Estimation of dynamically evolving ellipsoids with applications to medical imaging

The estimation of dynamically evolving ellipsoids from noisy lower-dimensional projections is examined. In particular, this work describes a model-based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left-ventricular ejection fraction from a gated set of planar myocardial perfusion images. The proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate. For this work, the left ventricle is modeled as a dynamically evolving three-dimensional (3-D) ellipsoid. The left-ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic, two-dimensional (2-D) ellipsoid, obtained as the projection of the former 3-D ellipsoid. This data is processed in two ways: first, as a 3-D dynamic ellipsoid reconstruction problem; second, each view is considered as a 2-D dynamic ellipse estimation problem and then the 3-D ejection fraction is obtained by combining the effective 2-D ejection fractions of each view. The approximating ellipsoids are reconstructed using a Rauch-Tung-Striebel smoothing filter, which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set; in contrast, traditional ejection fraction estimates are based only on true frames of data. Further, numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented, providing a rational basis for specifying system parameters. This investigation includes estimation of ejection fraction from both simulated and real data.     

Neighbor-constrained segmentation with level set based 3-D deformable models

A novel method for the segmentation of multiple objects from three-dimensional (3-D) medical images using interobject constraints is presented. Our method is motivated by the observation that neighboring structures have consistent locations and shapes that provide configurations and context that aid in segmentation. We define a maximum a posteriori (MAP) estimation framework using the constraining information provided by neighboring objects to segment several objects simultaneously. We introduce a representation for the joint density function of the neighbor objects, and define joint probability distributions over the variations of the neighboring shape and position relationships of a set of training images. In order to estimate the MAP shapes of the objects, we formulate the model in terms of level set functions, and compute the associated Euler-Lagrange equations. The contours evolve both according to the neighbor prior information and the image gray level information. This method is useful in situations where there is limited interobject information as opposed to robust global atlases. In addition, we compare our level set representation of the object shape to the point distribution model. Results and validation from experiments on synthetic data and medical imagery in two-dimensional and 3-D are demonstrated.     

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.     

3-D reconstruction of coronary arterial tree to optimize angiographic visualization

Due to vessel overlap and foreshortening, multiple projections are necessary to adequately evaluate the coronary tree with arteriography. Catheter-based interventions can only be optimally performed when these visualization problems are successfully solved. The traditional method provides multiple selected views in which overlap and foreshortening are subjectively minimized based on two dimensional (2-D) projections. A pair of images acquired from routine angiographic study at arbitrary orientation using a single-plane imaging system were chosen for three-dimensional (3-D) reconstruction. After the arterial segment of interest (e.g., a single coronary stenosis or bifurcation lesion) was selected, a set of gantry angulations minimizing segment foreshortening was calculated. Multiple computer-generated projection images with minimized segment foreshortening were then used to choose views with minimal overlapped vessels relative to the segment of interest. The optimized views could then be utilized to guide subsequent angiographic acquisition and interpretation. Over 800 cases of coronary arterial trees have been reconstructed, in which more than 40 cases were performed in room during cardiac catheterization. The accuracy of 3-D length measurement was confirmed to be within an average root-mean-square (rms) 3.5% error using eight different pairs of angiograms of an intracoronary guidewire of 105-mm length with eight radiopaque markers of 15-mm interdistance. The accuracy of similarity between the additional computer-generated projections versus the actual acquired views was demonstrated with the average rms errors of 3.09 mm and 3.13 mm in 20 LCA and 20 RCA cases, respectively. The projections of the reconstructed patient-specific 3-D coronary tree model can be utilized for planning optimal clinical views: minimal overlap and foreshortening. The assessment of lesion length and diameter narrowing can be optimized in both interventional cases and studies of disease progression and regression.     

Three-dimensional interferometric ISAR imaging for targetscattering diagnosis and modeling

Two-dimensional (2-D) inverse synthetic aperture radar (ISAR) imaging has been widely used in target scattering diagnosis, modeling and target identification. A major shortcoming is that a 2-D ISAR image cannot provide information on the relative altitude of each scattering center on the target. In this paper, we present an interferometric inverse synthetic aperture radar (IF-ISAR) image processing technique for three-dimensional (3-D) target altitude image formation. The 2-D ISAR images are obtained from the signature data acquired as a function of frequency and azimuthal angle. A 3-D IF-ISAR altitude image can then be derived from two 2-D images reconstructed from the measurements by antennas at different altitudes. 3-D altitude image formation examples from both indoor and outdoor test range data are demonstrated on complex radar targets.     

