3-D image reconstruction from averaged Fourier transform magnitudeby parameter estimation

An object model and estimation procedure for three-dimensional (3-D) reconstruction of objects from measurements of the spherically averaged Fourier transform magnitudes is described. The motivating application is the 3-D reconstruction of viruses based on solution X-ray scattering data. The object model includes symmetry, positivity and support constraints and has the form of a truncated orthonormal expansion and the parameters are estimated by maximum likelihood methods. Successful 3-D reconstructions based on synthetic and experimental measurements from Cowpea mosaic virus are described.     

单幅高分辨率SAR图像建筑物三维模型重构

提出了一种利用高分辨率SAR图像进行建筑物提取和三维重构的方法.首先,分析了高分辨率SAR图像建筑物产生的电磁散射的类型,给出了不同类型散射区域的后向散射计算方法,并在此基础上给出了一种利用建筑物三维CAD模型进行SAR建筑物特征区域图像仿真的方法;其次,给出了利用建筑物的二次散射结构确定建筑物底部轮廓位置和方向的方法,并提出了一种基于分布密度函数差异的仿真图像迭代匹配方法,进行建筑物高度的反演.仿真SAR图像后向散射系数用来划分建筑物不同的散射区域,通过计算特征区域之间的分布密度函数差异,以取得最大匹配度值的仿真图像对应的检验高度作为建筑物的反演高度;最后,选用了两幅不同屋顶类型的实际机载高分辨率SAR图像进行建筑物提取和三维重构实验,试验结果较为理想,验证了所提方法的可行性和有效性.     

Pattern tracking and 3-D motion reconstruction of a rigid body from a 2-D image sequence

This paper presents an integrated method to identify an object pattern from an image, and track its movement over a sequence of images. The sequence of images comes from a single perspective video source, which is capturing data from a precalibrated scene. This information is used to reconstruct the scene in three-dimension (3-D) within a virtual environment where a user can interact and manipulate the system. The steps that are performed include the following: i) Identify an object pattern from a two-dimensional perspective video source. The user outlines the region of interest (ROI) in the initial frame; the procedure builds a refined mask of the dominant object within the ROI using the morphological watershed algorithm. ii) The object pattern is tracked between frames using object matching within the mask provided by the previous and next frame, computing the motion parameters. iii) The identified object pattern is matched with a library of shapes to identify a corresponding 3-D object. iv) A virtual environment is created to reconstruct the scene in 3-D using the 3-D object and the motion parameters. This method can be applied to real-life application problems, such as traffic management and material flow congestion analysis.     

3-D Kalman filter for image motion estimation

This paper presents a new three-dimensional (3-D) Markov model for motion vector fields. The three dimensions consist of the two space dimensions plus a scale dimension. We use a compound signal model to handle motion discontinuity in this 3-D Markov random field (MRF). For motion estimation, we use an extended Kalman filter as a pel-recursive estimator. Since a single observation can be sensitive to local image characteristics, especially when the model is not accurate, we employ windowed multiple observations at each pixel to increase accuracy. These multiple observations employ different weighting values for each observation, since the uncertainty in each observation is different. Finally, we compare this 3-D model with earlier proposed one-dimensional (1-D) (coarse-to-fine scale) and two-dimensional (2D) spatial compound models, in terms of motion estimation performance on a synthetic and a real image sequence.     

Tomographic reconstruction of 3-D vector fields using inner productprobes

Inner product probe measurements are defined for tomographic reconstruction of 3-D vector fields. It is shown that one set of measurements is required to reconstruct an irrotational field, two are required to reconstruct a solenoidal field and special probes are required to reconstruct the components of an arbitrary field.     

Three-dimensional parameter estimation from stereo image sequences for model-based image coding

It is shown that the analysis of moving image sequences for 3D modelling can be performed in a relatively straightforward manner if the scene is captured in stereo. Output from a stereo disparity estimation process using calibrated cameras gives absolute 3D surface coordinates from a single stereo pair. When combined with monocular motion cues, the true 3D motion parameters of moving objects can be accurately calculated. Further analysis enables segmentation of body elements according to motion while the 3D surface feature structure, although available from the start, can be integrated and checked for anomalies over the sequence. These results are expected to alleviate the known problems of ambiguity suffered by monocular-source model-based coders.     

