Three-dimensional reconstruction of microcalcification clustersfrom two mammographic views

Classification of benign/malignant microcalcification clusters is a major diagnostic challenge for radiologists. Clinical studies have revealed that the shape of the cluster, and the spatial distribution of individual microcalcifications within it, are important indicators of its malignancy. However, mammographic images of clustered microcalcifications confound their three-dimensional (3-D) distribution with image projection and breast compression. This paper presents a novel model-based method for reconstructing microcalcification clusters in 3-D from two mammographic views (cranio-caudal and medio-lateral oblique--"shoulder to the opposite hip" or lateral-medio). We develop a 3-D breast representation and a parameterised breast compression model which constraints geometrically the possible 3-D positions of a calcification in a two-dimensional image. Corresponding calcifications in the two views are matched using an estimate of the calcification volume. Both the geometric constraint and the matching criterion are utilized in the final reconstruction step to build the 3-D reconstructed clusters. Validation experiments are described using 30 clusters to verify the individual steps of the model, and results consistent with known ground truth are obtained. Some of the approximations in the model and future work are discussed in the concluding section.     

3-D freehand echocardiography for automatic left ventricle reconstruction and analysis based on multiple acoustic windows

A new method is proposed to reconstruct and analyze the left ventricle (LV) from multiple acoustic window three-dimensional (3-D) ultrasound acquired using a transthoracic 3-D rotational probe. Prior research in this area has been based on one acoustic window acquisition. However, the data suffers from several limitations that degrade the reconstruction and reduce the clinical value of interpretation, such as the presence of shadow due to bone (ribs) and air (in the lungs) and motion of the probe during the acquisition. In this paper, we show how to overcome these limitations by automatically fusing information from multiple acoustic window sparse-view acquisitions and using a position sensor to track the probe in real time. Geometric constraints of the object shape, and spatiotemporal information relating to the image acquisition process, are used in new algorithms for 1) grouping endocardial edge cues from an initial image segmentation and 2) defining a novel reconstruction method that utilizes information from multiple acoustic windows. The new method has been validated on a phantom and three real heart data sets. In the phantom study, one finger of a latex glove was scanned from two acoustic windows and reconstructed using the new method. The volume error was measured to be less than 4%. In the clinical case study, 3-D ultrasound and magnetic resonance imaging (MRI) scanning were performed on the same healthy volunteers. Quantitative ejection fractions (EFs) and volume-time curves over a cardiac cycle were estimated using the new method and compared to cardiac MRI measurements. This showed that the new method agrees better with MRI measurements than the previous approach we have developed based on a single acoustic window. The EF errors of the new method with respect to MRI measurements were less than 6%. A more extensive clinical validation is required to establish whether these promising first results translate to a method suitable for routine clinical use.     

Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud

Medical images in nuclear medicine are commonly represented in three dimensions as a stack of two-dimensional images that are reconstructed from tomographic projections. Although natural and straightforward, this may not be an optimal visual representation for performing various diagnostic tasks. A method for three-dimensional (3-D) tomographic reconstruction is developed using a point cloud image representation. A point cloud is a set of points (nodes) in space, where each node of the point cloud is characterized by its position and intensity. The density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution. The reconstructed volume, which in general could be of any resolution, size, shape, and topology, is represented by a set of nonoverlapping tetrahedra defined by the nodes. The intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron. This approach creates a continuous piecewise linear intensity over the reconstruction domain. The reconstruction provides a distinct multiresolution representation, which is designed to accurately and efficiently represent the 3-D image. The method is applicable to the acquisition of any tomographic geometry, such as parallel-, fan-, and cone-beam; and the reconstruction procedure can also model the physics of the image detection process. An efficient method for evaluating the system projection matrix is presented. The system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud. Examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a Jaszczak cardiac torso phantom are presented. This work creates a framework for voxel-less multiresolution representation of images in nuclear medicine.     

Optimization of geometrical calibration in pinhole SPECT

Previously, we developed a method to determine the acquisition geometry of a pinhole camera. This information is needed for the correct reconstruction of pinhole single photon emission computed tomography images. The method uses a calibration phantom consisting of three point sources and their positions in the field of view (FOV) influence the accuracy of the geometry estimate. This paper proposes two particular configurations of point sources with specific positions and orientations in the FOV for optimal image reconstruction accuracy. For the proposed calibration setups, inaccuracies of the geometry estimate due to noise in the calibration data, only cause subresolution inaccuracies in reconstructed images. The calibration method also uses a model of the point source configuration, which is only known with limited accuracy. The study demonstrates, however, that, with the proposed calibration setups, the error in reconstructed images is comparable to the error in the phantom model.     

Tomographic reconstruction of dynamic cardiac image sequences.

