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This paper proposes a three-dimensional (3-D) medical image compression method for computed tomography (CT) and magnetic resonance (MR) that uses a separable nonuniform 3-D wavelet transform. The separable wavelet transform employs one filter bank within two-dimensional (2-D) slices and then a second filter bank on the slice direction. CT and MR image sets normally have different resolutions within a slice and between slices. The pixel distances within a slice are normally less than 1 mm and the distance between slices can vary from 1 mm to 10 mm. To find the best filter bank in the slice direction, the authors use the various filter banks in the slice direction and compare the compression results. The results from the 12 selected MR and CT image sets at various slice thickness show that the Haar transform in the slice direction gives the optimum performance for most image sets, except for a CT image set which has 1 mm slice distance. Compared with 2-D wavelet compression, compression ratios of the 3-D method are about 70% higher for CT and 35% higher for MR image sets at a peak signal to noise ratio (PSNR) of 50 dB, In general, the smaller the slice distance, the better the 3-D compression performance.

Analysis of brain images often requires accurate localization of cortical convolutions. Although magnetic resonance (MR) brain images offer sufficient resolution for identifying convolutions in theory, the nature of tomographic imaging prevents clear definition of convolutions in individual slices. Existing methods for solving this problem rely on heuristic adaptation of brain atlases created from a small number of individuals. These methods do not usually provide high accuracy because of large biological variations among individuals. The authors propose to localize convolutions by linking realistic visualizations of the cortical surface with the original image volume. They have developed a system so that a user can quickly localize key convolutions in several visualizations of an entire brain surface. Because of the links between the visualizations and the original volume, these convolutions are simultaneously localized in the original image slices. In the process of the authors' development, they have implemented a fast and easy method for visualizing cortical surfaces in MR images, thereby making their scheme usable in practical applications.

The authors model tissue as a collection of point scatterers embedded in a uniform media, and show that the higher-order statistics (HOS) of the scatterer spacing distribution can be estimated from digitized radio frequency (RF) scan line segments and be used in obtaining tissue signatures. The authors assume that RF echoes are non-Gaussian, on the grounds of empirical/theoretical justifications presented in the literature. Based on their model for tissue microstructure, the authors develop schemes for the estimation of reasonable periodicity as well as correlations among nonperiodic scatterers, Using HOS of the scattered signal, the authors define as tissue "color" a quantity that describes the scatterer spatial correlations, show how to evaluate it from the higher-order correlations of the digitized RF scan line segments, and investigate its potential as a tissue signature. The tools employed, i.e., HOS, were chosen as the most appropriate ones because they suppress Gaussian processes, such as the one arising from the diffused scatterers. HOS, unlike second-order statistics, also preserve the Fourier-phase of the signature, the color of the tissue response. Working on simulated and clinical data, the authors show that the proposed periodicity estimation technique is superior to the widely used power spectrum and cepstrum techniques in terms of the accuracy of estimations. The authors also show that even when there is no significant periodicity in data, they are still able to characterize tissues using signatures based on the higher-order cumulant structure of the scatterer spacing distribution.

In many applications in computer vision and signal processing, it is necessary to assimilate data from multiple sources. This is a particularly important issue in medical imaging, where information on a patient may be available from a number of different modalities. As a result, there has been much recent research interest in this area. The authors suggest an additional Bayesian method which generates a segmented classification concurrently with improving reconstructions of a set of registered images. A synthetic example is used to demonstrate the subjectives and benefits of this proposed approach. Two medical applications, one fusing computed tomography (CT) and single photon emission computed tomography (SPECT) brain scans, and the other magnetic resonance (MR) images at two different resolutions, are considered.

The number of nerve fibers (axons) in a nerve, the axon size, and shape can all be important neuroanatomical features in understanding different aspects of nerves in the brain. However, the number of axons in a nerve is typically in the order of tens of thousands and a study of a particular aspect of the nerve often involves many nerves. Potentially meaningful studies are often prohibited by the huge number involved when manual measurements have to be employed. A method that automates the analysis of axons from electron-micrographic images is presented. It begins with a rough identification of all the axon centers by use of an elliptical Hough transform procedure. Boundaries of each axons are then extracted based on active contour model, or snakes, approach where physical properties of the axons and the given image data are used in an optimization scheme to guide the snakes to converge to axon boundaries for accurate sheath measurement. However, false axon detection is still common due to poor image quality and the presence of other irrelevant cell features, thus a conflict resolution scheme is developed to eliminate false axons to further improve the performance of detection. The developed method has been tested on a number of nerve images and its results are presented.

