Image reconstruction from nonuniformly sampled frequency domain data is an important problem that arises in computed imaging. The current reconstruction techniques suffer from fundamental limitations in their model and implementation that result in blurred reconstruction and/or artifacts. Here, we present a new approach for solving this problem that relies on a more realistic model and involves an explicit measure for the reconstruction accuracy that is optimized iteratively. The image is assumed piecewise constant to impose practical display constraints using pixels. We express the mapping of these unknown pixel values to the available frequency domain values as a linear system. Even though the system matrix is shown to be dense and too large to solve for practical purposes, we observe that applying a simple orthogonal transformation to the rows of this matrix converts the matrix into a sparse format. The transformed system is subsequently solved using the conjugate gradient method. The proposed method is applied to reconstruct images of a numerical phantom as well as actual magnetic resonance images using spiral sampling. The results support the theory and show that the computational load of this method is similar to that of other techniques. This suggests its potential for practical use.

We investigate a new, provably convergent OSEM-like (ordered-subsets expectation-maximization) reconstruction algorithm for emission tomography. The new algorithm, which we term C-OSEM (complete-data OSEM), can be shown to monotonically increase the log-likelihood at each iteration. The familiar ML-EM reconstruction algorithm for emission tomography can be derived in a novel way. One may write a single objective function with complete, incomplete data and the reconstruction variables as in the EM approach. But in the objective function approach, there is no E-step. Instead, a suitable alternating descent on the complete data and then the reconstruction variables results in two update equations that can be shown to be equivalent to the familiar EM algorithm. Hence, minimizing this objective becomes equivalent to maximizing the likelihood. We derive our C-OSEM algorithm by modifying the above approach to update the complete data only along ordered subsets. The resulting update equation is quite different from OSEM, but still retains the speed-enhancing feature of the updates due to the limited backprojection facilitated by the ordered subsets. Despite this modification, we are able to show that the objective function decreases at each iteration, and (given a few more mild assumptions regarding the number of fixed points) conclude that the C-OSEM algorithm provides a monotonic convergence toward the maximum likelihood solution. We simulated noisy and noiseless emission projection data, and reconstructed them using the ML-EM, and the proposed C-OSEM with 4 subsets. We also reconstruct the data using the OSEM method. Anecdotal results show that the C-OSEM algorithm is much faster than ML-EM though slower than OSEM.

Based on Kunyansky's and our previous work, an efficient, analytical solution to the reconstruction problem of myocardial perfusion SPECT has been developed that allows simultaneous compensation for non-uniform attenuation, scatter, and system-dependent resolution variation, as well as suppression of signal-dependent Poisson noise. To avoid reconstructed images being corrupted by the presence of Poisson noise, a Karhunen-Loeve (K-L) domain adaptive Wiener filter is applied first to suppress the noise in the primary- and scatter-window measurements. The scatter contribution to the primary-energy-window measurements is then removed by our scatter estimation method, which is energy spectrum based, modified from the triple-energy-window acquisition protocol. The resolution variation is corrected by the depth-dependent deconvolution, which, being based on the central-ray approximation and the distance-frequency relation, deconvolves the scatter-free data with the accurate detector-response kernel in frequency domain. Finally, the deblurred projection data are analytically reconstructed with non-uniform attenuation by an algorithm based on Novikov's explicit inversion formula. The preliminary Monte Carlo simulation results using a realistic human thoracic phantom demonstrate that, for parallel-beam geometry, the proposed analytical reconstruction scheme is computationally comparable to filtered backprojection and quantitatively equivalent to iterative maximum a posteriori expectation-maximization reconstruction. Extension to other geometries is under progress.

We propose an alternating minimization (AM) image estimation algorithm for iteratively reconstructing transmission tomography images. The algorithm is based on a model that accounts for much of the underlying physics, including Poisson noise in the measured data, beam hardening of polyenergetic radiation, energy dependence of the attenuation coefficients and scatter. It is well-known that these nonlinear phenomena can cause severe artifacts throughout the image when high-density objects are present in soft tissue, especially when using the conventional technique of filtered back projection (FBP). If we assume no prior knowledge of the high-density object(s), our proposed algorithm yields much improved images in comparison to FBP, but retains significant streaking between the high-density regions. When we incorporate the knowledge of the attenuation and pose parameters of the high-density objects into the algorithm, our simulations yield images with greatly reduced artifacts. To accomplish this, we adapted the algorithm to perform a search at each iteration (or after every n iterations) to find the optimal pose of the object before updating the image. The final iteration returns pose values within 0.1 millimeters and 0.01 degrees of the actual location of the high-density structures.

Dual-energy (DE) X-ray computed tomography (CT) has shown promise for material characterization and for providing quantitatively accurate CT values in a variety of applications. However, DE-CT has not been used routinely in medicine to date, primarily due to dose considerations. Most methods for DE-CT have used the filtered backprojection method for image reconstruction, leading to suboptimal noise/dose properties. This paper describes a statistical (maximum-likelihood) method for dual-energy X-ray CT that accommodates a wide variety of potential system configurations and measurement noise models. Regularized methods (such as penalized-likelihood or Bayesian estimation) are straightforward extensions. One version of the algorithm monotonically decreases the negative log-likelihood cost function each iteration. An ordered-subsets variation of the algorithm provides a fast and practical version.

3D image reconstruction from cone-beam projections on a circular short-scan is analyzed using the tools of CB reconstruction theory. By definition, CB Data on a circular short-scan do not provide enough information for exact reconstruction outside the plane of the source path. However, circular short-scans are attractive in many applications due to practical constraints on the data acquisition geometry. This work attemps at determining the optimal tomographic capabilities of CB imaging with circular short-scan. Two new algorithms are suggested for reconstruction and tested on the FORBILD head phantom with a large cone angle. The results are very encouraging.

Since the recent introduction of multi-slice helical computed tomography (MHCT), new clinical applications have experienced tremendous growth in recent years. MHCT offers improved volume coverage, faster scan speed, more isotropic spatial resolution, and reduced x-ray tube loading. Similar to the single slice helical CT, the projection data collected in MHCT is inherently inconsistent due to the constant table motion. In addition, cone beam effects in MHCT produce additional complexity and image artifacts. Although the cone angle is quite smaller even for the 16-slice configuration, the impact on image artifacts cannot be ignored. Many reconstruction algorithms have been proposed and investigated recently to combat image artifacts associated with the MHCT data acquisition. In this paper, we propose a cone-angle dependent generalized weighting scheme for 16-slice helical CT that allows the production of MHCT images with only 2D backprojection. The cone-angle dependency of the algorithm suppresses image artifacts due to the cone beam effect and the generalized weighting portion enables interpolation be performed with conjugate samples for the 16-slice helical dataset. With the proposed algorithm, image artifacts are significantly reduced.

This paper describes an automated 3-D surface recovery algorithm for consistent and quantitative evaluation of the deformation in the ONH (optic nerve head). Additional measures, such as the changes in the volume of the cup and the disc as an improvement to the traditional cup to disc ratios, can thus be developed for longitudinal follow-up study of a patient. We propose an automated computerized technique for stereo pair registration and surface visualization of the ONH. Power cepstrum and zero mean cross correlation are embedded in the registration and a 3-D surface recovery technique is proposed. Preprocessing, as well as an overall registration, is performed upon stereo pairs. Then a coarse to fine feature matching strategy is used to reduce the ambiguity in finding the conjugate pair of the same point within the constraints of the epipolar plane. A cubic B-spline interpolation smooths the representation of the ONH obtained, while superimposition of features such as blood vessels is added. Studies show high correlation between traditional cup/disc measures derived from manual segmentation by ophthalmologists and computer generated cup/disc volume ratio. Such longitudinal studies over a large population of glaucoma patients are currently in progress for validation of the surface recovery algorithm.

The task of image segmentation implies estimation of the number and associated parameters of the classes within an image, and the class label for each image voxel. In this work, an over-segmentation of the data is first obtained using a Bayesian restoration algorithm. The method incorporates a novel spatial interaction prior, in which neighboring voxels can be classified differently so long as the distance between the centroids of their intensity distributions are within a certain extent. The corresponding functional is iteratively minimized using a series of local optimizations for the label field and a half-quadratic algorithm for the restoration. Redundant classes are then grouped in a second step by making use of information obtained in the initial restoration about the degree of affinity or interaction between the classes. The method is demonstrated on MRI images of the head.

During the last couple of years virtual endoscopic systems (VES) have emerged as standard tools that are nowadays close to be utilized in daily clinical practice. Such tools render hollow human structures, allowing a clinician to visualize their inside in an endoscopic-like paradigm. It is common practice that the camera of a virtual endoscope is attached to the centerline of the structure of interest, to facilitate navigation. This centerline has to be determined manually or automatically, prior to an investigation. While there exist techniques that can straightforwardly handle simple tube-like structures (e.g. colon, aorta), structures like the tracheobronchial tree still represent a challenge due to their complex branching. In these cases it is necessary to determine all branching points within the tree which is - because of the complexity - impractical to be accomplished in a manual manner. This paper presents a simultaneous segmentation/skeletonization algorithm that extracts all major airway branches and large parts of the minor distal branches (up to 7th order) using a front propagation approach. During the segmentation the algorithm keeps track of the centerline of the segmented structure and detects all branching points. This in turn allows the full reconstruction of the tracheobronchial tree.

The abdominal aorta is the most common site for an aneurysm, which may lead to hemorrhage and death, to develop. The aim of this study was to develop a semi-automated method to de-lineate the vessels and detect the center-line of these vessels to make measurements necessary for stent design from multi-detector computed tomograms. We developed a robust method of tracking the aortic vessel tree with branches from a user selected seed point along the vessel path using scale space approaches, central transformation measures, vessel direction findings, iterative corrections and a priori information in determining the vessel branches. Fifteen patients were scanned with contrast on Mx8000 CT scanner (Philips Medical Systems), with a 3.2 mm thickness, 1.5 mm slice spacing, and a stack of 512x512x320 volume data sets were reconstructed. The algorithm required an initial user input to locate the vessel seen in axial CT slice. Next, the automated image processing took approximately two minutes to compute the centerline and borders of the aortic vessel tree. The results between the manually and automatically generated vessel diameters were compared and statistics were computed. We observed our algorithm was consistent (less than 0.01 S.D) and similar (less than 0.1 S.D) to manual results.