基于造影图像的冠状动脉三维定量分析的研究

由于X射线造影成像把血管三维空间结构投影到二维图像上,基于二维造影图像的传统诊治方法存在很大局限性.本文在冠状动脉树三维重建的基础上,研究了冠状动脉的三维定量分析方法,提出血管直径、分支夹角和血管段长度的三维测量方法.并利用冠状动脉树实物模型进行实验,对二维和三维定量分析结果进行了比较.实验结果表明,三维定量分析能够有效地提高临床医学参数的测量精度.因此,在冠心病的临床诊断和介入治疗中,该方法能够可靠地诊断血管狭窄及选择和放置支架.     

Nonrigid registration of 3-d multichannel microscopy images of cell nuclei.

We present an intensity-based nonrigid registration approach for the normalization of 3-D multichannel microscopy images of cell nuclei. A main problem with cell nuclei images is that the intensity structure of different nuclei differs very much; thus, an intensity-based registration scheme cannot be used directly. Instead, we first perform a segmentation of the images from the cell nucleus channel, smooth the resulting images by a Gaussian filter, and then apply an intensity-based registration algorithm. The obtained transformation is applied to the images from the nucleus channel as well as to the images from the other channels. To improve the convergence rate of the algorithm, we propose an adaptive step length optimization scheme and also employ a multiresolution scheme. Our approach has been successfully applied using 2-D cell-like synthetic images, 3-D phantom images as well as 3-D multichannel microscopy images representing different chromosome territories and gene regions. We also describe an extension of our approach, which is applied for the registration of 3D + t (4-D) image series of moving cell nuclei.     

Lognormal Random-Field Models and Their Applications to Radar Image Synthesis

Lognormal random fields with multiplicative spatial interaction are proposed for modeling radar image intensity. Two particular classes of two-dimensional (2-D) lognormal random fields are introduced: multiplicative autoregressive (MAR), and multiplicative Mnrkov random fields (MMRF). The MAR and MMRF models are formulated as invertible point-transformations of Gaussian autoregressive and Gaussian Markov random fields (GMRF) and therefore possess many desirable properties. Least squares and maximum likelihood estimates for random-field parameters are presented, a decision rule is developed for selecting model order and transformations to normality as well, and techniques for synthesizing 2-D lognormal random fields are provided. Several Seasat synthetic aperture radar (SAR) images were tested using the decision rule developed in this paper and using the Kolmogorov-Smirnov (K-S) goodness-of-fit test. With both tests they were found to possess a good fit to lognormal statistics. MAR and MMRF models were fit to Seasat SAR images, and then the models were used to generate synthetic images that closely resemble the original SAR images both visually and in their variograms. This demonstrates the generality and appropriateness of the MAR and MMRF models for radar imagery.     

Quantitative analysis of reconstructed 3-D coronary arterial tree and intracoronary devices

Traditional quantitative coronary angiography is performed on two-dimensional (2-D) projection views. These views are chosen by the angiographer to minimize vessel overlap and foreshortening. With 2-D projection views that are acquired in this nonstandardized fashion, however, there is no way to know or estimate how much error occurs in the QCA process. Furthermore, coronary arteries possess a curvilinear shape and undergo a cyclical deformation due to their attachment to the myocardium. Therefore, it is necessary to obtain three-dimensional (3-D) information to best describe and quantify the dynamic curvilinear nature of the human coronary artery. Using a patient-specific 3-D coronary reconstruction algorithm and routine angiographic images, a new technique is proposed to describe: 1) the curvilinear nature of 3-D coronary arteries and intracoronary devices; 2) the magnitude of the arterial deformation caused by intracoronary devices and due to heart motion; and 3) optimal view(s) with respect to the desired "pathway" for delivering intracoronary devices.     