An optimal image sampling schedule for tracer dynamic studies with positron emission tomography (PET) is proposed. This schedule incorporates the characteristics of PET measurement and uses a new cost function and the D-optimal criterion. A detailed case study of the estimation of the local cerebral metabolic rate of glucose (LCMRGLc) using the tracer fluorodeoxyglucose (FDG) and the four-parameter FDG model is presented. As the sampling schedule designed requires only four dynamic images, the storage space and data processing time are greatly reduced, while the precision of the parameter estimates is almost the same as that achieved with a commonly used schedule. The effects of intersubject and intrasubject parameter variations on parameter estimation with the use of this optimal sampling schedule are investigated by computer simulation. The simulation results show that the estimation of parameters is sufficiently robust with respect to these intersubject and intrasubject variations. The optimal sampling schedule is quite suitable therefore for PET regional parameter estimation, as well as for image-wide parameter estimation, for different subjects.

An unbiased algorithm of generalized linear least squares (GLLS) for parameter estimation of nonuniformly sampled biomedical systems is proposed. The basic theory and detailed derivation of the algorithm are given. This algorithm removes the initial values required and computational burden of nonlinear least regression and achieves a comparable estimation quality in terms of the estimates' bias and standard deviation. Therefore, this algorithm is particular useful in image-wide (pixel-by-pixel based) parameter estimation, e.g., to generate parametric images from tracer dynamic studies with positron emission tomography. An example is presented to demonstrate the performance of this new technique. This algorithm is also generally applicable to other continuous system parameter estimation.

To segment brain tissues in magnetic resonance images of the brain, the authors have implemented a stochastic relaxation method which utilizes partial volume analysis for every brain voxel, and operates on fully three-dimensional (3-D) data. However, there are still problems with automatically or semi-automatically segmenting thick magnetic resonance (MR) slices, particularly when trying to segment the small lesions present in MR images of multiple sclerosis patients. To improve lesion segmentation the authors have extended their method of stochastic relaxation by both pre- and post-processing the MR images. The preprocessing step involves image enhancement using homomorphic filtering to correct for nonhomogeneities in the coil and magnet. Because approximately 95% of all multiple sclerosis lesions occur in the white matter of the brain, the post-processing step involves application of morphological processing and thresholding techniques to the intermediate segmentation in order to develop a mask image containing only white matter and Multiple Sclerosis (MS) lesion. This white/lesion masked image is then segmented by again applying the authors' stochastic relaxation technique. The process has been applied to multispectral MRI scans of multiple sclerosis patients and the results compare favorably to manual segmentations of the same scans obtained independently by radiology health professionals.

The authors present a new method for analyzing the motion of the heart's left ventricle (LV) from tagged magnetic resonance imaging (MRI) data. Their technique is based on the development of a new class of physics-based deformable models whose parameters are functions. They allow the definition of new parameterized primitives and parameterized deformations which can capture the local shape variation of a complex object. Furthermore, these parameters are intuitive and require no complex post-processing in order to be used by a physician. Using a physics-based approach, the authors convert the geometric models into dynamic models that deform due to forces exerted from the datapoints and conform to the given dataset. The authors present experiments involving the extraction of the shape and motion of the LV's mid-wall during systole from tagged MRI data based on a few parameter functions. Furthermore, by plotting the variations over time of the extracted LV model parameters from normal and abnormal heart data along the long axis, the authors are able to quantitatively characterize their differences.

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registering magnetic resonance images to atlas images.

In obtaining human head range data with a laser scanner, noise results from system errors and rough surfaces. The noise can be reduced with a suitable filter. Two aspects need to be considered in smoothing head scan data: one is finding a filter to eliminate noise without creating new artifacts; the other is determining the parameters of this filter to achieve optimal smoothing. The Gaussian filter has been shown to have unique characteristics which preserve the integrity of the data. A cross-validation method based on regularization theory has been derived for estimating the correct filter size for smoothing head range data. The authors discuss the justification and implementation of the statements above. Generalized cross-validation is derived in the two-dimensional case. Experimental results are presented that show the technique is effective and robust.

This article compares four widely utilized, yet fundamentally different, approaches for registering medical scans of the head. Comparisons are made on the basis of method, accuracy, robustness, computer requirements, and usability. This examination is intended to provide a means for determining an appropriate method for any given application. These approaches are: 1) an iterative method based on the repeated manual selection of 1-2 corresponding points, 2) an approach using the manual selection of 9-15 corresponding points, 3) an automatic surface matching method, and 4) an automatic approach based on voxel similarity. The methods are tested both on simulated data to provide a gold standard of accuracy, and on real data. All registrations are performed in the same visualization environment created for multipurpose image processing. Simulated data tests provided mean transformation errors and time requirements for the different methods, as well as the displacement errors for a set of anatomical landmarks. These results show all of the methods provide good accuracy when the data is not highly distorted and has a large amount of overlap. From the tests using real data both transformations and time requirements are tabulated for comparison. All of the techniques successfully aligned the real data with the exception of surface matching, which failed on the PET-MRI. Each method exhibits strengths and weaknesses that should be understood in order to utilize the most appropriate technique for a given problem. Based on the authors' examination, the voxel-similarity approach proved in general to be the method of choice.

This paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain, which is a key problem in several applications, including morphological analysis of the brain, and spatial normalization and registration of brain images. A parameterization of the outer cortex is first obtained using a deformable surface algorithm which, motivated by the structure of the cortex, is constructed to find the central layer of thick surfaces. Based on this parameterization, a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales. Various experiments on magnetic resonance data are presented.

A motion immune dual-energy subtraction technique in which X-ray tube voltage and beam filtration were switched at 30 Hz between 60 kVp (2.0 mm Al filter) and 120 kVp (2.00 mm Al+2.5 mm Cu filter) was previously reported. In this study the effects of camera lag on the dual-energy iodine signal is investigated. The temporal lag of the lead oxide vidicon tested reduced the dual-energy iodine signal by a factor of 2.3, as compared to a mode that included 4 scrub frames between low- and high-energy images, for an iodine phantom with thicknesses of 0-86.0 mg/cm(2), imaged over a 15 cm thick Lucite phantom. On the other hand, the Charge-Coupled Device (CCD) camera has inherently no temporal lag and its versatile scanning characteristics make it near ideal for dual-energy DSA. The CCD camera eliminates the reduction of dual-energy iodine signal, since it does not mix low- and high-energy image data. Another benefit of the CCD camera is that the separation time between low and high-energy images is not limited to the frame period, as is the lead oxide vidicon; and as small as a 5-msec time difference is possible. The short time interval between low and high-energy images minimizes motion misregistration artifacts. Due to these advantages, the CCD camera significantly improves the utility of dual-energy DSA.

In order to quantitate anatomical and physiological parameters such as vessel dimensions and volumetric blood flow, it is necessary to make corrections for scatter and veiling glare, which are the major sources of nonlinearities in videodensitometric digital subtraction angiography (DSA). A convolution filtering technique has been investigated to estimate scatter-glare distribution in DSA images without the need to sample the scatter-glare intensity for each patient. This technique utilizes exposure parameters and image gray levels to assign equivalent Lucite thickness for every pixel in the image. The thickness information is then used to estimate scatter-glare intensity on a pixel-by-pixel basis. To test its ability to estimate scatter-glare intensity, the correction technique was applied to images of a Lucite step phantom, anthropomorphic chest phantom, head phantom, and animal models at different thicknesses, projections, and beam energies. The root-mean-square (rms) percentage error of these estimates was obtained by comparison with direct scatter-glare measurements made behind a lead strip. The average rms percentage errors in the scatter-glare estimate for the 25 phantom studies and the 17 animal studies were 6.44% and 7.96%, respectively. These results indicate that the scatter-glare intensity can be estimated with adequate accuracy for a wide range of thicknesses, projections, and beam energies using exposure parameters and gray level information.

A new method to correct the barrel distortion of an electronic endoscope image is presented. A correction model assuming circularly symmetric distortion is introduced with the following model parameters: the center of distortion and the coefficients of polynomials representing the distortion correction in the radial direction. If the imaging system is distortion-free, straight lines in the object space should be imaged as straight lines. Based on this criterion, a distorted image of a standard pattern consisting of a grid of several straight lines is recorded, and the model parameters are then estimated as a basis for straightening distorted lines. This method has the advantage of not needing a careful placement of the standard pattern for calibration. Correction results are presented for the grid pattern chart to verify a sufficient degree of correction. Examples of distortion correction of real intestinal images and physicians' comments are also presented.

The purpose of this work was to determine the feasibility of using positron emitting isotopes that emit prompt gammas to acquire quantitative positron emission tomography (PET) data using standard PET instrumentation. Prompt gammas can contaminate PET data by increasing dead time, converting singles into invalid coincidences, and producing multiple coincidences which can lead to the replacement of valid coincidences by invalid coincidences. The measurements in this work were made by scanning point sources containing F-18, Na-22, and Co-60 and studying the effects of the prompt gammas on the PET data, We found that for the Na-22 point source, the annihilation photon coincidence rate was about 25 times the prompt gamma-annihilation photon coincidence rate in the entire active volume of the scanner. With scatter, the Na-22 prompt gamma-annihilation photon coincidence rate was 1.3 times higher than the F-18 scatter coincidence rate. The most significant effect of the prompt gamma was to increase dead time; the dead time correction factor for Cu-60 was 2.4 times higher than the correction factor for N-13 for the same source activity. We conclude that, in many cases, quantitative PET data can be readily obtained with isotopes that emit prompt gammas, using standard PET 2-D instrumentation. However there are some cases, such as 3-D PET, where prompt gammas could significantly contaminate the PET data.