This paper presents an extension of the theory and algorithms for fuzzy connectedness. In this framework, a strength of connectedness is assigned to every pair of image elements by finding the strongest connecting path between them. The strength of a path is the weakest affinity between successive pairs of elements along the path. Affinity specifies the degree to which elements hang together locally in the image. A fuzzy connected object containing a particular seed element is computed via dynamic programming. In all reported works so far, the minimum of affinities has been considered for path strength and the maximum of path strengths for fuzzy connectedness. The question thus remained all along as to whether there are other valid formulations for fuzzy connectedness. One of the main contributions of this paper is a theoretical investigation under reasonable axioms to establish that maximum of path strengths of minimum of affinities along each path is indeed the one and only valid choice. The second contribution here is to generalize the theory and algorithms of fuzzy connectedness to the multi-seeded case. The importance of multi-seeded fuzzy connectedness is illustrated with examples taken from several real medical imaging applications.

This paper describes the theory and algorithms of fuzzy distance transform (FDT). Fuzzy distance is defined as the length of the shortest path between two points. The length of a path in a fuzzy subset is defined as the integration of fuzzy membership values of the points along the path. The shortest path between two points is the one with the minimum length among all (infinitely many) paths between the two points. It is demonstrated that, unlike in the binary case, the shortest path in a fuzzy subset is not necessarily a straight-line segment. The support of a fuzzy subset is the set of points with nonzero membership values. It is shown that, for any fuzzy subset, fuzzy distance is a metric for the interior of its support. FDT is defined as the process on a fuzzy subset that assigns at each point the smallest fuzzy distance from the boundary of the support. The theoretical framework of FDT in continuous space is extended to digital spaces and a dynamic programming-based algorithm is presented for its computation. Several potential medical imaging applications are presented including the quantification of blood vessels and trabecular bone thickness in the regime of limited special resolution.

Segmentation of fluoroscopy images is useful for fluoroscopy-to-CT image registration. However, it is impossible to assign a unique tissue type to each pixel. Rather each pixel corresponds to an entire path of tissue types encountered along a ray from the X-ray source to the detector plate. Furthermore, there is an inherent many-to-one mapping between paths and pixel values. We address these issues by assigning to each pixel not a scalar value but a fuzzy vector of tissue probabilities. We perform this segmentation in a probabilistic way by first learning typical distributions of bone, air, and soft tissue that correspond to certain fluoroscopy image values and then assigning each value to a probability distribution over its most likely generating paths. We then evaluate this segmentation on ground truth patient data.

Accurate computation of the thickness of articular cartilage in 3D is crucial in diagnosis of joint diseases. The purpose of this research project is to develop an unsupervised method to produce three-dimensional (3D) thickness map of articular cartilage with magnetic resonance imaging (MRI). The method consists of two main parts, cartilage extraction and thickness map computation. The initial segmentation for cartilage extraction is achieved using a recently proposed algorithm which depends on region-growing. The regions produced during this process are labeled as cartilage or non-cartilage using a voting procedure which essentially depends on local 2-class clustering and makes use of prior knowledge about cartilage regions. Following cartilage extraction, femoral and tibial cartilages are separated by detecting the interface between them using a deformable model. After the separation, the cartilage surfaces are reconstructed as a triangular mesh and divided into two plates according to the relation between surface normal at each vertex and principal axes of the structure. For surface reconstruction, we propose an algorithm which incorporates a simple MR imaging model which allows surface representations with sub-voxel accuracy. Our thickness computation algorithm treats each plate separately as a deformable model while considering the other plate as the target surface towards which it is deformed. At the end of deformation, the thickness values at each vertex is defined as the distance between the locations at pre and post-deformation instances. The performance of the cartilage segmentation is compared to manual tracing. Also, the performance evaluation of the thickness computation algorithm on phantoms resulted in RMS errors on the order of 1%.

Optical coherence tomography (OCT) provides a non-contact and non-invasive means to visualize the corneal anatomy at micron scale resolution. We obtained corneal images from an arc-scanning (converging) OCT system operating at a wavelength of 830nm and a fan-shaped-scanning high-speed OCT system with an operating wavelength of 1310nm. Different scan protocols (arc/fan) and data acquisition rates, as well as wavelength dependent bio-tissue backscatter contrast and optical absorption, make the images acquired using the two systems different. We developed image-processing algorithms to automatically detect the air-tear interface, epithelium-Bowman's layer interface, laser in-situ keratomileusis (LASIK) flap interface, and the cornea-aqueous interface in both kinds of images. The overall segmentation scheme for 830nm and 1310nm OCT images was similar, although different strategies were adopted for specific processing approaches. Ultrasound pachymetry measurements of the corneal thickness and Placido-ring based corneal topography measurements of the corneal curvature were made on the same day as the OCT examination. Anterior/posterior corneal surface curvature measurement with OCT was also investigated. Results showed that automated segmentation of OCT images could evaluate anatomic outcome of LASIK surgery.

With the improvements in techniques for generating surface models from magnetic resonance (MR) images, it has recently become feasible to study the morphological characteristics of the human brain cortex in vivo. Studies of the entire surface are important for measuring global features, but analysis of specific cortical regions of interest provides a more detailed understanding of structure. We have previously developed a method for automatically segmenting regions of interest from the cortical surface using a watershed transform. Each segmented region corresponds to a cortical sulcus and is thus termed a sulcal region. In this work, we describe three important augmentations of this methodology. First, we describe a user interface that allows for the efficient labeling of the segmented sulcal regions called the Interactive Program for Sulcal Labeling (IPSL). Two additional augmentations of the methodology allow for even finer division of regions on the cortex. Both employ the fast marching technique to track curves of interest on the cortical surface. These curves are then used to separate segmented regions. Validation experiments indicate that the proposed methodology gives highly repeatable results.

In previous work, the authors presented a multi-stage procedure for the semi-automatic reconstruction of the cerebral cortex from magnetic resonance images. This method suffered from several disadvantages. First, the tissue classification algorithm used can be sensitive to noise within the image. Second, manual interaction was required for masking out undesired regions of the brain image, such as the ventricles and putamen. Third, iterated median filters were used to perform a topology correction on the initial cortical surface, resulting in an overly smoothed initial surface. Finally, the deformable surface used to converge to the cortex had difficulty capturing narrow gyri. In this work, all four disadvantages of the procedure have been addressed. A more robust tissue classification algorithm is employed and the manual masking step is replaced by an automatic method involving level set deformable models. Instead of iterated median filters, an algorithm developed specifically for topology correction is used. The last disadvantage is addressed using an algorithm that artificially separates adjacent sulcal banks. The new procedure is more automated but also more accurate than the previous one. Its utility is demonstrated by performing a preliminary study on data from the Baltimore Longitudinal Study of Aging.

Other researchers have proposed that the brain parenchymal fraction (or brain atrophy) may be a good surrogate measure for disease progression in patients with Multiple Sclerosis. This paper considers various factors influencing the measure of the brain parenchymal fraction obtained from dual spin-echo PD and T2-weighted head MRI scans. We investigate the robustness of the brain parenchymal fraction with respect to two factors: brain-mask border placement which determines the brain intra-dural volume, and brain scan incompleteness. We show that an automatic method for brain segmentation produces an atrophy measure which is fairly sensitive to the brain-mask placement. We also show that a robust, reproducible brain atrophy measure can be obtained from incomplete brain scans, using data in a centrally placed subvolume of the brain.

This paper proposes an image analysis system to segment multiple sclerosis lesions of magnetic resonance (MR) brain volumes consisting of 3 mm thick slices using three channels (images showing T1-, T2- and PD -weighted contrast). The method uses the statistical model of Markov Random Fields (MRF) both at low and high levels. The neighborhood system used in this MRF is defined in three types: (1) Voxel to voxel: a low-level heterogeneous neighborhood system is used to restore noisy images. (2) Voxel to segment: a fuzzy atlas, which indicates the probability distribution of each tissue type in the brain, is registered elastically with the MRF. It is used by the MRF as a-priori knowledge to correct miss-classified voxels. (3) Segment to segment: Remaining lesion candidates are processed by a feature based classifier that looks at unary and neighborhood information to eliminate more false positives. An expert's manual segmentation was compared with the algorithm.

In this study, subsets of MR slices were examined to assess their ability to optimally predict the total cerebral volume of gray matter, white matter and CSF. Patients underwent a clinical imaging protocol consisting of T1-, T2-, PD-, and FLAIR-weighted images after obtaining informed consent. MR imaging sets were registered, RF-corrected, and then analyzed with a hybrid neural network segmentation and classification algorithm to identify normal brain parenchyma. After processing the data, the correlation between the image subsets and the total cerebral volumes of gray matter, white matter and CSF were examined. The 29 subjects (18F, 11M) assessed in this study were 1.7 ? 18.7 (median = 5.2) years of age. The five subsets accounted for 5%, 15%, 24%, 56%, and 79% of the total cerebral volume. The predictive correlation for gray matter, white matter, and CSF in each of these subsets were: 5% (R= 0.94, 0.92, 0.91), 15% (R= 0.93, 0.95, 0.94), 24% (R= 0.92, 0.95, 0.94), 56% (R= 0.75, 0.95, 0.89), and 79% (R= 0.89, 0.98, 0.99) respectively. All subsets of slices examined were significantly correlated (p<0.001) with the total cerebral volume of gray matter, white matter, and CSF.

Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected in medical imaging applications, mostly as a consequence of what one may call the bad press phenomenon. Thanks to some recent research efforts in signal processing and wavelet-related techniques, the virtues of splines have been revived in our community. There is now compelling evidence (several independent studies) that splines offer the best cost-performance tradeoff among available interpolation methods. In this presentation, we will argue that the spline representation is ideally suited for all processing tasks that require a continuous model of signals or images. We will show that most forms of spline fitting (interpolation, least squares approximation, smoothing splines) can be performed most efficiently using recursive digital filters. We will also have a look at their multiresolution properties which make them prime candidates for constructing wavelet bases and computing image pyramids. Typical application areas where these techniques can be useful are: image reconstruction from projection data, sampling grid conversion, geometric correction, visualization, rigid or elastic image registration, and feature extraction including edge detection and active contour models.