2-D rake receiver based on space-time channel parameter estimation

2-D RAKE receiver is an efficient way to realize the space-time processing for CDMA systems with aperiodic spreading codes. The Direction Of Arrival (DOA) and the relative time delay of every user's multipath must be known to realize the 2-D RAKE receiver. In the third generation CDMA mobile communication system, auxiliary pilot channel is used in the uplink channels. The different user's Vector Channel Impulse Response (VCIR) can be estimated from the pilot channel easily. The VCIR contains spatial and temporal information. In this paper, by utilizing the known pulse shape function, a parameter matrix method used to estimate the Spatial Signature Vector (SSV) and the relative time delay is proposed in frequency domain. The DOA can be estimated from the SSV. By reconstructing the SSV and utilizing approximate Capon space filter, the performance of the 2-D RAKE receiver with uniform circular array can be improved with a little additional computation work.     

Optimum asymmetric half-plane autoregressive lattice parameter modeling of 2-D fields

In this paper, we present a new optimum asymmetric half-plane (ASHP) autoregressive lattice parameter modeling of two-dimensional (2-D) random fields. This structure introduces 4N points into the prediction support region when the order of the model increases from (N-1) to N. Starting with a given data field, a set of four auxiliary prediction errors are generated in order to obtain the growing number of 2-D ASHP reflection coefficients at successive stages. The theory has been applied to the high-resolution radar imaging problem and has also been proven using the concepts of vector space, orthogonal projection, and subspace decomposition. It is shown that the proposed ASHP structure generates the orthogonal realization subspaces for different recurse directions. In addition to developing the basic theory, the presentation includes a comparison between the proposed theory and other alternative structures, both in terms of conceptual background and complexity. While the recently developed reduced-complexity ASHP lattice modeling structure requires O(4N/sup 3/) lattice sections with N equal to the order of the error filter, the proposed configuration requires only O(2N/sup 2/) lattice sections.     

基于均匀圆阵的近场源三维参数估计

基于均匀圆阵,提出一种近场源距离-方位角-俯仰角联合估计算法。利用阵元观测数据,构造一组高阶累积量矩阵,通过矩阵联合对角化技术得到阵列流形矩阵的估计。根据阵列流形矩阵的估计以及近场和远场条件下方位角相同的结论,获得方位角的估计。利用阵列流形矩阵和方位角的估计,得到距离和俯仰角的估计。该方法无需二维频域峰值搜索或参数配对。计算机仿真验证了算法的有效性。     

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.     

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.     

Three-dimensional guide-wire reconstruction from biplane image sequences for integrated display in 3-D vasculature

Using three-dimensional rotational X-ray angiography (3DRA), three-dimensional (3-D) information of the vasculature can be obtained prior to endovascular interventions. However, during interventions, the radiologist has to rely on fluoroscopy images to manipulate the guide wire. In order to take full advantage of the 3-D information from 3DRA data during endovascular interventions, a method is presented that yields an integrated display of the position of the guide wire and vasculature in 3-D. The method relies on an automated method that tracks the guide wire simultaneously in biplane fluoroscopy images. Based on the calibrated geometry of the C-arm, the 3-D guide-wire position is determined and visualized in the 3-D coordinate system of the vasculature. The method is evaluated in an intracranial anthropomorphic vascular phantom. The influence of the angle between projections, distortion correction of the projection images, and accuracy of geometry knowledge on the accuracy of 3-D guide-wire reconstruction from biplane images is determined. If the calibrated geometry information is used and the images are corrected for distortion, a mean distance to the reference standard of 0.42 mm and a tip distance of 0.65 mm is found, which means that accurate guide-wire reconstruction from biplane images can be performed.     