In pattern classification problems, the choice of variables to include in the feature vector is a difficult one. The authors have investigated the use of stepwise discriminant analysis as a feature selection step in the problem of segmenting digital chest radiographs. In this problem, locally calculated features are used to classify pixels into one of several anatomic classes. The feature selection step was used to choose a subset of features which gave performance equivalent to the entire set of candidate features, while utilizing less computational resources. The impact of using the reduced/selected feature set on classifier performance is evaluated for two classifiers: a linear discriminator and a neural network. The results from the reduced/selected feature set were compared to that of the full feature set as well as a randomly selected reduced feature set. The results of the different feature sets were also compared after applying an additional postprocessing step which used a rule-based spatial information heuristic to improve the classification results. This work shows that, in the authors' pattern classification problem, using a feature selection step reduced the number of features used, reduced the processing time requirements, and gave results comparable to the full set of features.

Measurement of the local cerebral metabolic rate of glucose (LCMRGlc) and the individual rate constant parameters of the [(18 )F]2-fluoro-2-deoxy-D-glucose (FDG) model can provide a clearer understanding and insight to the physiological processes in the human brain, and a quicker and more accurate means of diagnosis in clinical applications. A systematic study using simulated and clinical tissue time activity data is presented to evaluate several existing and newly developed major algorithms used for determining LCMRGlc and the individual rate constants from positron emission tomography dynamic data. The computational and statistical properties of the autoradiographic approach, weighted and unweighted nonlinear least squares methods, Patlak graphic approach, weighted integration method, linear least squares and generalized linear least squares methods are investigated and discussed in this paper.

Fourier inversion is an efficient method for image reconstruction in a variety of applications, for example, in computed tomography and magnetic resonance imaging. Fourier inversion normally consists of two steps, interpolation of data onto a rectilinear grid, if necessary, and inverse Fourier transformation. Here, the authors present interpolation by the scan-line method, in which the interpolation algorithm is implemented in a form consisting only of row operations and data transposes. The two-dimensional inverse Fourier transformation can also be implemented with only row operations and data transposes. Accordingly, Fourier inversion can easily be implemented on a parallel computer that supports row operations and data transposes on row distributed data. The conditions under which the scan-line implementations are algorithmically equivalent to the original serial computer implementation are described and methods for improving accuracy outside of those conditions are presented. The scan-line algorithm is implemented on the iWarp parallel computer using the Adapt language for parallel image processing. This implementation is applied to magnetic resonance data acquired along radial-lines and spiral trajectories through Fourier transform space.

Human investigators instinctively segment medical images into their anatomical components, drawing upon prior knowledge of anatomy to overcome image artifacts, noise, and lack of tissue contrast. The authors describe: 1) the development and use of a brain tissue probability model for the segmentation of multiple sclerosis (MS) lesions in magnetic resonance (MR) brain images, and 2) an empirical comparison of the performance of statistical and decision tree classifiers, applied to MS lesion segmentation. Based on MR image data obtained from healthy volunteers, the model provides prior probabilities of brain tissue distribution per unit voxel in a standardized 3-D "brain space". In comparison to purely data-driven segmentation, the use of the model to guide the segmentation of MS lesions reduced the volume of false positive lesions by 50-80%

An algorithm for detection of posterior rib borders in chest radiographs is presented. The algorithm first determines the thoracic cage boundary to restrict the area of search for the ribs. It then finds approximate rib borders using a knowledge-based Hough transform. Finally, the algorithm localizes the rib borders using an active contour model. Results of the proposed rib finding algorithm on 10 chest radiographs are presented.

Low-pass filtering computed tomography (CT) images to reduce noise may smooth or modify image features which are very important to the physician. Image features are often more easily identified and processed in the time-frequency plane. The authors use time-frequency distributions for spatially varying filtering of noisy CT images, constraining time-frequency representation coefficients of the projection data or of the reconstructed image to be zero in certain regions of the time-frequency plane. The authors consider two different applications: 1) filtering the projection data and then performing image reconstruction; and 2) filtering the reconstructed image directly. Criteria minimized, subject to constraints, may be either a deterministic minimum weighted perturbation of the given projection data or a stochastic minimum mean-square error in colored Gaussian noise. Results show improvement over processing the image with a linear spatially invariant filter.