Clinical procedures that rely on biplane x-ray images for three-dimensional (3-D) information may be enhanced by three-dimensional reconstructions. However, the accuracy of reconstructed images is dependent on the uncertainty associated with the parameters that define the geometry of the camera system. In this paper, we use a numerical simulation to examine the effect of these uncertainties and to determine the limits required for adequate three-dimensional reconstruction. We then test our conclusions with images of a calibration phantom recorded using a clinical system. A set of reconstruction routines, developed for a cardiac mapping system, were used in this evaluation. The routines include procedures for correcting image distortion and for automatically locating catheter electrodes. Test images were created using a numerical simulation of a biplane x-ray projection system. The reconstruction routines were then applied using accurate and perturbed camera geometries and error maps were produced. Our results indicate that useful catheter reconstructions are possible with reasonable bounds on the uncertainty of camera geometry provided the locations of the camera isocenters are accurate. The results of this study provide a guide for the specification of camera geometry display systems and for researchers evaluating possible methodologies for determining camera geometry.

X-ray rotational angiography has recently gained increasing interest for computer-assisted quantitative analysis. It provides more accurate assessment of vascular diseases and precise inspection of complex structure of the arterial network via three-dimensional (3D) vascular reconstruction. The 3D spatial information can be obtained via a stereoscopic analysis of the two-dimensional (2D) projections of the opacified blood vessels. In this work, we focus on the problem of automatic 3D reconstruction of blood vessel networks for telediagnostic applications and therefore from uncalibrated X-ray rotational angiography image sequence. Three main issues are addressed: 1) automatic accurate subpixel vascular median axis network detection from non-subtracted 2D angiography images, 2) robust matching of the extracted features by using an original method based on statistical tests, and 3) three-dimensional reconstruction through epipolar geometry determination from uncalibrated 2D images. Our reconstruction method has the advantage to be independent of the angiography acquisition system. It is therefore interesting for telemedicine and specially for telediagnostic systems.

We have developed a technique based on epipolar geometry which allows reconstruction of vessel lumina containing asymmetries for arbitrary lumen orientation. Vessel centerlines and the imaging geometry are determined using previously described methods. Epipolar planes are established for pairs of centerline points and intensity profiles are extracted along epipolar lines. Extracted profiles are fitted to projection curves corresponding to elliptical cross-sections. The original vessel intensity profile is subtracted from the best-fit profile yielding the plaque profile. Corresponding best-fit profiles are used to reconstruct elliptical cross sections by backprojecting and identifying ray intersection points which lie within the model cross section. Assuming that the deformation of an otherwise elliptical lumen occurs as a result of plaque growing inward from the periphery, asymmetries are generated by deforming the cross sections to an extent consistent with the plaque profile in both views. The three-dimensional lumen may be obtained by combining individual cross sections in consecutive epipolar planes. The technique was evaluated using noiseless simulated angiograms. Reconstructed asymmetric lumen cross sections were found to be accurate to 95%, where accuracy was determined using area and distance criteria.

The purpose of this paper is to describe a framework for evaluating image segmentation algorithms. Image segmentation consists of object recognition and delineation. For evaluating segmentation methods, three factors - precision (reproducibility), accuracy (agreement with truth, validity), and efficiency (time taken) - need to be considered for both recognition and delineation. To assess precision, we need to choose a figure of merit, repeat segmentation considering all sources of variation, and determine variations in figure of merit via statistical analysis. It is impossible usually to establish true segmentation. Hence, to assess accuracy, we need to choose a surrogate of true segmentation and proceed as for precision. In determining accuracy, it may be important to consider different landmark areas of the structure to be segmented depending on the application. To assess efficiency, both the computational and the user time required for algorithm and operator training and for algorithm execution should be measured and analyzed. Precision, accuracy, and efficiency are interdependent. It is difficult to improve one factor without affecting others. Segmentation methods must be compared based on all three factors. The weight given to each factor depends on application.

In this work, we present a unique set of 3D MRI brain data that is appropriate for testing the intra and inter-site variability of image analysis methods. A single subject was scanned two times within a 24 hour time window each at five different MR sites over a period of six weeks using GE and Phillips 1.5 T scanners. The imaging protocol included T1 weighted, Proton Density and T2 weighted images. We applied three quantitative image analysis methods and analyzed their results via the coefficients of variability (COV) and the intra correlation coefficient. The tested methods include two multi-channel tissue segmentation techniques based on an anatomically guided manual seeding and an atlas-based seeding. The third tested method was a single-channel semi-automatic segmentation of the hippocampus. The results show that the outcome of image analysis methods varies significantly for images from different sites and scanners. With the exception of total brain volume, which shows consistent low variability across all images, the COV's were clearly larger between sites than within sites. Also, the COV's between sites with different scanner types are slightly larger than between sites with the same scanner type. The presented existence of a significant inter-site variability requires adaptations in image methods to produce repeatable measurements. This is especially of importance in multi-site clinical research.

We propose an evaluation process for segmentation which is made up of three different levels. It enables us to carry out the time consuming steps only for those segmentation methods for which a successful segmentation is foreseeable. In the first level the developer of a segmentation method does a coarse analysis of the usefulness of the individual segmentation methods by means of visual assessment of the results for few image examples. Methods which have been judged useful at the first level are investigated in a second evaluation step as to the stability of the segmentation results in case of slight deviations in the images. For the reproduction of the image formation process a multitude of realizations of a given region of interest are produced by means of the bootstrap technique. At the third level of the evaluation process the segmentation methods are tested for segmentation errors. The segmentation methods are judged by means of empirical discrepancy values, and the effectiveness of a method chosen for the respective task is finally estimated.

We describe the evaluation of a non-rigid image registration method for multi-modal data. The evaluation is made difficult by the absence of gold standard test data, for which the true transformation from one image to another is known. Different approaches have been used to deal with this deficiency, e.g., by using synthetically warped data, by comparison of anatomic regions of interest identified either manually or automatically, and by direct comparison of the registered data. Each of these approaches are limited and in this paper, we illustrate some of the problems that arise based on their application to the evaluation of our multi-modal non-rigid registration method.

For implementation of computer-aided diagnostic systems for chest radiographs, it is important to correctly identify the view position, i.e., posteroanterior (PA) or lateral view. Our purpose is to develop an advanced computerized method by using a template matching technique for correctly identifying either PA or lateral view, and to apply this method to approximately 48,000 PA and 16,000 lateral chest radiographs. To evaluate the similarity with templates, correlation values of a chest image with various templates were obtained and compared for determining whether a chest image is either a PA or a lateral view. By considering the variation in terms of patient's sizes, lung opacities, and lung sizes, we produced 24 templates of PA and lateral views. In the first step, two largest correlation values of an unknown case with 3 PA and 2 lateral templates for medium-size patients were compared for determining the view position. In the second step, the unidentifiable cases in the first step were re-examined by comparison of the correlation values with 11 to 19 templates for small and large patients. With the computerized method based on a template matching technique, 99.99%(=63,788/63,791) of chest images in the large database were correctly identified in terms of PA or lateral views.

High reproducibility of volumetric measurements is an important prerequisite for follow-up of small lung nodules in order to differentiate malignant from benign lesions in a lung cancer screening setting. This study was aimed to evaluate the measurement reproducibility of a new software tool for pulmonary nodule volumetry. In an ongoing study, 147 pulmonary nodules (size 1.6-17.5 mm) were examined with low-dose multidetector CT (Siemens Somatom Volume Zoom, 120 kVp, 20 mAs, detector collimation 4x1 mm, normalized pitch 1.75, slice thickness 1.25 mm, reconstruction increment 0.8 mm). Two consecutive low-dose scans covering the whole lung volume were performed within a few minutes. Between both scans, patients were asked to leave the CT scanner, and the second scan was planned independently from the first one. For all visually detected pulmonary nodules with a diameter <20 mm nodule volume was determined on both scans using a software prototype containing segmentation and volumetry algorithms. Results from both scans were compared. Nodule volume differences were determined as difference between the first and second measurement and ranged from 169 to 87%. The performance of the diagnostic test was measured using ROC analysis. For the detection of a volume doubling the area under curve (A_z) was 0.98, for a growth of 50% the A_z was 0.89. Further refinement of the segmentation algorithm should lead to more consistent measurements in ill-defined nodules. In conclusion, volumetric measurement of pulmonary nodules in multislice CT data sets is a reliable tool for the detection of growth in small pulmonary nodules.

Ultrasonic strain images describe the stiffness of soft tissues. Strain estimates are obtained from the spatial derivative of local displacements between echo fields acquired prior to and after applying a small compressive force. Multi-scale displacement measurements using correlation estimates yield the highest quality strain images but are computationally extensive. An approach to strain reconstruction is proposed that constrains the correlation search based on physical priors in order to accelerate and optimize the estimation of local displacements. The data correlation kernel is chosen large in regions of constant displacement to minimize noise and small in regions of varying displacement to maximize spatial resolution for strain. Multiple echo fields were acquired using a Siemens Elegra system with a 7.5 MHz linear array while slowly compressing phantoms and tissues. Gel phantoms with simulated stiff lesions and flow channels, as well as ex vivo muscle and in vivo breast tissues were examined. The new algorithm provided images with equal or lower noise as compared to the traditional algorithm. Adaptively limiting the search in smoothly compressed regions reduced computational time by a factor of 1.5 to 8 depending on the applied compression and complexity of motion.

Correction of motion artifacts in MRI due to interview in-plane 2-D rigid body translations is possible using only the raw data of two standard 2DFT images acquired of the same object with phase encode direction swapped. Previous techniques simply use multiple or orthogonal images to reduce artifacts by ghost interference or geometric averaging. The orthogonal k-space phase difference (ORKPHAD) provides an overdetermined system of linear equations that can be solved directly to compensate for the phase errors caused by the translation. This technique was used to correct images of a volunteer's moving wrist. For all slices of the motion corrupted data volumes, artifacts were dramatically reduced. Though the algorithm only accounts for interview translational motion, it is robust enough to correct real in vivo images that may also be corrupted by small amounts of rotational or out-of-plane motion. Experiments underway show the algorithm can tolerate bulk rotation of several degrees between orthogonal image pairs and that corrections using fractional NEX scans are possible. The current results and such ongoing advancements should make this correction technique practical for certain clinical scenarios vulnerable to in-plane translation.

