导波结构三维不连续性问题的高次六面体边缘元分析

该文从全磁场矢量泛函出发,讨论了一种54参量六面体边缘元的空间构造。这种高次三维边缘元方法不但有效地消除了伪解,而且具有很高的计算精度。用这种方法对导波结构三维不连续性散射问题的分析,证实了它的有效性和可靠性。与12参量六面体边缘元计算结果的比较表明:本文方法具有更高的精度和计算效率,是一种求解三维不连续性问题的高效数值方法,有着推广应用的实际价值。     

各向异性介质填充波导散射特性的三维54参量边缘元分析

本文将54参量边缘元和"边界行进"及Galerkin法相结合,分析了各向异性介质填充波导的散射特性.该方法有效地提高了计算精度和效率,明显地降低了对内存的需求,并消除了伪解.文中给出的计算实例,很好地证实了本文方法的这些优点.     

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

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

Vertex-based diffusion for 3-D mesh denoising.

We present a vertex-based diffusion for 3-D mesh denoising by solving a nonlinear discrete partial differential equation. The core idea behind our proposed technique is to use geometric insight in helping construct an efficient and fast 3-D mesh smoothing strategy to fully preserve the geometric structure of the data. Illustrating experimental results demonstrate a much improved performance of the proposed approach in comparison with existing methods currently used in 3-D mesh smoothing.     

Multi-spectral and hyperspectral image fusion using 3-D wavelet transform

Image fusion is performed between one band of multi-spectral image and two bands of hyperspectral image to produce fused image with the same spatial resolution as source multi-spectral image and the same spectral resolution as source hyperspeetral image. According to the characteristics and 3-Dimensional （3-D） feature analysis of multi-spectral and hyperspectral image data volume, the new fusion approach using 3-D wavelet based method is proposed. This approach is composed of four major procedures： Spatial and spectral resampling, 3-D wavelet transform, wavelet coefficient integration and 3-D inverse wavelet transform. Especially, a novel method, Ratio Image Based Spectral Resampling （RIBSR）method, is proposed to accomplish data resampling in spectral domain by utilizing the property of ratio image. And a new fusion rule, Average and Substitution （A＆S） rule, is employed as the fusion rule to accomplish wavelet coefficient integration. Experimental results illustrate that the fusion approach using 3-D wavelet transform can utilize both spatial and spectral characteristics of source images more adequately and produce fused image with higher quality and fewer artifacts than fusion approach using 2-D wavelet transform. It is also revealed that RIBSR method is capable of interpolating the missing data more effectively and correctly, and A＆S rule can integrate coefficients of source images in 3-D wavelet domain to preserve both spatial and spectral features of source images more properly.     

Computation of 3-D velocity fields from 3-D cine CT images of a human heart

A method of computing the three-dimensional (3-D) velocity field from 3-D cine computer tomographs (CTs) of a beating heart is proposed. Using continuum theory, the authors develop two constraints on the 3-D velocity field generated by a beating heart. With these constraints, the computation of the 3-D velocity field is formulated as an optimization problem and a solution to the optimization problem is developed using the Euler-Lagrange method. The solution is then discretized for computer implementation. The authors present the results for both simulated images and clinical cine CT images of a beating heart.     

3-D tracking and motion estimation using hierarchical Kalman filter

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

An efficient Fourier method for 3-D radon inversion in exactcone-beam CT reconstruction

The radial derivative of the three-dimensional (3-D) radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. The authors briefly review Grangeat's (1991) approach for calculating radon derivative data from cone-beam projections and then present a new, efficient method for 3-D radon inversion, i.e., reconstruction of the image from the radial derivative of the 3-D radon transform, called direct Fourier inversion (DFI). The method is based directly on the 3-D Fourier slice theorem. From the 3-D radon derivative data, which is assumed to be sampled on a spherical grid, the 3-D Fourier transform of the object is calculated by performing fast Fourier transforms (FFTs) along radial lines in the radon space. Then, an interpolation is performed from the spherical to a Cartesian grid using a 3-D gridding step in the frequency domain. Finally, this 3-D Fourier transform is transformed back to the spatial domain via 3-D inverse FFT. The algorithm is computationally efficient with complexity in the order of N ³ log N. The authors have done reconstructions of simulated 3-D radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography (CT)     

Reversible 3-D decorrelation of medical images

Two methods, namely, differential pulse code modulation (DPCM) and hierarchical interpolation (HINT), are considered. It is shown that HINT cannot be extended straightforwardly to 3-D images as contrasted with DPCM. A 3-D HINT is therefore proposed which is based on a combination of 2-D and 3-D filters. Both decorrelation methods were applied to three-dimensional computed tomography (CT), magnetic resonance (MR), and single-photon-emission CT (SPECT) images. It was found that a 3-D approach is optimal for some studies, while for other studies 2-D or even 1-D decorrelation performs better. The optimal dimensionality of DPCM is related to the magnitudes of the local correlation coefficients (CCs). However, the nonlocal nature of HINT makes the local correlation coefficients useless as indicators of the dimensionality; a better candidate is the image voxel size. For images with cubic or nearly cubic voxels 3-D HINT is generally optimal. For images in which the slice thickness is large compared to the pixel size a 2-D (intraslice) HINT is best. In general, the increase in efficiency obtained by extending 2-D decorrelation method to 3-D is small.     