Presents a new method to determine the orientation or pose of the left ventricle (LV) of the heart from cardiac SPECT (single photon emission computed tomography) data. This proposed approach offers an accurate, fast, and robust delineation of the LV long-axis. The location and shape of the generated long-axis can then be utilized to define automatically the tomographic slices for enhanced visualization and quantification of the clinical data. The methodology is broadly composed of two main steps: (1) volume segmentation of cardiac SPECT data; and (2) topological goniometry, a novel approach incorporating volume visualization and computer graphics ideas to determine the overall shape of 3-D objects. The outcome of the algorithm is a 3-D curve representing the overall pose of the LV long-axis. Experimental results on both phantom and clinical data (50 technetium-99m and 74 thallium-201) are presented. An interactive graphical interface to visualize the volume (3-D) data, the left ventricle, and its pose is an integral part of the overall methodology. This technique is completely data driven and expeditious, making it viable for routine clinical use.

Accurate tumor staging depends on finding all tumor sites, and curative surgery requires the removal of ail cancerous tissue from those sites. One technique for locating tumors is to inject patients before surgery with a radiotracer that is preferentially taken up by cancerous tissue. Then, an intraoperative gamma-sensitive probe is used to locate the tumors. Small (<1-cm diameter) tumors, often undetectable by external imaging and by the standard surgical inspection with sight and touch, can be found with probes, Simple calculations and measurements with radioactive tumor models show that small tumors should be detected by single-element probes, but often such probes fail to detect these small tumors in practice. This discrepancy is often caused by the use of a uniform background to predict probe performance, Real backgrounds are nonuniform and can decrease probe performance dramatically. Dual-element, coincidence, or imaging probes may solve the background problem. The authors devised a method to predict probe performance in a realistic background which includes variations in normal organ uptakes. They predict the relative performance of both existing probes and those in the design stage so that optimal detector and collimator configurations can be determined. The procedure includes a Monte-Carlo-calculated point-response function, a numerical torso phantom, and measured biodistributions of a monoclonal antibody. The Hotelling Trace Value, a measure of tumor-detection performance, is computed from the probe responses in simulated studies.

Introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations. The authors show that efficient representations may be identified within a continuum of scale-space and used to enhance features of importance to mammography. Methods of contrast enhancement are described based on three overcomplete multiscale representations: 1) the dyadic wavelet transform (separable), 2) the phi-transform (nonseparable, nonorthogonal), and 3) the hexagonal wavelet transform (nonseparable). Multiscale edges identified within distinct levels of transform space provide local support for image enhancement. Mammograms are reconstructed from wavelet coefficients modified at one or more levels by local and global nonlinear operators. In each case, edges and gain parameters are identified adaptively by a measure of energy within each level of scale-space. The authors show quantitatively that transform coefficients, modified by adaptive nonlinear operators, can make more obvious unseen or barely seen features of mammography without requiring additional radiation. The authors' results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features. They demonstrate that features extracted from multiresolution representations can provide an adaptive mechanism for accomplishing local contrast enhancement. By improving the visualization of breast pathology, one can improve chances of early detection while requiring less time to evaluate mammograms for most patients.

A method of computing the velocity field and pressure distribution from a sequence of ultrafast CT (UFCT) cardiac images is demonstrated. UFCT multi-slice cine imaging gives a series of tomographic slices covering the volume of the heart at a rate of 17 frames per second. The complete volume data set can be modeled using equations of continuum theory and through regularization, velocity vectors of both blood and tissue can be determined at each voxel in the volume. The authors present a technique to determine the pressure distribution throughout the volume of the left ventricle using the computed velocity field. A numerical algorithm is developed by discretizing the pressure Poisson equation (PPE), which Is based on the Navier-Stokes equation. The algorithm is evaluated using a mathematical phantom of known velocity and pressure-Couette flow. It is shown that the algorithm based on the PPE can reconstruct the pressure distribution using only the velocity data. Furthermore, the PPE is shown to be robust in the presence of noise. The velocity field and pressure distribution derived from a UFCT study of a patient are also presented.

The eigenimage filter generates a composite image in which a desired feature is segmented from interfering features. The signal-to-noise ratio (SNR) of the eigenimage equals its contrast-to-noise ratio (CNR) and is directly proportional to the dissimilarity between the desired and interfering features. Since image gray levels are analytical functions of magnetic resonance imaging (MRI) parameters, it is possible to maximize this dissimilarity by optimizing these parameters. For optimization, the authors consider four MRI pulse sequences: multiple spin-echo (MSE); spin-echo (SE); inversion recovery (IR); and gradient-echo (GE). The authors use the mathematical expressions for MRI signals along with intrinsic tissue parameters to express the objective function (normalized SNR of the eigenimage) in terms of MRI parameters. The objective function along with a set of diagnostic or instrumental constraints define a multidimensional nonlinear constrained optimization problem, which the authors solve by the fixed point approach. The optimization technique is demonstrated through its application to phantom and brain images. The authors show that the optimal pulse sequence parameters for a sequence of four MSE and one IR images almost doubles the smallest normalized SNR of the brain eigenimages, as compared to the conventional brain protocol.