In many medical imaging applications, due to the limited field of view of imaging devices, often, acquired images include only a part of a structure. In such situations, it is impossible to guarantee that the images will contain exactly the same physical extent of the structure at different scans, which leads to difficulties in registration and in many other tasks, such as the analysis of the morphology, architecture, and kinematics. To facilitate such analysis, we developed a general method, referred to as isoshaping, that generates structures of the same shape from segmented images. The basis for this method is to automatically find a set of key points, called shape centers, in the segmented partial anatomic structure such that these points are present in all images and that they represent the same physical location in the object, and then trim the structure using these points as reference. The application area considered here is the analysis of the morphology, architecture, and kinematics of the foot joints from MR images acquired at different joint positions, load conditions, and longitudinal time instances. The accuracy of the method is studied and it is quantitatively demonstrated that isoshaping improves the results of registration.

In the last decade in the field of diagnostic imaging, the problem of variability of reader skill as well as patient case difficulty has given rise to a multivariate approach to receiver operating characteristic (ROC) analysis. The multivariate approach is the so-called multiple-reader, multiple-case (MRMC) ROC paradigm in which every reader reads every patient case and, where possible, in each of two modalities under comparison. The present paper demonstrates the isomorphism between patient cases, image readers, and imaging modalities in diagnostic imaging and, respectively, test sets, training sets, and competing discriminant algorithms in the field of statistical pattern recognition (SPR). Thus, the MRMC paradigm can be brought directly across from imaging to SPR. Recent MRMC ROC analytical methods are demonstrated in the context of SPR for the task of analyzing the natural components of variance in that problem involving test sets, training sets, and competing discriminants. Monte Carlo trials reported here indicate that the conventional wisdom that the variance of measures of classifier accuracy comes mainly from the finite test set is only true when assessing a single algorithm in a very limited context. In particular, it is generally not true when comparing competing discriminant algorithms; in that case the variance is dominated by the finite training set.

The purpose of this study was to identify and characterize clusters in a heterogeneous breast cancer computer-aided diagnosis database. Identification of subgroups within the database could help elucidate clinical trends and facilitate future model building. Agglomerative hierarchical clustering and k-means clustering were used to identify clusters in a large, heterogeneous computer-aided diagnosis database based on mammographic findings (BI-RADS) and patient age. The clusters were examined in terms of their feature distributions. The clusters showed logical separation of distinct clinical subtypes such as architectural distortions, masses, and calcifications. Moreover, the common subtypes of masses and calcifications were stratified into clusters based on age groupings. The percent of the cases that were malignant was notably different among the clusters. Cluster analysis can provide a powerful tool in discerning the subgroups present in a large, heterogeneous computer-aided diagnosis database.

Statistical as well as adaptive clustering approaches are being currently used for both segmentation and vector quantization of medical images. However, a comparative evaluation of both approaches has rarely been done to identify the efficacy of such approaches to specific applications, for example, image segmentation and vector quantization. The rate distortion functions of three clustering algorithms, namely, the statistical based deterministic annealing, the adaptive fuzzy leader clustering algorithm, and LBG, have been computed for vector quantization using multi-scale vectors in the wavelet domain. Such comparative evaluation serves as a guide for proper selection of clustering algorithms for global codebook generation in vector quantization and for image segmentation.

We tested on an edge map computed from a local homogeneity measurement, which is a potential replacement for the traditional gradient-based edge map in level-set segmentation. In existing level-set methods, the gradient information is used as a stopping criteria for curve evolution, and also provides the attracting force to the zero level-set from the target boundary. However, in a discrete implementation, the gradient-based term can never fully stop the level-set evolution even for ideal edges, leakage is often unavoidable. Also the effective distance of the attracting force and blurring of edges become a trade-off in choosing the shape and support of the smoothing filter. The proposed homogeneity measurement provides easier and more robust edge estimation, and the possibility of fully stopping the level-set evolution. The homogeneity term decreasing from a homogenous region to the boundary, which dramatically increases the effective distance of the attracting force and also provides additional measurement of the overall approximation to the target boundary. Therefore, it provides a reliable criteria of adaptively changing the advent speed. By using this term, the leakage problem was avoided effectively in most cases compared to traditional level-set methods. The computation of the homogeneity is fast and its extension to the 3D case is straightforward.

Image segmentation is concerned with partitioning an image into non-overlapping, constituent regions, which are homogeneous with respect to certain features. In magnetic resonance imaging (MRI), the most discriminative and commonly used features are the image intensities themselves. However, due to noise, partial volume effects, natural and spurious intensity variations, intensity distributions of distinct tissues generally overlap, which makes segmentation difficult and less precise. Using multi-spectral MR images and mapping intensities into a multidimensional feature space may help in segmentation. To further facilitate segmentation, we map the intensities and second derivatives of multi-spectral images into a common multidimensional feature space. Integration of intensity and spatial information may yield complex clusters that cannot be described by Gaussian mixture models or by hyper-spherical shapes. For this reason we devise a novel segmentation method based on non-parametric valley-seeking clustering. The valleys are found by estimating feature density gradients. The proposed segmentation method, with and without spatial information, is tested on simulated and real, single- and multi-spectral, MR brain images. The segmentation results are highly consistent with the gold standard, especially when combined with a procedure for intensity non-uniformity correction, presented in MI 4684-177.

High-resolution multichannel textures are difficult to characterize with simple statistics and the high level of detail makes the selection of a particular contour using classical gradient-based methods not effective. We have developed a hybrid method that combines fuzzy connectedness and Voronoi diagram classification for the segmentation of color and multichannel objects. The multi-step classification process relies on homogeneity measures derived from moment statistics and histogram information. These color features have been optimized to best combine individual channel information in the classification process. The segmentation initialization requires only a set of interior and exterior seed points, minimizing user intervention and the influence of the initialization on the overall quality of the results. The method was tested on volumes from the Visible Human and on brain multi-protocol MRI data sets. The hybrid segmentation produced robust, rapid and finely detailed contours with good visual accuracy. The addition of quantized statistics and color histogram distances as classification features improved the robustness of the method with regards to initialization when compared to our original implementation.

An automatic segmentation method for detecting the prostate boundary in transrectal ultrasound (TRUS) images was developed. The TRUS images were preprocessed by using an adaptive directional filtering and an automatic attenuation compensation for noise removal and contrast enhancement. A directional search strategy was used to locate key-points on the prostate boundary. The prostate contour was interpolated from the key-points under the supervision of a morphological prostate boundary model, which had been trained from prior manual segmentation of a large number of TRUS images. A new prostate center was calculated based on the intermediate segmentation result. The algorithm is reiterated until the prostate boundary and center reach a stable state. The overall performance of the method was compared to manual segmentation of an expert radiologist. About 78% out of 282 TRUS images (excluding base and apex slices) from three types of ultrasound machine (Acuson, Siemens, and B&K) were correctly delineated. The segmentation error was 0.9 mm averaged on 30 selected images, 10 for each type of machine. The computation time for a typical series of TRUS images is approximately 1 minute on a Pentium-II computer.

This paper presents a three-dimensional (3-D) tissue analysis method and its applications in partial volume correction and change analysis. The method uses a stochastic model-based approach and consists of two steps: (1) unsupervised tissue quantification and (2) 3-D segmentation. Firstly, the MR image volume is modeled by the standard finite normal mixture (SFNM) distribution. It has been shown that the SFNM converges to the true distribution when the pixel images are asymptotically independent. Secondly, the tissue quantification is achieved through (1) model selection by minimum description length (MDL) criterion; (2) parameter initialization by optimal histogram quantization and (3) parameter estimation by a fast EM algorithm using the global 3-D histogram rather than conventionally the raw data. Finally, we develop a 3-D segmentation method using the maximum likelihood (ML) classification and contextual Bayesian relaxation labeling (CBRL). The CBRL is developed to obtain a consistent labeling solution, based on localized SFNM formulation by using neighborhood contextual regularities. The method has been applied to partial volume correction for PET brain images and change analysis for MR breast images.

Active Appearance Models (AAMs) are useful for the segmentation of cardiac MR images since they exploit prior knowledge about the cardiac shape and image appearance. However, traditional AAMs only process 2D images, not taking into account the 3D data inherent to MR. This paper presents a novel, true 3D Active Appearance Model that models the intrinsic 3D shape and image appearance of the left ventricle in cardiac MR data. In 3D-AAM, shape and appearance of the Left Ventricle (LV) is modeled from a set of expert drawn contours. The contours are then resampled to a manually defined set of landmark points, and subsequently aligned. Appearance variations in both shape and texture are captured using Principal Component Analysis (PCA) on the training set. Segmentation is achieved by minimizing the model appearance-to-target differences by adjusting the model eigen-coefficients using a gradient descent approach. The clinical potential of the 3D-AAM is demonstrated in short-axis cardiac magnetic resonance (MR) images. The method's performance was assessed by comparison with manually-identified independent standards in 56 clinical MR sequences. The method showed good agreement with the independent standards using quantitative indices such as border positioning errors, endo- and epicardial volumes, and left ventricular mass. The 3D AAM method shows high promise for successful segmentation of three-dimensional images in MR.

In this paper we propose an appearance-based method to heart detection by principal component analysis (PCA). In contrast to conventional methods of PCA-based training, there is no brightness and contrast normalization since such normalization is usually based on maximum and minimum intensity values and is very sensitive to noises. We propose to integrate the normalization procedure into the detection phase. This is achieved by projecting the intensity-transformed image (with unknown scale and shift parameters) onto the eigen-images and minimizing the error of fit. This leads to a set of equations on both the intensity transformation parameters and the projection coefficients. By using the least-squares method, these equations can be easily solved for the scale and shift parameters. After an initial detection of heart positions is conducted, robust fitting of the heart trajectory is used to correct any detection errors. Besides, we also propose an eigen-image re-orthonormalization method for multiple resolution detection without extra training on multiple scales.

A novel 3-D Active Appearance Model (3-D AAM) is applied to fully automated endocardial contour detection in 2-D + time (2DT) 4-chamber ultrasound sequences, without knowledge of cardiac phase (ED/ES frames). 2DT appearance of the heart is modeled in 3-D by converting the stack of 2-D time slices into a 3-D voxel space. In a training set, an expert defines corresponding endocardial contour points for one complete cardiac cycle (ED to ED). 2DT shape is represented as a 3-D surface. Image appearance is modeled as a vector of voxel intensities in a volume-patch spanned by the 3-D surface. Principal Component Analysis extracts eigenvariations of 3-D shape and appearance, capturing typical cardiac motion patterns. 3-D AAM segments the image volume by minimizing 3-D model-to-target intensity differences, adjusting eigenvariation coefficients and 3-D pose using gradient descent minimization. This provides time-continuous border localization for one beat in both time and space. The method was used on 3-beat sequences from 129 patients split randomly into a training (65) and a test set (64). An independent expert manually drew all endocardial contours. 3-D AAM converged well in 89% of test cases. Average absolute temporal error was 37.0 msec, spatial error 3.35 mm, comparable to human inter-observer variabilities.