A quantitative analysis of 3-D coronary modeling from two or more projection images

A method is introduced to examine the geometrical accuracy of the three-dimensional (3-D) representation of coronary arteries from multiple (two and more) calibrated two-dimensional (2-D) angiographic projections. When involving more then two projections, (multiprojection modeling) a novel procedure is presented that consists of fully automated centerline and width determination in all available projections based on the information provided by the semi-automated centerline detection in two initial calibrated projections. The accuracy of the 3-D coronary modeling approach is determined by a quantitative examination of the 3-D centerline point position and the 3-D cross sectional area of the reconstructed objects. The measurements are based on the analysis of calibrated phantom and calibrated coronary 2-D projection data. From this analysis a confidence region (alpha degrees approximately equal to [35 degrees - 145 degrees]) for the angular distance of two initial projection images is determined for which the modeling procedure is sufficiently accurate for the applied system. Within this angular border range the centerline position error is less then 0.8 mm, in terms of the Euclidean distance to a predefined ground truth. When involving more projections using our new procedure, experiments show that when the initial pair of projection images has an angular distance in the range alpha degrees approximately equal to [35 degrees - 145 degrees], the centerlines in all other projections (gamma = 0 degrees - 180 degrees) were indicated very precisely without any additional centering procedure. When involving additional projection images in the modeling procedure a more realistic shape of the structure can be provided. In case of the concave segment, however, the involvement of multiple projections does not necessarily provide a more realistic shape of the reconstructed structure.     

A computationally efficient approach to the estimation of two- and three-dimensional hidden Markov models.

Statistical modeling methods are becoming indispensable in today's large-scale image analysis. In this paper, we explore a computationally efficient parameter estimation algorithm for two-dimensional (2-D) and three-dimensional (3-D) hidden Markov models (HMMs) and show applications to satellite image segmentation. The proposed parameter estimation algorithm is compared with the first proposed algorithm for 2-D HMMs based on variable state Viterbi. We also propose a 3-D HMM for volume image modeling and apply it to volume image segmentation using a large number of synthetic images with ground truth. Experiments have demonstrated the computational efficiency of the proposed parameter estimation technique for 2-D HMMs and a potential of 3-D HMM as a stochastic modeling tool for volume images.     

Segmentation of skin lesions in 2-D and 3-D ultrasound images using a spatially coherent generalized Rayleigh mixture model

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images.     

Reconstruction of three-dimensional coronary arterial dynamics from multi-view angiogram sequences

Since actual cardiac and arterial motion is non-rigidand non-uniformbothin space andinti me[1],the quan-tification of dynamic 3-Dcurves with 2-D projections isinaccurate and sensitive to view angles . Ruan[2]andPuentes[3]reconstructed 3-D arterial centerl…     

Three-dimensional path planning for virtual bronchoscopy

Multidetector computed-tomography (MDCT) scanners provide large high-resolution three-dimensional (3-D) images of the chest. MDCT scanning, when used in tandem with bronchoscopy, provides a state-of-the-art approach for lung-cancer assessment. We have been building and validating a lung-cancer assessment system, which enables virtual-bronchoscopic 3-D MDCT image analysis and follow-on image-guided bronchoscopy. A suitable path planning method is needed, however, for using this system. We describe a rapid, robust method for computing a set of 3-D airway-tree paths from MDCT images. The method first defines the skeleton of a given segmented 3-D chest image and then performs a multistage refinement of the skeleton to arrive at a final tree structure. The tree consists of a series of paths and branch structural data, suitable for quantitative airway analysis and smooth virtual navigation. A comparison of the method to a previously devised path-planning approach, using a set of human MDCT images, illustrates the efficacy of the method. Results are also presented for human lung-cancer assessment and the guidance of bronchoscopy.     

Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models

The aim of this paper is to present a hybrid approach to accurate quantification of vascular structures from magnetic resonance angiography (MRA) images using level set methods and deformable geometric models constructed with 3-D Delaunay triangulation. Multiple scale filtering based on the analysis of local intensity structure using the Hessian matrix is used to effectively enhance vessel structures with various diameters. The level set method is then applied to automatically segment vessels enhanced by the filtering with a speed function derived from enhanced MRA images. Since the goal of this paper is to obtain highly accurate vessel borders, suitable for use in fluid flow simulations, in a subsequent step, the vessel surface determined by the level set method is triangulated using 3-D Delaunay triangulation and the resulting surface is used as a parametric deformable model. Energy minimization is then performed within a variational setting with a first-order internal energy; the external energy is derived from 3-D image gradients. Using the proposed method, vessels are accurately segmented from MRA data.     

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.     