Variable temporal-length 3-D discrete cosine transform coding

Three-dimensional discrete cosine transform (3-D DCT) coding has the advantage of reducing the interframe redundancy among a number of consecutive frames, while the motion compensation technique can only reduce the redundancy of at most two frames. However, the performance of the 3-D DCT coding will be degraded for complex scenes with a greater amount of motion. This paper presents a 3-D DCT coding with a variable temporal length that is determined by the scene change detector. Our idea is to let the motion activity in each block be very low, while the efficiency of the 3-D DCT coding could be increased. Experimental results show that this technique is indeed very efficient. The present approach has substantial improvement over the conventional fixed-length 3-D DCT coding and is also better than that of the Moving Picture Expert Group (MPEG) coding.     

3-D/2-D registration of CT and MR to X-ray images

A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration.     

Ray phase space approach for 3-D imaging and 3-D optical data representation

We propose a framework to model, analyze and design three-dimensional (3-D) imaging systems. A system engineering approach is adopted which relates 3-D images (real or synthesized) to 3-D objects (real or synthesized) using a novel representation of the optical data which we call "ray phase space". The framework provides a powerful tool for determining the performance of 3-D imaging systems, for generating computational reconstruction of 3-D images and for optimizing 3-D imaging systems.     

3-D model localization using high-resolution reconstruction ofmonocular image sequences

In this paper, we present a complete system for the recognition and localization of a three-dimensional (3-D) model from a sequence of monocular images with known motion. The originality of this system is twofold. First, it uses a purely 3-D approach, starting from the 3-D reconstruction of the scene and ending by the 3-D matching of the model. Second, unlike most monocular systems, we do not use token tracking to match successive images. Rather, subpixel contour matching is used to recover more precisely complete 3-D contours. In contrast with the token tracking approaches, which yield a representation of the 3-D scene based on disconnected segments or points, this approach provides us with a denser and higher level representation of the scene. The reconstructed contours are fused along successive images using a simple result derived from the Kalman filter theory. The fusion process increases the localization precision and the robustness of the 3-D reconstruction. Finally, corners are extracted from the 3-D contours. They are used to generate hypotheses of the model position, using a hypothesize-and-verify algorithm that is described in detail. This algorithm yields a robust recognition and precise localization of the model in the scene. Results are presented on infrared image sequences with different resolutions, demonstrating the precision of the localization as well as the robustness and the low computational complexity of the algorithms.     

Hierarchical 3-D Floorplanning Algorithm for Wirelength Optimization

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

Model-based quantitation of 3-D magnetic resonance angiographic images

Quantification of the degree of stenosis or vessel dimensions are important for diagnosis of vascular diseases and planning vascular interventions. Although diagnosis from three-dimensional (3-D) magnetic resonance angiograms (MRA's) is mainly performed on two-dimensional (2-D) maximum intensity projections, automated quantification of vascular segments directly from the 3-D dataset is desirable to provide accurate and objective measurements of the 3-D anatomy. A model-based method for quantitative 3-D MRA is proposed. Linear vessel segments are modeled with a central vessel axis curve coupled to a vessel wall surface. A novel image feature to guide the deformation of the central vessel axis is introduced. Subsequently, concepts of deformable models are combined with knowledge of the physics of the acquisition technique to accurately segment the vessel wall and compute the vessel diameter and other geometrical properties. The method is illustrated and validated on a carotid bifurcation phantom, with ground truth and medical experts as comparisons. Also, results on 3-D time-of-flight (TOF) MRA images of the carotids are shown. The approach is a promising technique to assess several geometrical vascular parameters directly on the source 3-D images, providing an objective mechanism for stenosis grading.     

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     

Minimally Redundant 2-D Array Designs for 3-D Medical Ultrasound Imaging

In real-time ultrasonic 3-D imaging, in addition to difficulties in fabricating and interconnecting 2-D transducer arrays with hundreds of elements, there are also challenges in acquiring and processing data from a large number of ultrasound channels. The coarray (spatial convolution of the transmit and receive arrays) can be used to find efficient array designs that capture all of the spatial frequency content (a transmit–receive element combination corresponds to a spatial frequency) with a reduced number of active channels and firing events. Eliminating the redundancies in the transmit–receive element combinations and firing events reduces the overall system complexity and improves the frame rate. Here we explore four reduced redundancy 2-D array configurations for miniature 3-D ultrasonic imaging systems. Our approach is based on 1) coarray design with reduced redundancy using different subsets of linear arrays constituting the 2-D transducer array, and 2) 3-D scanning using fan-beams (narrow in one dimension and broad in the other dimension) generated by the transmit linear arrays. We form the overall array response through coherent summation of the individual responses of each transmit–receive array pairs. We present theoretical and simulated point spread functions of the array configurations along with quantitative comparison in terms of the front-end complexity and image quality.      

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

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

Reconstruction of 3-D horizons from 3-D seismic datasets

We propose a method for extracting automatically and simultaneously the quasi-horizontal surfaces in three-dimensional (3-D) seismic data. The proposed algorithm identifies connected sets of points which form surfaces in 3-D space. To improve reliability, this algorithm takes into consideration the relative positions of all horizons, and uses globally self-consistent connectivity criteria which respect the temporal order of horizon creation. The first stage of the algorithm consists of the preliminary estimation of the local direction of each horizon at each point of the 3-D space. The second stage consists of smoothing the signal along the detected layer structure to reduce noise. The last stage consists of the simultaneous building of all 3-D horizons. The output of the processing is a set of 3-D horizons represented by a series of triangulated surfaces.     

Fast fully 3-D image reconstruction in PET using planograms

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.