An automated method for the segmentation of thrombus in abdominal aortic aneurysms from CTA data is presented. The method is based on Active Shape Model (ASM) fitting in sequential slices, using the contour obtained in one slice as the initialisation in the adjacent slice. The optimal fit is defined by maximum correlation of grey value profiles around the contour in successive slices, in contrast to the original ASM scheme as proposed by Cootes and Taylor, where the correlation with profiles from training data is maximised. An extension to the proposed approach prevents the inclusion of low-intensity tissue and allows the model to refine to nearby edges. The applied shape models contain either one or two image slices, the latter explicitly restricting the shape change from slice to slice. To evaluate the proposed methods a leave-one-out experiment was performed, using six datasets containing 274 slices to segment. Both adapted ASM schemes yield significantly better results than the original scheme (p<0.0001). The extended slice correlation fit of a one-slice model showed best overall performance. Using one manually delineated image slice as a reference, on average a number of 29 slices could be automatically segmented with an accuracy within the bounds of manual inter-observer variability.

Knowledge about the location of the diaphragm dome surface, which separates the lungs and the heart from the abdominal cavity, is of vital importance for applications like automated segmentation of adjacent organs (e.g., liver) or functional analysis of the respiratory cycle. We present a new 3D Active Appearance Model (AAM) approach to segmentation of the top layer of the diaphragm dome. The 3D AAM consists of three parts: a 2D closed curve (reference curve), an elevation image and texture layers. The first two parts combined represent 3D shape information and the third part image intensity of the diaphragm dome and the surrounding layers. Differences in height between dome voxels and a reference plane are stored in the elevation image. The reference curve is generated by a parallel projection of the diaphragm dome outline in the axial direction. Landmark point placement is only done on the (2D) reference curve, which can be seen as the bounding curve of the elevation image. Matching is based on a gradient-descent optimization process and uses image intensity appearance around the actual dome shape. Results achieved in 60 computer generated phantom data sets show a high degree of accuracy (positioning error -0.07+/-1.29 mm). Validation using real CT data sets yielded a positioning error of -0.16+/-2.95 mm. Additional training and testing on in-vivo CT image data is ongoing.

A 3D surface model for the segmentation of organic structures in CT-and MR-datasets has been developed. The training dataset for the surface model is computed from semiautomatically generated voxelsets. Triangulated meshes of the voxelsets representing the objects' surfaces are generated. The surface model is able to learn the shape variations in the training dataset by a principal component analysis of the information provided by the points forming the triangulated surface-meshes. Furthermore, the image information at the mesh points is also added into gray value models describing the gray value distribution at this particular surface section. The optimization of the model is performed by iteratively moving the surface points of the model towards image structures fitting to the gray value models. During the optimization process the models shape information assures that the surface stays plausible. A 3D-model of the spleen consisting of 10 objects, and a kidney model generated from 7 left kidneys have been developed. The models have been tested on 3 unknown spleen- and 3 unknown kidney-datasets. The total cover between the model and the organs varied between 65% and 75%, which is a respectable result in the face of the small training datasets the models were generated from.

The aim of this work is to explore the performance of active appearance models (AAMs) in reconstruction and interpretation of bones in hand radiographs. AAM is a generative approach that unifies image segmentation and image understanding. Initial locations for the AAM search are generated by an exhaustive filtering method. A series of AAMs for smaller groups of bones are used. It is found that AAM successful reconstructs 99% of metacarpals, proximal and medial phalanges and the distal 3 cm of radius and ulna. The rms accuracy is better than 240 microns (point-to-curve). The generative property is used (1) to define a measure of fit that allows the models to self-evaluate and chose between the multiple found solutions, (2) to overcome obstacles in the image in the form of rings by predicting the missing part, and (3) to detect anomalies, e.g. rheumatoid arthritis. The shape scores are used as biometrics to check the identity of patients in a longitudinal study. The conclusion is that AAM provides a highly efficient and unified framework for various tasks in diagnosis and assessment of bone related disorders.

This paper describes a novel approach to register 3D computed tomography (CT) or magnetic resonance (MR) images to a set of 2D X-ray images. Such a registration may be a valuable tool for intraoperative determination of the precise position and orientation of some anatomy of interest, defined in preoperative images. The registration is based solely on the information present in 2D and 3D images. It does not require fiducial markers, X-ray image segmentation, or construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3D MR or CT data, and gradients of intraoperative X-ray images, which are back-projected towards the X-ray source. The registration is then concerned with finding that rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. The method is tested on a lumbar spine phantom. Gold standard registration is obtained by fidicual markers attached to the phantom. Volumes of interest, containing single vertebrae, are registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the gold standard position. Target registration errors and rotation errors are in order of 0.3 mm and 0.35 degrees for the CT to X-ray registration and 1.3 mm and 1.5 degrees for MR to X-ray registration. The registration is shown to be fast and accurate.

This paper focuses on the problem of ill-posedness of deformable point set registration and we propose a new approach to restrict the solution space using shape information. The basic elements of the investigated kind of registration algorithm are a cost functional, an optimization strategy and a motion model. The motion model determines the kind of motions and deformations that are allowed and how they are restricted. The motion model itself is mainly determined by the kind of parameterized transformation used to express the motion/deformation. Here, we observe that matching with more degrees of freedom (the parameters of the transformation) than necessary can introduce mismatches due to a higher sensitivity to noise or by destroying local shape information. In this paper we propose a cost functional which is robust to noise and we introduce a new method to specify a shape adapted deformation model based on thin-plate splines and initial control point placing using point clustering. We show that these initial positions have a strong impact on the match and we define them as cluster centers where we cluster on one of the point sets (weighting each point of this set with its distance to the other point set). Our experiments with known ground truth show that the shape adapted model recovers constantly very accurately corresponding points. In our evaluation with more than 1200 single experiments we showed that, compared to a conventional octree based scheme, we could save more than 60% of degrees of freedom while preserving matching quality.

We are investigating interventional MRI guided radio- frequency (RF) thermal ablation for the minimally invasive treatment of prostate cancer. Among many potential applications of registration, we wish to compare registered MR images acquired before and immediately after RF ablation in order to determine whether a tumor is adequately treated. Warping registration is desired to correct for potential deformations of the pelvic region and movement of the prostate. We created a two-step, three-dimensional (3D) registration algorithm using mutual information and thin plate spline (TPS) warping for MR images. First, automatic rigid body registration was used to capture the global transformation. Second, local warping registration was applied. Interactively placed control points were automatically optimized by maximizing the mutual information of corresponding voxels in small volumes of interest and by using a 3D TPS to express the deformation throughout the image volume. Images were acquired from healthy volunteers in different conditions simulating potential applications. A variety of evaluation methods showed that warping consistently improved registration for volume pairs whenever patient position or condition was purposely changed between acquisitions. A TPS transformation based on 180 control points generated excellent warping throughout the pelvis following rigid body registration. The prostate centroid displacement for a typical volume pair was reduced from 3.4 mm to 0.6 mm when warping was added.

The generation of patient specific meshes for Finite Element Methods (FEM) with application to brain deformation is a time consuming process, but is essential for the modeling of intra-operative deformation of the brain during neurosurgery using FEM techniques. We present an automatic method for the generation of FEM meshes fitting patient data. The method is based on non-rigid registration of patient MR images to an atlas brain image, followed by deformation of a high-quality mesh of this atlas brain. We demonstrate the technique on brain MRI images from 12 patients undergoing neurosurgery. We show that the FEM meshes generated by our technique are of good quality. We then demonstrate the utility of these FEM meshes by simulating simple neuro-surgical scenarios on example patients, and show that the deformations predicted by our brain model match the observed deformations. The meshes generated by our technique are of good quality, and are suitable for modeling the types of deformation observed during neurosurgery. The deformations predicted by a simple loading scenario match well with those observed following the actual surgery. This paper does not attempt an exhaustive study of brain deformation, but does provide an essential tool for such a study - a method of rapidly generating Finite Element Meshes fitting individual subject brains.

This work presents a validation study for non-rigid registration of 3D contrast enhanced magnetic resonance mammography images. We are using our previously developed methodology for simulating physically plausible, biomechanical tissue deformations using finite element methods to compare two non-rigid registration algorithms based on single-level and multi-level free-form deformations using B-splines and normalized mutual information. We have constructed four patient-specific finite element models and applied the solutions to the original post-contrast scans of the patients, simulating tissue deformation between image acquisitions. The original image pairs were registered to the FEM-deformed post-contrast images using different free-form deformation mesh resolutions. The target registration error was computed for each experiment with respect to the simulated gold standard on a voxel basis. Registration error and single-level free-form deformation resolution were found to be intrinsically related: the smaller the spacing, the higher localized errors, indicating local registration failure. For multi-level free-form deformations, the registration errors improved for increasing mesh resolution. This study forms an important milestone in making our non-rigid registration framework applicable for clinical routine use.

Of the papers dealing with the task of mammogram registration, the majority deal with the task by matching corresponding control-points derived from anatomical landmark points. One of the caveats encountered when using pure point-matching techniques is their reliance on accurately extracted anatomical features-points. This paper proposes an innovative approach to matching mammograms which combines the use of a similarity-measure and a point-based spatial transformation. Mutual information is a cost-function used to determine the degree of similarity between the two mammograms. An initial rigid registration is performed to remove global differences and bring the mammograms into approximate alignment. The mammograms are then subdivided into smaller regions and each of the corresponding subimages is matched independently using mutual information. The centroids of each of the matched subimages are then used as corresponding control-point pairs in association with the Thin-Plate Spline radial basis function. The resulting spatial transformation generates a nonrigid match of the mammograms. The technique is illustrated by matching mammograms from the MIAS mammogram database. An experimental comparison is made between mutual information incorporating purely rigid behavior, and that incorporating a more nonrigid behavior. The effectiveness of the registration process is evaluated using image differences.