In this paper, we propose an approach for the reconstruction of dynamic images from a gated cardiac data acquisition. The goal is to obtain an image sequence that can show simultaneously both cardiac motion and time-varying image activities. To account for the cardiac motion, the cardiac cycle is divided into a number of gate intervals, and a time-varying image function is reconstructed for each gate. In addition, to cope with the under-determined nature of the problem, the time evolution at each pixel is modeled by a B-spline function. The dynamic images for the different gates are then jointly determined using maximum a posteriori estimation, in which a motion-compensated smoothing prior is introduced to exploit the similarity among the different gates. The proposed algorithm is evaluated using a dynamic version of the 4-D gated mathematical cardiac torso phantom simulating a gated single photon emission computed tomography perfusion acquisition with Technitium-99m labeled Teboroxime. We thoroughly evaluated the performance of the proposed algorithm using several quantitative measures, including signal-to-noise ratio analysis, bias-variance plot, and time activity curves. Our results demonstrate that the proposed joint reconstruction approach can improve significantly the accuracy of the reconstruction.     

Quantitative evaluation of three calibration methods for 3-D freehand ultrasound

In this paper, three different calibration methods for three-dimensional (3-D) freehand ultrasound (US) are evaluated. Calibration is the process of estimating the rigid transformation from US image coordinates to the coordinate system of the tracking sensor mounted onto the probe. Calibration accuracy has an important impact on quantitative studies. Geometrical precision can also be crucial in many interventions and surgery. The proposed evaluation framework relies on a single point phantom and a 3-D US phantom which mimics the US characteristics of human liver. Four quality measures are used: 3-D point localization criterion, distance and volume measurements, and shape based criterion. Results show that during the acquisition procedure, volumetric measurements and shapes of the reconstructed object depend on probe motion used, particularly fan motions for which errors are larger. It is also shown that accurate calibration is essential to obtain reliable quantitative information.     

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.     

A 3-D reconstruction system for the human jaw using a sequence of optical images

This paper presents a model-based vision system for dentistry that will assist in diagnosis, treatment planning, and surgical simulation. Dentistry requires an accurate three-dimensional (3-D) representation of the teeth and jaws for diagnostic and treatment purposes. The proposed integrated computer vision system constructs a 3-D model of the patient's dental occlusion using an intraoral video camera. A modified shape from shading (SFS) technique, using perspective projection and camera calibration, extracts the 3-D information from a sequence of two-dimensional (2-D) images of the jaw. Data fusion of range data and 3-D registration techniques develop the complete jaw model. Triangulation is then performed, and a solid 3-D model is reconstructed. The system performance is investigated using ground truth data, and the results show acceptable reconstruction accuracy.     

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.     

Comparison of 3-D maximum a posteriori and filtered backprojection algorithms for high-resolution animal imaging with microPET

We have evaluated the performance of two three-dimensional (3-D) reconstruction algorithms with data acquired from microPET, a high resolution tomograph dedicated to small animal imaging. The first was a linear filtered-backprojection algorithm (FBP) with reprojection of the missing data, and the second was a statistical maximum a posteriori probability algorithm (MAP). The two algorithms were evaluated in terms of their resolution performance, both in phantoms and in vivo. Sixty independent realizations of a phantom simulating the brain of a baby monkey were acquired, each containing three million counts. Each of these realizations was reconstructed independently with both algorithms. The ensemble of the 60 reconstructed realizations was used to estimate the standard deviation as a measure of the noise for each reconstruction algorithm. More detail was recovered in the MAP reconstruction without an increase in noise relative to FBP. Studies in a simple cylindrical compartment phantom demonstrated improved recovery of known activity ratios with MAP. Finally, in vivo studies also demonstrated a clear improvement in spatial resolution using the MAP algorithm. The quantitative accuracy of the MAP reconstruction was also evaluated by comparison with autoradiography and direct well counting of tissue samples and was shown to be superior.     

基于共形对应的球面图像的计算全息图

研究了基于共形对应的球面图像的计算全息图(CGH)的生成和重现.通常,当用平面波照射全息图时,所重现的图像一般显示在平面上.共形对应在计算机图形学中被广泛应用,它可以将平面图像和任意曲面对应.相对于简单的坐标变换,共形对应关系具有很多优点,如它可以保持变换前后图像之间的几何形状不变性等.将共形对应引入计算机全息图的生成过程中,利用平面与球面的共形对应关系,生成显示于球面的二维图像的计算全息图,并由所生成全息图得到原始图像,从而实现整个全息记录和重现过程的计算机模拟.二维图像重现于球面实际上了产生三维显示,因此上述方法在从计算全息图重现三维图像方面起到重要的作用.     

Resolution and noise properties of MAP reconstruction for fully 3-D PET

We derive approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, we show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. We also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.     

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources.     

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.     

Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography

A 3-D reconstruction of the coronary arteries offers great advantages in the diagnosis and treatment of cardiovascular disease, compared to 2-D X-ray angiograms. Besides improved roadmapping, quantitative vessel analysis is possible. Due to the heart's motion, rotational coronary angiography typically provides only 5–10 projections for the reconstruction of each cardiac phase, which leads to a strongly undersampled reconstruction problem. Such an ill-posed problem can be approached with regularized iterative methods. The coronary arteries cover only a small fraction of the reconstruction volume. Therefore, the minimization of the ${mbi L}_1$ norm of the reconstructed image, favoring spatially sparse images, is a suitable regularization. Additional problems are overlaid background structures and projection truncation, which can be alleviated by background reduction using a morphological top-hat filter. This paper quantitatively evaluates image reconstruction based on these ideas on software phantom data, in terms of reconstructed absorption coefficients and vessel radii. Results for different algorithms and different input data sets are compared. First results for electrocardiogram-gated reconstruction from clinical catheter-based rotational X-ray coronary angiography are presented. Excellent 3-D image quality can be achieved.      

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.     

Characterization of pinhole SPECT acquisition geometry

A method is presented to estimate the acquisition geometry of a pinhole single photon emission computed tomography (SPECT) camera with a circular detector orbit. This information is needed for the reconstruction of tomographic images. The calibration uses the point source projection locations of a tomographic acquisition of three point sources located at known distances from each other. It is shown that this simple phantom provides the necessary and sufficient information for the proposed calibration method. The knowledge of two of the distances between the point sources proves to be essential. The geometry is estimated by fitting analytically calculated projections to the measured ones, using a simple least squares Powell algorithm. Some mild a priori knowledge is used to constrain the solutions of the fit. Several of the geometrical parameters are however highly correlated. The effect of these correlations on the reconstructed images is evaluated in simulation studies and related to the estimation accuracy. The highly correlated detector tilt and electrical shift are shown to be the critical parameters for accurate image reconstruction. The performance of the algorithm is finally demonstrated by phantom measurements. The method is based on a single SPECT scan of a simple calibration phantom, executed immediately after the actual SPECT acquisition. The method is also applicable to cone-beam SPECT and X-ray CT.     

Scatter correction in 3-D PET

Modern multiring positron emission tomographs allow the acquisition of 3-D data sets to increase their sensitivity. A substantial part of this data is due to scattered radiation. The authors describe the experimental dependence of point source scatter distributions on energy window setting, source location, and scatter volume in geometries relevant for brain studies. The point source scatter distribution was parametrized accurately by a broad, 2-D Gaussian, which included a shift parameter to account for asymmetry of the scatter medium relative to the source. This parametrization was used to formulate two fast scatter correction algorithms suitable for brain scans. In both algorithms, a 2-D subset of the measured projections was transformed into a scatter projection. An image of the 3-D scatter distribution was reconstructed using 2-D algorithms. It was then subtracted from the total (true+scattered) 3-D image. Both algorithms were implemented in different combinations with the additional attenuation correction and were tested on point source and phantom measurements. It was shown that, for the situation typical for brain scans, reconstructed scatter fractions could be reduced to 5% or less.     

Noise characteristics of 3-D and 2-D PET images

The authors analyzed the noise characteristics of two-dimensional (2-D) and three-dimensional (3-D) images obtained from the GE Advance positron emission tomography (PET) scanner. Three phantoms were used: a uniform 20-cm phantom, a 3-D Hoffman brain phantom, and a chest phantom with heart and lung inserts. Using gated acquisition, the authors acquired 20 statistically equivalent scans of each phantom in 2-D and 3-D modes at several activity levels. From these data, they calculated pixel normalized standard deviations (NSD's), scaled to phantom mean, across the replicate scans, which allowed them to characterize the radial and axial distributions of pixel noise. The authors also performed sequential measurements of the phantoms in 2-D and 3-D modes to measure noise (from interpixel standard deviations) as a function of activity. To compensate for the difference in axial slice width between 2-D and 3-D images (due to the septa and reconstruction effects), they developed a smoothing kernel to apply to the 2-D data. After matching the resolution, the ratio of image-derived NSD values (NSD_2D/NSD_3D)² averaged throughout the uniform phantom was in good agreement with the noise equivalent count (NEC) ratio (NEC_3D/NEC_2D). By comparing different phantoms, the authors showed that the attenuation and emission distributions influence the spatial noise distribution. The estimates of pixel noise for 2-D and 3-D images produced here can be applied in the weighting of PET kinetic data and may be useful in the design of optimal dose and scanning requirements for PET studies. The accuracy of these phantom-based noise formulas should be validated for any given imaging situation, particularly in 3-D, if there is significant activity outside the scanner field of view     

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.