Atlas-based indexing of brain sections via 2-D to 3-D image registration

A 2-D to 3-D nonlinear intensity-based registration method is proposed in which the alignment of histological brain sections with a volumetric brain atlas is performed. First, sparsely cut brain sections were linearly matched with an oblique slice automatically extracted from the atlas. Second, a planar-to-curved surface alignment was employed in order to match each section with its corresponding image overlaid on a curved-surface within the atlas. For the latter, a PDE-based registration technique was developed that is driven by a local normalized-mutual-information similarity measure. We demonstrate the method and evaluate its performance with simulated and real data experiments. An atlas-guided segmentation of mouse brains' hippocampal complex, retrieved from the Mouse Brain Library (MBL) database, is demonstrated with the proposed algorithm.     

3-D reconstruction of 2-D crystals in real space

A new algorithm for three-dimensional reconstruction of two-dimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that it works in real space, rather than in Fourier space, and it is iterative. This has the advantage of making it convenient to introduce additional constraints (such as the support of the function to be reconstructed, which may be known from alternative measurements) and has the potential of more accurately modeling the TEM image formation process. Phantom experiments indicate the superiority of the new approach even without the introduction of constraints in addition to the projection data.     

Parallelization of the EM algorithm for 3-D PET image reconstruction

The EM algorithm for PET image reconstruction has two major drawbacks that have impeded the routine use of the EM algorithm: the long computation time due to slow convergence and a large memory required for the image, projection, and probability matrix. An attempt is made to solve these two problems by parallelizing the EM algorithm on multiprocessor systems. An efficient data and task partitioning scheme, called partition-by-box, based on the message passing model is proposed. The partition-by-box scheme and its modified version have been implemented on a message passing system, Intel iPSC/2, and a shared memory system, BBN Butterfly GP1000. The implementation results show that, for the partition-by-box scheme, a message passing system of complete binary tree interconnection with fixed connectivity of three at each node can have similar performance to that with the hypercube topology, which has a connectivity of log(2) N for N PEs. It is shown that the EM algorithm can be efficiently parallelized using the (modified) partition-by-box scheme with the message passing model.     

Towards 3-D scene reconstruction from broadcast video

Three-dimensional (3-D) scene reconstruction from broadcast video is a challenging problem with many potential applications, such as 3-D TV, free-view TV, augmented reality or three-dimensionalization of two-dimensional (2-D) media archives. In this paper, a flexible and effective system capable of efficiently reconstructing 3-D scenes from broadcast video is proposed, with the assumption that there is relative motion between camera and scene/objects. The system requires no a priori information and input, other than the video sequence itself, and capable of estimating the internal and external camera parameters and performing a 3-D motion-based segmentation, as well as computing a dense depth field. The system also serves as a showcase to present some novel approaches for moving object segmentation, sparse and dense reconstruction problems. According to the simulations for both synthetic and real data, the system achieves a promising performance for typical TV content, indicating that it is a significant step towards the 3-D reconstruction of scenes from broadcast video.     

Iterative image reconstruction using inverse fourier rebinning for fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully three-dimensional (3-D) positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a two-dimensional (2-D) projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing line of responses (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.     

Iterative image reconstruction using inverse Fourier rebinning for fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.     

The effect of image distortion on 3-D reconstruction of coronary bypass grafts from angiographic views

Three-dimensional (3-D) reconstructions of coronary bypass grafts performed from X-ray angiographic images may become increasingly important for the investigation of damaging mechanical stresses imposed to these vessels by the cyclic movement of the heart. Contrary to what we had experienced with coronary arteries, appreciable reconstruction artifacts frequently occur with grafts. In order to verify the hypothesis that those are caused by distortions present in the angiographic images (acquired with image intensifiers), we have implemented a grid correction technique in our 3-D reconstruction method and studied its efficiency with phantom experiments. In this article, the nature of the encountered artifacts and the way in which the dewarping correction eliminates them are illustrated by a phantom experiment and by the reconstruction of a real coronary bypass vein graft.