This paper is an extension of work first published by Fitzpatrick et al. in 1998, and concerns accuracy prediction in point-based image registration. Fitzpatrick et al. derived a formula to predict target registration error (TRE), i.e the error introduced in identifying a target point because of the inherent errors in locating the point used to calculate the registration transform. In this work, we extend Fitzpatrick's derivation to the case in which an optically tracked probe has its position measured relative to a coordinate reference frame (CRF), which is an optically tracked device that is rigidly affixed to the patient. In this case, the registration transformation is actually a composition of two transforms. Our derivation shows that the existing TRE theory may be applied independently to the two transforms that compose the registration, and the resulting values add in quadrature to give the overall TRE. We have confirmed this result using statistical numerical simulations. This derivation has important implications for designing optically tracked instruments for image-guided surgery. Probes and CRFs may be designed separately so that each has maximal accuracy, and the configuration of the two instruments will remain optimal when they are used in conjunction.

Registration of 2-D projection images and 3-D volume images is still a largely unsolved problem. In order to register a pre-operative CT image to an intra-operative 2-D x-ray image, one typically computes simulated x-ray images from the attenuation coefficients in the CT image (Digital Reconstructed Radiograph, DRR). The simulated images are then compared to the actual image using intensity-based similarity measures to quantify the correctness of the current relative pose. However, the spatial information present in the CT is lost in the process of computing projections. This paper first introduces a probabilistic extension to the computation of DRRs that preserves much of the spatial separability of tissues along the simulated rays. In order to handle the resulting non-scalar data in intensity-based registration, we propose a way of computing entropy-based similarity measures such as mutual information (MI) from probabilistic images. We give an initial evaluation of the feasibility of our novel image similarity measure for 2-D to 3-D registration by registering a probabilistic DRR to a deterministic DRR computed from patient data used in frameless stereotactic radiosurgery.

This paper describes a new MRI simulator that provides realistic images for arbitrary pulse sequences executed in the presence of static field inhomogeneities including those due to magnetic susceptibility, errors in the applied field, and chemical shift. In contrast to previous simulators, this system generates object-specific inhomogeneity patterns from first principles and propagates the consequent frequency offsets and intravoxel dephasing through the acquisition protocols to produce images with realistic artifacts. The simulator consists of two parts. Part 1 calculates a frequency offset for each voxel. It calculates the size of the static field offset at each voxel in the image based on the known magnetic susceptibility of each of the components at all voxels. It uses a novel implementation of the ?Boundary Element Method? and takes advantage of the superposition principle of magnetism to include voxels with mixtures of substances of differing susceptibilities. Part 2 produces both a signal and a reconstructed image. Its inputs include the 3D digital brain phantom introduced by the McConnell Brain Imaging Centre, frequency offsets computed by part 1, applied static field errors, chemical shift values, and a description of the acquisition protocol.

Medicine today relies on palpation as a first line of investigation in the detection and diagnosis of breast cancer. Tissue stiffness (e.g. a lump found in breast tissue) can signal the growth of a potential life threatening cell mass. As such, elastographic imaging techniques (i.e. direct imaging of tissue stiffness) have recently become of great interest to scientists. In this paper, a new method called Modality Independent Elastography (MIE) will be investigated within the context of a mammographic imaging alternative/complement. This new approach uses measures of image similarity in conjunction with computational models to reconstruct images of tissue stiffness. The real strength in MIE is that any imaging modality (e.g. magnetic resonance, computed tomography, ultrasound) in which the image intensity data remains consistent from a pre- to a post-deformed state could be used in this paradigm. Results illustrate: (1) the encoding of stiffness information within the context of a regional image similarity criterion, (2) the methodology for an iterative elastographic imaging framework and (3) successful elasticity reconstructions.

A method for 3D temporal tracking of a 3D coronary tree model through a sequence of biplane cineangiography images has been developed. A registration framework is formulated in which the coronary tree centerline model deforms in an external potential field defined by a multiscale analysis response map computed from the angiogram images. To constrain the procedure and to improve convergence, a set of three motion models is hierarchically used: a 3D rigid-body transformation, a 3D affine transformation, and a 3D B-spline deformation field. This 3D motion tracking approach has significant advantages over 2D methods: (1) coherent deformation of a single 3D coronary reconstruction preserves the topology of the arterial tree; (2) constraints on arterial length and regularity, which lack meaning in 2D projection space, are directly applicable in 3D; and (3) tracking arterial segments through occlusions and crossings in the projection images is simplified with knowledge of the 3D relationship of the arteries. The method has been applied to patient data and results are presented.

In the paper, we deal with the analysis of blood and bone marrow smears. The main aim of this long term project is to obtain a relative frequency histogram of the white blood cells of different lineage and maturity. Especially for clinical application, a proper image normalization and segmentation of the color images of blood and bone marrow smears are necessary. For the image normalization, two approaches were adopted: a) active image processing for pre acquisition standardization and b) a histogram based method for post acquisition standardization. Both methods are based on the HSI (Hue Saturation Intensity) Transform. We have developed a robust method for the declustering of the inevitable clusters of white blood cells based on a thresholded distance transform and an extended region growing algorithm that in contrast to active contours does not need any parameterization. For a successful classification, medical morphologic features are translated into feature extraction operators: the mesh structure of the cells' nucleus is analyzed using watershed transform and Gabor features, the shape of cell and nucleus is analyzed using a set of rotational invariant contour based features. The color and granularity of the cytoplasm yield further features for classification. Current work is focused on classification using the presented features.

Support Vector Machines (SVMs) are a new and radically different type of classifiers and learning machines that use a hypothesis space of linear functions in a high dimensional feature space. This relatively new paradigm, based on Statistical Learning Theory (SLT) and Structural Risk Minimization (SRM), has many advantages when compared to traditional neural networks, which are based on Empirical Risk Minimization (ERM). Unlike neural networks, SVM training always finds a global minimum. Furthermore, SVMs have inherent ability to solve pattern classification without incorporating any problem-domain knowledge. In this study, the SVM was employed as a pattern classifier, operating on mammography data used for breast cancer detection. The main focus was to formulate the best learning machine configurations for optimum specificity and positive predictive value at very high sensitivities. Using a mammogram database of 500 biopsy-proven samples, the best performing SVM, on average, was able to achieve (under statistical 5-fold cross-validation) a specificity of 45.0% and a positive predictive value (PPV) of 50.1% at 100% sensitivity. At 97% sensitivity, a specificity of 55.8% and a PPV of 55.2% were obtained.

Subsecond multi-slice spiral CT has now been recognized with its great potential in cardiac imaging, in particularly for the coronary calcification detection (CCD). Different reconstruction algorithms have been developed in order to optimize the temporal resolution and to improve the measurement accuracy. These algorithms typically incorporate retrospectively gated reconstructions based on a synchronized electrocardiography (ECG) recording. However, these algorithms consist of different approaches in choosing spatial filters, setting ECG delays, and employing the reconstruction geometry (direct fan-beam vs. parallel rebining). These differences are likely to contribute to the intrascanner and interscanner variability in the coronary calcium measurements. This paper investigates in detail about the quantitative effect on calcium detection among different approaches.

Our research builds on the hypothesis that white matter damage, in children treated for cancer with cranial spinal irradiation, spans a continuum of severity that can be reliably probed using non-invasive MR technology and results in potentially debilitating neurological and neuropsychological problems. This longitudinal project focuses on 341 quantitative volumetric MR examinations from 58 children treated for medulloblastoma (MB) with cranial irradiation (CRT) of 35-40 Gy. Quadratic mixed effects models were used to fit changes in tissue volumes (white matter, gray matter, CSF, and cerebral) with time since CRT and age at CRT as covariates. We successfully defined algorithms that are useful in the prediction of brain development among children treated for MB.

In this paper we present a robust and automated algorithm to segment lung nodules in three dimensional (3D) Computed Tomography (CT) volume dataset. The nodule is segmented out in slice-per-slice basis, that is, we first process each CT slice separately to extract two dimensional (2D) contours of the nodule which can then be stacked together to get the whole 3D surface. The extracted 2D contours are optimal as we utilize dynamic programming based optimization algorithm. To extract each 2D contour, we utilize a shape based constraint. Given a physician specified point on the nodule, we blow a circle which gives us rough initialization of the nodule from where our dynamic programming based algorithm estimates the optimal contour. As a nodule can be calcified, we pre-process a small region-of-interest (ROI), around the physician selected point on the nodule boundary, using the Expectation Maximization (EM) based algorithm to classify and remove calcification. Our proposed approach can be consistently and robustly used to segment not only the solitary nodules but also the nodules attached to lung walls and vessels.

Most of the previous approaches to computer aided lung nodule detection have been designed for and tested on conventional CT with slice thickness of 5-10 mm. In this paper, we report results of a specifically designed detection algorithm which is applied to 1 mm slice data from multi slice CT. We see two prinicipal advantages of high resolution CT data with respect to computer aided lung nodule detection: First of all, the algorithm can evaluate the fully isotropic three dimensional shape information of potential nodules and thus resolve ambiguities between pulmonary nodules and vessels. Secondly, the use of 1 mm slices allows the direct utilization of the Hounsfield values due to the absence of the partial volume effect (for objects larger than 1 mm). Computer aided detection of small lung nodules (>= 2 mm) may thus experience a break-through in clinical relevance with the use of high resolution CT. The detection algorithm has been applied to image data sets from patients in clinical routine with a slice thickness of 1\ts mm and reconstruction intervals between 0.5 and 1 mm, with hard- and soft-tissue reconstruction filters. Each thorax data set comprises 300-500 images. More than 20 000 CT slices from 50 CT studies were analyzed by the computer program, and 12 studies have so far been reviewed by an experienced radiologist. Of 203 nodules with diameter >= 2 mm (including pleura-attached nodules), the detection algorithm found 193 (sensitivity of 95%), with 4.4 false positives per patient. Nodules attached to the lung wall are algorithmically harder to detect, but we observe the same high detection rate. The false positive rate drops below 1 per study for nodules >= 4 mm.