Motion estimation of skeletonized angiographic images using elastic registration

An approach for estimating the motion of arteries in digital angiographic image sequences is proposed. Binary skeleton images are registered using an elastic registration algorithm in order to estimate the motion of the corresponding arteries. This algorithm operates recursively on the skeleton images by considering an autoregressive (AR) model of the deformation in conjunction with a dynamic programming (DP) algorithm. The AR model is used at the pixel level and provides a suitable cost function to DP through the innovation process. In addition, a moving average (MA) model for the motion of the entire skeleton is used in combination with the local AR model for improved registration results. The performance of this motion estimation method is demonstrated on simulated and real digital angiographic image sequences. It is shown that motion estimation using elastic registration of skeletons is very successful especially with low contrast and noisy angiographic images.     

Vessel surface reconstruction with a tubular deformable model

Three-dimensional (3-D) angiographic methods are gaining acceptance for evaluation of atherosclerotic disease. However, measurement of vessel stenosis from 3-D angiographic methods can be problematic due to limited image resolution and contrast. We present a method for reconstructing vessel surfaces from 3-D angiographic methods that allows for objective measurement of vessel stenosis. The method is a deformable model that employs a tubular coordinate system. Vertex merging is incorporated into the coordinate system to maintain even vertex spacing and to avoid problems of self-intersection of the surface. The deformable model was evaluated on clinical magnetic resonance (MR) images of the carotid (n=6) and renal (n=2) arteries, on an MR image of a physical vascular phantom and on a digital vascular phantom. Only one gross error occurred for all clinical images. All reconstructed surfaces had a realistic, smooth appearance. For all segments of the physical vascular phantom, vessel radii from the surface reconstruction had an error of less than 0.2 of the average voxel dimension. Variability of manual initialization of the deformable model had negligible effect on the measurement of the degree of stenosis of the digital vascular phantom     

一种虚条纹相移算法在结构光三维测量中的应用

相移法测量三维轮廓具有原理简单、计算速度快等优点。然而此法至少需要采集3幅以上干涉图像,且在实际操作中由于很难产生绝对的相移量而给测量带来误差。应用虚条纹相移算法只需要采集一幅图像便可恢复出物体的三维轮廓,其基本手段是先获得原始图像的基频值f0,根据此频率通过计算机生成具有π/2相位差的两虚条纹图像cos(2πf0x)和sin(2πf0x)。然后分别与原始图像进行混叠,将混叠后得到的图像进行低通滤波,再结合相移算法恢复出原始物体的三维轮廓。此法既保持了相移法本身的优点又解决了其需要采集多幅图像以及无法实现绝对相移的问题。另外低通滤波本身的去噪特性给在非陡变物体测量中高频噪声的去除带来方便。     

Improving gamut mapping color constancy

The color constancy problem, that is, estimating the color of the scene illuminant from a set of image data recorded under an unknown light, is an important problem in computer vision and digital photography. The gamut mapping approach to color constancy is, to date, one of the most successful solutions to this problem. In this algorithm the set of mappings taking the image colors recorded under an unknown illuminant to the gamut of all colors observed under a standard illuminant is characterized. Then, at a second stage, a single mapping is selected from this feasible set. In the first version of this algorithm Forsyth (1990) mapped sensor values recorded under one illuminant to those recorded under a second, using a three-dimensional (3-D) diagonal matrix. However because the intensity of the scene illuminant cannot be recovered Finlayson (see IEEE Trans. Pattern Anal. Machine Intell. vol.18, no.10, p.1034-38, 1996) modified Forsyth's algorithm to work in a two-dimensional (2-D) chromaticity space and set out to recover only 2-D chromaticity mappings. While the chromaticity mapping overcomes the intensity problem it is not clear that something has not been lost in the process. The first result of this paper is to show that only intensity information is lost. Formally, we prove that the feasible set calculated by Forsyth's original algorithm, projected into 2-D, is the same as the feasible set calculated by the 2-D algorithm. Thus, there is no advantage in using the 3-D algorithm and we can use the simpler, 2-D version of the algorithm to characterize the set of feasible illuminants. Another problem with the chromaticity mapping is that it is perspective in nature and so chromaticities and chromaticity maps are perspectively distorted. Previous work demonstrated that the effects of perspective distortion were serious for the 2-D algorithm. Indeed, in order to select a sensible single mapping from the feasible set this set must first be mapped back up to 3-D. We extend this work to the case where a constraint on the possible color of the illuminant is factored into the gamut mapping algorithm. We show here that the illumination constraint can be enforced during selection without explicitly intersecting the two constraint sets. In the final part of this paper we reappraise the selection task. Gamut mapping returns the set of feasible illuminant maps. Our new algorithm is tested using real and synthetic images. The results of these tests show that the algorithm presented delivers excellent color constancy.