projections acquired with the focal spot constrained on a planar orbit cannot provide a complete set of data to reconstruct the object function exactly. There are severe distortions in the reconstructed noncentral transverse planes when the cone angle is large. In this work, a new method is proposed which can obtain a complete set of data by acquiring cone-beam projections along a circle-plus-arc orbit. A reconstruction algorithm using this circle-plus-arc orbit is developed, based on the Radon transform and Grangeat's formula. This algorithm first transforms the cone-beam projection data of an object to the first derivative of the three-dimensional (3-D) Radon transform, using Grangeat's formula, and then reconstructs the object using the inverse Radon transform. In order to reduce interpolation errors, new rebinning equations have been derived accurately, which allows one-dimensional (1-D) interpolation to be used in the rebinning process instead of 3-D interpolation. A noise-free Defrise phantom and a Poisson noise-added Shepp-Logan phantom were simulated and reconstructed for algorithm validation. The results from the computer simulation indicate that the new cone-beam data-acquisition scheme can provide a complete set of projection data and the image reconstruction algorithm can achieve exact reconstruction. Potentially, the algorithm can be applied in practice for both a standard CT gantry-based volume tomographic imaging system and a C-arm-based cone-beam tomographic imaging system, with little mechanical modification required.     

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18° axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard “exact” 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time     

Three-dimensional (3-D) reconstruction of the spine from a single X-ray image and prior vertebra models

The lateral bending test is routinely used by clinicians for the preoperative assessment of spinal mobility. The evaluation of bending motion is usually based on the qualitative analysis of a two-dimensional (2-D) antero-posterior X-ray image. The aim of this paper is to introduce a novel three-dimensional (3-D) reconstruction technique that is a prerequisite for the quantitative 3-D analysis of lateral bending motion. An algorithm was developed for the 3-D reconstruction of the spine from a single X-ray image. The X-ray is calibrated using a small calibration object and an explicit calibration algorithm. The information contained in the single X-ray is completed by registering a priori 3-D geometric models of individual vertebrae. Part of the error yielded by the 3-D/2-D registration is corrected by a vertebral alignment constraint that aims to minimize intervertebral dislocations. Three-dimensional models of 15 different scoliosis patients, obtained from a standard stereo-radiographic 3-D reconstruction, were used in simulation and validation experiments. Experimental results show that the new method is robust and accurate. With pessimistic levels of simulated noise, the average root mean square reconstruction error is 2.89 mm, which is appropriate for common clinical applications.     

Elastic registration of fMRI data using Bézier-spline transformations

A three-dimensional (3-D) elastic registration algorithm has been developed to find a veridical transformation that maps activation patterns from functional magnetic resonance imaging (fMRI) experiments onto a 3-D high-resolution anatomical dataset. The proposed algorithm uses trilinear Bézier-splines and a 3-D voxel-based optimization technique to determine the transformation that maps the functional data onto the coordinate system of the anatomical dataset. Simple conditions are presented which guarantee that the data are mapped one-to-one on each other. Two voxel-based similarity measures, the linear correlation coefficient and the entropy correlation coefficient, are used. Their performance with respect to the registration of fMRI data is compared. Tests on simulated and real data have been performed to evaluate the accuracy of the method. Our results demonstrate that subvoxel accuracy can be achieved even for noisy low-resolution multislice datasets with local distortions up to 10 mm. Although the method is optimized for the registration of functional and anatomical MR images, it can also be used for solving other elastic registration problems.     

A fast multipole method for layered media based on the application of perfectly matched layers - the 2-D case

An efficient fast multipole method (FMM) formalism to model scattering from two-dimensional (2-D) microstrip structures is presented. The technique relies on a mixed potential integral equation (MPIE) formulation and a series expression for the Green functions, based on the use of perfectly matched layers (PML). In this way, a new FMM algorithm is developed to evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. Novel iteration schemes have been implemented and a computational complexity of order O(N) is achieved. The theory is validated by means of several illustrative, numerical examples. This paper aims at elucidating the PML-FMM-MPIE concept and can be seen as a first step toward a PML based multilevel fast multipole algorithm (MLFMA) for 3-D microstrip structures embedded in layered media.