Multi-slice computed tomography (CT) provides a promising technology for lung cancer detection and treatment. To optimize automatic detections of a more complete spectrum of lung nodules on CT requires multiple specialized algorithms in a coherently integrated detection system. We have developed a knowledge-based system for automatic lung nodule detection and analysis, which coherently integrates several robust novel detection algorithms to detect different types of nodules, including those attached to the chest wall, nodules adjacent to or fed by vessels, and solitary nodules, simultaneously. The system architecture can be easily extended in the future to include a still greater range of nodule types, most importantly so-called ground-glass opacities (GGOs). In addition, automatic local adaptive histogram analysis, dynamic cross-correlation analysis, and the automatic volume projection analysis by using by data dimension reduction method, are used in nodule detection. The proposed system has been applied to 10 patients screened with low-dose multi-slice CT. Preliminary clinical tests show that (1) the false positive rate averages about 3.2 per study; and (2) by using the system radiologists are able to detect nearly twice the number of nodules as compared with working alone.

We have developed a series of directional edge enhancement and edge extraction methods that can accurately segment posterior and anterior ribs in chest radiography. These methods can also separate the lower and upper edges of ribs. The edges were first enhanced by two sets of proximate parabola curve models for left and right sides of the image. We used a directional edge filtering technique to remove low signals and noises on the edge enhanced image in the multiresolution domain. Finally, we employed a rib curve projection and reasoning method to reconstruct the rib edges and remove false edges for the upper and lower bound of the rib edges independently. A two-step registration, corresponding to global and local matching, is applied for current and prior images assisted by their corresponding edge images. The subtraction images were then processed by a rule-based CAD system. The FROC results were compared to that obtained by the original image using a CAD system consisting of rule-based and convolution neural network processing. The majority of lung cancer in temporal subtraction images were lit-up. The FROC results were significantly improved using the subtraction image with the rule-based CAD.

The detection rate of small pulmonary lesions has recently increased due to the advances in imaging technology such as Multi-slice CT scanner. In assessing the malignant potential of small pulmonary nodules in thin-section CT images, it is important to examine the nodule internal structure. In our previous work, we found that internal structure features derived from CT density and curvature indexes such as shape index and curvedness were useful for differentiating malignant and benign nodules in 3-D thoracic CT images. This may be attributed to the texture changes in the nodule region due to a developing malignancy. The relationship between nodules and their surrounding structures such as vessel, bronchi, and pleura are another important cue to classification between malignant and benign nodules. We therefore develop a scheme to analyze surrounding structures of the nodule using differential geometry based vector fields in 3-D thoracic images. In addition we present a joint histogram-based representation approach of the internal and surrounding structures of the nodule to visualize the characteristics between nodules. In the present study, we explore the feasibility of combining internal and surrounding structure features for classification of pulmonary nodules.

In this paper we propose a new recognition method of lung nodules from x-ray CT images using 3D Markov random field (MRF) models. Pathological shadow candidates are detected by our Quoit filter which is a kind of mathematical morphology filter, and volume of interest (VOI) areas which include the shadow candidates are extracted. The probabilities of the hypotheses that the VOI areas come from nodules (which are candidates of cancers) and blood vessels are calculated using nodule and blood vessel models evaluating the relations between these object models using 3D MRF models. If the probabilities for the nodule models are higher, the shadow candidates are determined to be abnormal. Otherwise, they are determined to be normal. Experimental results for 38 samples (patients) are shown.

The purpose was to evaluate the effect of incorporating negative but suspicious regions into a knowledge-based computer-aided detection (CAD) scheme of masses depicted in mammograms. To determine if a suspicious region is positive for a mass, the region was compared not only with actually positive regions (masses), but also with known negative regions. A set of quantitative measures (i.e., a positive, a negative, and a combined likelihood measure) was computed. In addition, a process was developed to integrate two likelihood measures that were derived using two selected features. An initial evaluation with 300 positive and 300 negative regions was performed to determine the parameters associated with the likelihood measures. Then, an independent set of 500 positive and 500 negative regions was used to test the performance of the CAD scheme. During the training phase, the performance was improved from Az=0.83 to 0.87 with the incorporation of negative regions and the integration process. During the independent test, the performance was improved from Az=0.80 to 0.83. The incorporation of negative regions and the integration process was found to add information to the scheme. Hence, it may offer a relatively robust solution to differentiate masses from normal tissue in mammograms.

This study attempted to accurately segment the masses and distinguish malignant from benign tumors. The masses were segmented using a technique that combines pixel aggregation with maximum likelihood analysis. We found that the segmentation method can delineate the tumor body as well as tumor peripheral regions covering typical mass boundaries and some spiculation patterns. We have developed a Multiple Circular Path Convolution Neural Network (MCPCNN) to analyze a set of mass intensity, shape, and texture features for determination of the tumors as malignant or benign. The features were also fed into a conventional neural network for comparison. We also used values obtained from the maximum likelihood values as inputs into a conventional backpropagation neural network. We have tested these methods on 51 mammograms using a grouped Jackknife experiment incorporated with the ROC method. Tumor sizes ranged from 6mm to 3cm. The conventional neural network whose inputs were image features achieved an A_z of 0.66. However the MCPCNN achieved an A_z value of 0.71. The conventional neural network whose inputs were maximum likelihood values achieved an Az value of 0.84. In addition, the maximum likelihood segmentation method can identify the mass body and boundary regions, which is essential to the analysis of mammographic masses.

In this study, we test a new method to automatically search for matched regions in bilateral digitized mammograms and to compute differences in region conspicuities in pairs of matched regions. One hundred pairs of bilateral images of the same view were selected for the experiment. Each pair of images depicted one verified mass. These 100 mass regions, along with 356 suspicious but actually negative mass regions, were first detected by a single-image-based CAD scheme. To find the matched regions in the corresponding bilateral images, a Procrustean-type technique was used to register the two images, which corrects the deformation of tissue structure between images by guaranteeing the registration of nipples, skin lines, and chest walls. Then, a region growth algorithm was applied to generate a growth region in the matched area, which has the same effective size as the suspicious region in the abnormal image. The conspicuities in the two matched regions, as well as their differences, were computed. Using the conspicuity in the original mass regions and the difference of conspicuities in the two matched regions as two identification indices to classify this set of 456 suspicious regions, the computed areas under the ROC curves (A_z) were 0.77 and 0.75, respectively. This preliminary study indicates that by comparing the difference of conspicuities in two matched regions that a very useful feature for the CAD schemes can be extracted.

We have previously demonstrated that interval change analysis can improve differentiation of malignant and benign masses. In this study, a new classification scheme using interval change information was developed to classify mammographic microcalcification clusters as malignant and benign. From each cluster, 20 run length statistic texture features (RLSF) and 21 morphological features were extracted. Twenty difference RLSF were obtained by subtracting a prior RLSF from the corresponding current RLSF. The feature space consisted of the current and the difference RLSF, as well as the current and the difference morphological features. A leave-one-case-out resampling was used to train and test the classifier using 65 temporal image pairs (19 malignant, 46 benign) containing biopsy-proven microcalcification clusters. Stepwise feature selection and a linear discriminant classifier, designed with the training subsets alone, were used to select and merge the most useful features. An average of 12 features were selected from the training subsets, of which 3 difference RLSF and 7 morphological features were consistently selected from most of the training subsets. The classifier achieved an average training A_z of 0.98 and a test A_z of 0.87. For comparison, a classifier based on the current single image features achieved an average training A_z of 0.88 and test A_z of 0.81. These results indicate that the use of temporal information improved the accuracy of microcalcification characterization.

We are developing new techniques to improve the accuracy of computerized microcalcification detection by using the joint two-view information on craniocaudal (CC) and mediolateral-oblique (MLO) views. After cluster candidates were detected using a single-view detection technique, candidates on CC and MLO views were paired using their radial distances from the nipple. Object pairs were classified with a joint two-view classifier that used the similarity of objects in a pair. Each cluster candidate was also classified as a true microcalcification cluster or a false-positive (FP) using its single-view features. The outputs of these two classifiers were fused. A data set of 38 pairs of mammograms from our database was used to train the new detection technique. The independent test set consisted of 77 pairs of mammograms from the University of South Florida public database. At a per-film sensitivity of 70%, the FP rates were 0.17 and 0.27 with the fusion and single-view detection methods, respectively. Our results indicate that correspondence of cluster candidates on two different views provides valuable additional information for distinguishing false from true microcalcification clusters.

One potential limitation of computer-aided diagnosis (CAD) studies is that a computerized method may be trained and tested on a database comprised of a limited number of cases. Thus, the performance of the CAD method may depend on the subtlety of the lesions (i.e., the case mix) in the database. The purpose of this study is to evaluate the effect of case-mix on feature selection and the performance of a computerized classification method trained on a limited database.

While investigators have been successful in developing methods for the computerized analysis of mammograms and ultrasound images, optimal output strategies for the effective and efficient use of such computer analyses are still undetermined. We have incorporated our computerized mass classification method into an intelligent workstation interface that displays known malignant and benign cases similar to lesions in question using a color-coding scheme that allows instant visual feedback to the radiologist. The probability distributions of the malignant and benign cases in the known database are also graphically displayed along with the graphical location of the unknown case relative to these two distributions. The effect of the workstation on radiologists' performance was demonstrated with two preliminary studies. In each study, participants were asked to interpret cases without and with the computer output as an aid for diagnosis. Results from our demonstration studies indicate that radiologists' performance, especially specificity, increases with the use of the aid.

In parallel beam computed tomography, the measured projections at conjugate views are mathematically identical, and, consequently, this symmetry can be exploited for reducing either the scanning angle or the size of the detector arrays. However, in single-photon emission computed tomography (SPECT), because the gamma-rays in the conjugate views suffer different photon attenuation, the measured projections at conjugate views are generally different. Therefore, it had been widely considered that projections measured data over a full angular range of 360 degrees and over the whole detector face are generally required for exactly reconstructing the distributions of gamma-ray emitters. Recently, it has been revealed that exact image can be reconstructed from projections acquired with a full detector over disjoint angular intervals whose summation is 180 degree when the attenuation medium is uniform. In this work, we show that exact SPECT images can also be reconstructed from projections over 360 degrees, but acquired with a half detector viewing half of the image space. We present an heuristic perspective that supports this claim for SPECT with both uniform and non-uniform attenuation.