The use of the expectation-maximization algorithm to obtain pseudo-maximum likelihood estimates (i.e. the EM-ML algorithm) of radiopharmaceutical distributions based on data collected from emission computed tomography (ECT) systems is now a well developed area, as witnessed by a number of recent articles on that topic, including the detailed study of the relative performance of EM-ML and FBP reconstructions provided in J. Llacer et al. (ibid., vol. 12, p. 215-31, 1993). However, there remains considerable confusion in the field regarding appropriate stopping rules for EM-ML algorithms, and in this correspondence the author attempts to detail a shortcoming of one of the more recent and innovative stopping rule criteria. In particular, the author discusses the effect of total photon counts on stopping criteria based on cross-validation.

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent rho filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e. detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.

B.D. Smith (ibid., vol.MI-4, p.15-25, 1985; Opt. Eng., vol.29, p.524-34, 1990) and P. Grangeat (These de doctorat, 1987; Lecture Notes in Mathematics 1497, p.66-97, 1991) derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's one, they have similar overall structures to each other. The contribution of the present paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's one can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam back projection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies.

Sampling a radiographic film containing grid line patterns during digitization may produce aliasing artifacts (Moire pattern). The authors propose a mathematical model based on the laser spot size of the digitizer, the distance and the angle between the grid line and the sampling direction to predict the amplitudes and the frequencies of aliasing artifacts. The predicted results are compared to the experimental results. Effective ways of avoiding or reducing aliasing artifacts without sacrificing too much image quality are proposed.

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.

The covariance matrices associated with each state of health or disease from a previous study are used as the basis of an image staining display technique for aid in quantitative differential diagnosis. A state of health or disease is chosen by the clinician: this selects the covariance matrix from the data base. A region of interest (ROI) is then scrolled through an abdominal B-scan. For each position of the ROI a point in the four-dimensional feature space is calculated. A natural measure of the distance of this point from the center of mass (multivariate mean) of the disease class is calculated in terms of the covariance matrix of this class; this measure is the Mahalanobis distance. The confidence level for acceptance or rejection of the hypothesized disease class is obtained from the probability distribution of this distance, the T(2) probability law. This confidence level is color coded and used as a color stain that overlays the original scan at that position. The variability of the calculated features is studied as a function of ROI size, or the spatial resolution of the color coded image, and it is found that for an ROI in the neighborhood of 4 cm(2) most of the variability due to the finite number of independent samples (speckles) is averaged out, leaving the "noise floor" associated with inter- and intra-patient variability. ROIs on the order of 1 cm(2) may result with technical advances in B-scan resolution. A small number of points on organ boundaries are entered by the user, to fit with arcs of ellipses to be used to switch between organ (liver and kidney) data bases as the ROI encounters the boundary. By selecting in turn various state-of-health or state-of-disease databases, such images of confidence levels may be used for quantitative differential diagnosis. The method is not limited to ultrasound, being applicable in principle to features obtained from any modality or multimodality combination.

Presents a new approach for the automatic tracking of SPAMM (Spatial Modulation of Magnetization) grid in cardiac MR images and consequent estimation of deformation parameters. The tracking is utilized to extract grid points from MR images and to establish correspondences between grid points in images taken at consecutive frames. These correspondences are used with a thin plate spline model to establish a mapping from one image to the next. This mapping is then used for motion and deformation estimation. Spatio-temporal tracking of SPAMM grid is achieved by using snakes-active contour models with an associated energy functional. The authors present a minimizing strategy which is suitable for tracking the SPAMM grid. By continuously minimizing their energy functionals, the snakes lock on to and follow the in-slice motion and deformation of the SPAMM grid. The proposed algorithm was tested with excellent results on 123 images (three data sets each a multiple slice 2D, 16 phase Cine study, three data sets each a multiple slice 2D, 13 phase Cine study and three data sets each a multiple slice 2D, 12 phase Cine study).

The sensitivity and resolution of a new 3D modular BGO detector system for positron emission tomography (PET) was examined in terms of its effect on the signal to noise ratio in the final image. The detector system uses custom hardware and firmware to adjust sensitivity and resolution to achieve optimum performance. This system utilizes lookup up tables (LUT) containing individually tailored positioning and energy windows to assure that events are correctly distributed among the detector elements. Without customizing the LUT, and for a common energy window, sensitivity was found to vary as much as a factor of 3.5 and resolution as much as 50% from center to edge within a single detector module. Eight different LUT configurations were tested, varying both energy window and positioning criteria. Typical intrinsic resolutions and sensitivities of the detector elements were determined in all configurations. The effect of nonuniformity of sensitivity of the detector system on image noise was evaluated by imaging uniform cylinders over a wide range of accumulated events. The effect of counting statistics in the measurement of detector sensitivities for the normalization of sinogram data was determined independently. The best of the LUT configurations provided an 16% improvement in effective sensitivity, while also providing a 10% improvement in the average intrinsic spatial resolution relative to the default configuration of the PET system.

Describes a technique for reconstructing the skeletal structure of coronary arteries from a succession of frames of a single-view cineangiogram. The authors use local features in each frame to determine correspondences of arterial segments in successive frames. They define a similarity measure in 2D image space as the change in angular coordinates of corresponding pairs. They use a form of gradient descent to find those depth coordinates that minimize the average deviation of the 3D angular coordinates of all points on the skeleton from the coordinates produced by a 3D scaling transformation. In experiments with software models the reconstruction error was approximately two pixels when the initial guessed reconstruction was as large as 30 pixels.

The authors build upon a technical report (Tech. Report OUEL 2009/93, Engng. Sci., Oxford Uni., Oxford, UK, 1993) in which they proposed a model of the mammographic imaging process for which scattered radiation is a key degrading factor. Here, the authors propose a way of estimating the scatter component of the signal at any pixel within a mammographic image, and they use this estimate for model-based image enhancement. The first step is to extend the authors' previous model to divide breast tissue into "interesting" (fibrous/glandular/cancerous) tissue and fat. The scatter model is then based on the idea that the amount of scattered radiation reaching a point is related to the energy imparted to the surrounding neighbourhood. This complex relationship is approximated using published empirical data, and it varies with the size of the breast being imaged. The approximation is further complicated by needing to take account of extra-focal radiation and breast edge effects. The approximation takes the form of a weighting mask which is convolved with the total signal (primary and scatter) to give a value which is input to a "scatter function", approximated using three reference cases, and which returns a scatter estimate. Given a scatter estimate, the more important primary component can be calculated and used to create an image recognizable by a radiologist. The images resulting from this process are clearly enhanced, and model verification tests based on an estimate of the thickness of interesting tissue present proved to be very successful. A good scatter model opens the was for further processing to remove the effects of other degrading factors, such as beam hardening.

Electrical impedance tomography (EIT) is a noninvasive imaging technique which aims to image the impedance within a body from electrical measurements made on the surface. The reconstruction of impedance images is a ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. The authors define an experimental measurement in EIT and calculate optimal experiments which maximize the distinguishability between the region to be imaged and a best-estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. The analysis clarifies the properties of different voltage measurement schemes. A reconstruction algorithm based on the use of optimal experiments is derived. It is shown to be many times faster than standard Newton-based reconstruction algorithms, and results from synthetic data indicate that the images that it produces are comparable.

A similarity measure based on the number of coincident bits in multichannel images is presented. The similarity criterion incorporated in the image registration algorithm uses a coincident bit counting (CBC) method to obtain the number of matching bits between the frames of interest. The CBC method not only performs favorably compared with traditional techniques, but also renders simpler implementation in conventional computing machines. An image registration algorithm that incorporates the CBC criterion is proposed to determine the translation motion among sequences of images. The errors caused by noise, misregistration, and a combination of these two are analyzed. Some experimental studies using low-contrast coronary images from a digital angiographic sequence are discussed. The results compare favorably with those obtained by using other nonparametric methods.

A simple and yet effective method for finding the borders of tumors is presented as an initial step towards the diagnosis of skin tumors from their color images. The method makes use of an adaptive color metric from the red, green, and blue planes that contains information for discriminating the tumor from the background. Using this suitable coordinate transformation, the image is segmented. The tumor portion is then extracted from the segmented image and borders are drawn. Experimental results that verify the effectiveness of this approach are given.

Clinical angiography requires hundreds of X-ray images, putting the patients and particularly the medical staff at risk. Dosage reduction involves an inevitable sacrifice in image quality. In this work, the latter problem is addressed by first modeling the signal-dependent, Poisson-distributed noise that arises as a result of this dosage reduction. The commonly utilized noise model for single images is shown to be obtainable from the new model. Stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle. The temporal versions of these filters as developed here are more suitable for filtering image sequences, as correlations along the time axis can be utilized. For these dynamic sequences, the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur.

Presents a knowledge-based approach to automatic classification and tissue labeling of 2D magnetic resonance (MR) images of the human brain. The system consists of 2 components: an unsupervised clustering algorithm and an expert system. MR brain data is initially segmented by the unsupervised algorithm, then the expert system locates a landmark tissue or cluster and analyzes it by matching it with a model or searching in it for an expected feature. The landmark tissue location and its analysis are repeated until a tumor is found or all tissues are labeled. The knowledge base contains information on cluster distribution in feature space and tissue models. Since tissue shapes are irregular, their models and matching are specially designed: 1) qualitative tissue models are defined for brain tissues such as white matter; 2) default reasoning is used to match a model with an MR image; that is, if there is no mismatch between a model and an image, they are taken as matched. The system has been tested with 53 slices of MR images acquired at different times by 2 different scanners. It accurately identifies abnormal slices and provides a partial labeling of the tissues. It provides an accurate complete labeling of all normal tissues in the absence of large amounts of data nonuniformity, as verified by radiologists. Thus the system can be used to provide automatic screening of slices for abnormality. It also provides a first step toward the complete description of abnormal images for use in automatic tumor volume determination.

With the advent of positron emission tomography (PET), a variety of techniques have been developed to measure local cerebral blood flow (LCBF) noninvasively in humans. A potential class of techniques, which includes linear least squares (LS), linear weighted least squares (WLS), linear generalized least squares (GLS), and linear generalized weighted least squares (GWLS), is proposed. The statistical characteristics of these methods are examined by computer simulation. The authors present a comparison of these four methods with two other rapid estimation techniques developed by Huang et al. (1982) and Alpert (1984), and two classical methods, the unweighted and weighted nonlinear least squares regression. The results show that these methods can take full advantage of the contribution from the fine temporal sampling data of modern tomographs, and thus provide statistically reliable estimates that are comparable to those obtained from nonlinear LS regression. These methods also have high computational efficiency, and the parameters can be estimated directly from operational equations in one single step. Therefore, they can potentially be used in image-wide estimation of local cerebral blood flow and distribution volume with PET.

The significance of each bit of the pixel in digital image data from various radiological modalities is tested to determine the contrast resolution. Two statistical methods, join-count statistic and chi-square goodness of fit test, are used to perform the test. Join-count statistic is used to measure the spatial coherence among pixels, while the chi-square test is used to determine if the bit data are randomly distributed. A residual image is formed by subtracting an original image from its smoothed version. The contrast revolution is determined by applying both statistics on each bit plane of the residual image starting from the least significant bit up to the bit plane whose statistic does not show a random pattern. Images from three digital modalities, computerized tomography, magnetic resonance, and computed radiography, are used to evaluate the gray-level dynamic range. Both methods are easy to implement and fast to perform.

A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. It is shown that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three.

The performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image (MRI) scene sequences for image enhancement and segmentation. Comparisons are made with principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature (SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison, analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied. Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a phantom study and a clinical case; advantages and weaknesses are discussed. The conclusion is that the eigenimage filter is the optimal linear filter that achieves SDF and CPV simultaneously.

An indirect method for determining the point-spread-function (PSF) in computed tomography (CT) is described. Unlike experimental techniques in which a resolution phantom is scanned to obtain the system PSF, the approach estimates the parameters of a model which describes the two-dimensional X-ray beam profile at each point as a convolution of the appropriately scaled focal spot intensity and detector sensitivity distributions. The model was validated by experimental measurement of the focal spot intensity distribution. Using known X-ray beam profiles, the PSF of a CT scanner can be derived by simulating the data collection process and applying conventional image reconstruction techniques. Visual comparison of directly measured and computed PSFs reveals an asymmetry resulting from misregistration of the phantom wires and the image grid.

An automatic method that can transform a sequence of tomographic image slices into an isotropic volume data set is described. In this method, correspondence is established between points in consecutive slices, and then this correspondence is used to estimate data between the slices by linear interpolation. The method takes advantage of the fact that consecutive slices have small geometric differences, and carries out the search in predicted small neighborhoods. Only points with high gradient magnitudes are used in the search process to increase the reliability of the correspondences. Mismatches that occur are detected and corrected using the continuity constraint in the correspondences. Experimental results showing the matching and interpolation of magnetic resonance slices and computed tomography slices are presented.

It is pointed out that to restore experimental computed tomography (CT) images which have been blurred by a spatially variant point spread function (PSF), a quadrant symmetry method which simultaneously optimizes storage requirements for the estimated PSFs and computational speed is used. The quadrant symmetry approach required less than 0.579 Megawords of storage for 9x9 pixel spatially variant PSFs in a 256x256 pixel image, allowing image restoration in Cartesian coordinates. A locally adaptive restoration method formulated using a noise prewhitening filter derived from the measured noise power spectrum, the conjugate gradient method was used to obtain a numerical solution. Restored images for a resolution phantom and for a cadaver femur are presented.