Multi-slice CT scanners use EKG gating to predict the cardiac phase during slice reconstruction from projection data. Cardiac phase is generally defined with respect to the RR interval. The implicit assumption made is that the duration of events in a RR interval scales linearly when the heart rate changes. Using a more detailed EKG analysis, we evaluate the impact of relaxing this assumption on image quality. We developed a reconstruction algorithm that analyzes the associated EKG waveform to extract the natural cardiac states. A wavelet transform was used to decompose each RR-interval into P, QRS, and T waves. Subsequently, cardiac phase was defined with respect to these waves instead of a percentage or time delay from the beginning or the end of RR intervals. The projection data was then tagged with the cardiac phase and processed using temporal weights that are function of their cardiac phases. Finally, the tagged projection data were combined from multiple cardiac cycles using a multi-sector algorithm to reconstruct images. The new algorithm was applied to clinical data, collected on a 4-slice (GE LightSpeed Qx/i) and 8-slice CT scanner (GE LightSpeed Plus), with heart rates of 40 to 80 bpm. The quality of reconstruction is assessed by the visualization of the major arteries, e.g. RCA, LAD, LC in the reformat 3D images. Preliminary results indicate that Cardiac State Driven reconstruction algorithm offers better image quality than their RR-based counterparts.

Because the effects of physical factors such as photon attenuation and spatial resolution are distance-dependent in single-photon emission computed tomography (SPECT), it has been widely assumed that accurate image reconstruction requires knowledge of the data function over 2(π) . In SPECT with uniform attenuation, Noo and Wagner recently showed that an accurate image can be reconstructed from knowledge of the data function over a contiguous (π) -segment. More generally, we proposed (π) -scheme SPECT that entails data acquisition over disjoint angular intervals without conjugate views, totaling to (π) radians, thereby allowing flexibility in choosing projection views at which the emitted gamma-rays may undergo the least attenuation and blurring. In this work, we study the general properties of the (π) -scheme inverse exponential Radon Transform, and discuss how to take advantage of the (π) -scheme flexibility to improve noise properties of short-scan SPECT.

In this paper the contrast source inversion method using a multiplicative weighted L²-norm total variation regularizer is applied to image reconstructions from electromagnetic microwave tomography experiments. This iterative method avoids solving a full forward problem in each iteration which makes the method suitable to handle a large scale computational problem. The numerical results from experimental data with high contrast biological phantom are presented and discussed.

We consider using spline interpolation to improve the standard filtered backprojection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram. The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation. We consider three different approaches. In the first, we simply adapt the standard FBP for spline interpolation. In the second approach, we replace the interpolation by an oblique projection onto the same spline space; this increases the peak signal-noise ratio by up to 2.5 dB. In the third approach, we perform an explicit discretization by observing that the ramp filter is equivalent to a fractional derivative operator that can be evaluated analytically for splines. This allows for an exact implementation of the ramp filter and improves the image quality by an additional 0.2 dB. This comparison is unique as the first method has been published only for degree n=0, whereas the two other methods are novel. We stress that the modification of the filter improve the reconstruction quality especially at low (faster) interpolation degrees n=0,1; the difference between the methods become marginal for cubic or higher degrees (n ≥ 3).

We present a novel reconstruction scheme for cardiac spiral imaging named Adaptive Cardiac Multiple Plane Reconstruction (ACMPR) which takes into account the conical shape of projection data. In cardiac imaging with multi-slice CT continuous data acquisition in spiral mode combined with the parallel acquisition of the patient's ECG enable retrospective gating of data segments for image reconstruction. ACMPR identified projection data segments <EQ(pi) using temporal information of the simultaneously recorded ECG. For each such data segment image stacks of double-oblique segment images are reconstructed and then reformatted to axial images separately. In case of multisector imaging using consecutive heart cycles for image formation the reformatted segment images have to be added to a complete CT image after the reformation step. Image results for multi-slice detector systems using an anthropomorphic computer model of the human heart will be shown. A detailed comparison to algorithms without cone- correction reveals that ACMPR does not lead to significant improvements for 16-slice detector systems but already for a 32-slice system ACMPR provides superior image quality, in particular coronaries and stents are images with less geometrical distortions.

Digital tomosynthesis mammography is an advanced x-ray application that can provide detailed 3D information about the imaged breast. We introduce a novel reconstruction method based on simple backprojection, which yields high contrast reconstructions with reduced artifacts at a relatively low computational complexity. The first step in the proposed reconstruction method is a simple backprojection with an order statistics-based operator (e.g., minimum) used for combining the backprojected images into a reconstructed slice. Accordingly, a given pixel value does generally not contribute to all slices. The percentage of slices where a given pixel value does not contribute, as well as the associated reconstructed values, are collected. Using a form of re-projection consistency constraint, one now updates the projection images, and repeats the order statistics backprojection reconstruction step, but now using the enhanced projection images calculated in the first step. In our digital mammography application, this new approach enhances the contrast of structures in the reconstruction, and allows in particular to recover the loss in signal level due to reduced tissue thickness near the skinline, while keeping artifacts to a minimum. We present results obtained with the algorithm for phantom images.

Nonrectilinear k-space trajectories are often used in MRI applications due to their inherent fast acquisition and immunity to motion and flow artifacts. In this work, we develop a more general formulation for the problem of resampling under the same assumptions as previous techniques. The new formulation allows the new technique to overcome the present problems with these techniques while maintaining a reasonable computational complexity. The image space is decomposed into a complete set of orthogonal basis functions. Each function is sampled twice, once with a rectilinear trajectory and the other with a nonrectilinear trajectory resulting in two vectors of samples. The mapping matrix that relates the two sets of vectors is obtained by solving the set of linear equations obtained using the training basis set. In order to reduce the computational burden at the reconstruction time, only a few nonrectilinear samples in the neighborhood of the point of interest are used. The proposed technique is applied to simulated data and the results show a superior performance of the proposed technique in both accuracy and noise resistance and demonstrate the usefulness of the new technique in the clinical practice.

The effect of reconstruction parameters on the fan-beam filtered backprojection method in myocardial defect detection was investigated using an observer performance study and receiver operating characteristics (ROC) analysis. A mathematical phantom of the human torso was used to model the anatomy and Thallium-201 (Tl-201) uptake in humans. Half-scan fan-beam realistic projections were simulated using a low-energy high resolution (LEHR) collimator that incorporated the effects of photon attenuation, spatially varying detector response, scatter, and Poison noise. A focal length of 55 cm and a radius of rotation of 25 cm were used, which resulted to a magnification of two at the center of rotation and a maximum magnification of three in the reconstructed region of interest. By changing the reconstruction pixel size, five different projection bin width to reconstruction pixel size (PBWRPS) ratios were obtained which resulted in five classes of reconstructed images. Myocardial defects were simulated as Gaussian-shaped decreases in Tl-201 uptake distribution. The total projection count per 3 mm image slice was 44,000. A total of 96 reconstructed transaxial images from each one of the five classes were shown to eight observers for evaluation. The results indicate that the reconstruction pixel size has a significant effect on the quality of fan-beam SPECT images. Moreover, the study indicated that in order to ensure best image quality the PBWRPS ratio should be at least as large as the maximum possible magnification inside the reconstructed image array.

A new method to reduce the streak artifacts caused by high attenuation objects in CT images has been developed. The key part of this approach is a preprocessing procedure based on the raw projection data using an adaptive scaling-plus-filtering method. The procedure is followed by the conventional filtered-back projection to reconstruct artifact-reduced images. Phantom and clinical studies have demonstrated that the proposed method can effectively reduce the streak artifacts caused by high attenuation objects for different anatomical structures and metal materials while still faithfully reproduce the positions and dimensions of the metal objects. The visualization of tissue features adjacent to metal objects is greatly improved. The proposed method is computational efficient and can be easily adapted to the current commercial CT scanners.

Vertebroplasty is one of the newest surgical approaches for the treatment of the osteoporotic spine. Recent studies have shown that it is a minimally invasive, safe, promising procedure for patients with osteoporotic fractures while providing structural reinforcement of the osteoporotic vertebrae as well as immediate pain relief. However, treatment failures due to excessive bone cement injection have been reported as one of complications. It is believed that control of bone cement volume seems to be one of the most critical factors in preventing complications. We believed that an optimal bone cement volume could be assessed based on CT data of a patient. Gray-level run length analysis was used to extract textural information of the trabecular. At initial stage of the project, four indices were used to represent the textural information: mean width of intertrabecular space, mean width of trabecular, area of intertrabecular space, and area of trabecular. Finally, the area of intertrabecular space was selected as a parameter to estimate an optimal bone cement volume and it was found that there was a strong linear relationship between these 2 variables (correlation coefficient = 0.9433, standard deviation = 0.0246). In this study, we examined several factors affecting overall procedures. The threshold level, the radius of rolling ball and the size of region of interest were selected for the sensitivity analysis. As the level of threshold varied with 9, 10, and 11, the correlation coefficient varied from 0.9123 to 0.9534. As the radius of rolling ball varied with 45, 50, and 55, the correlation coefficient varied from 0.9265 to 0.9730. As the size of region of interest varied with 58 x 58, 64 x 64, and 70 x 70, the correlation coefficient varied from 0.9685 to 0.9468. Finally, we found that strong correlation between actual bone cement volume (Y) and the area (X) of the intertrabecular space calculated from the binary image and the linear equation Y = 0.001722 X - 2.10922. We could see that this equation slightly overestimated bone cement volume and those amounts would not make any serious complications. We hope this will help to control a proper amount of bone cement volume injection during vertebroplasty.

We previously developed bone texture analysis methods to assess bone strength on digitized radiographs. Here, we compare the analyses performed on digitized screen-film to those obtained on peripheral bone densitometry images. A leg phantom was imaged with both a PIXI (GE Medical Systems; Milwaukee, WI) bone densitometer (0.200-mm pixel size) and a screen-film system, with the films being subsequently digitized by a laser film digitizer (0.100-mm pixel size). The phantom was radiographically scanned multiple times with the densitometer at the default parameters and for increasing exposure times. Fourier-based texture features were calculated from regions of interest from images from both modalities. The bone densitometry images contained more quantum noise than the radiographs resulting in increased values for the first moment of the power spectrum texture feature (1.22 times higher than from the standard radiograph). Presence of such noise may adversely affect the texture feature's ability to distinguish between strong and weak bone. By either increasing the exposure time or averaging multiple scans in the spatial frequency domain, we showed a reduction in the effect of the quantum mottle on the first moment of the power spectrum.

We present a new approach for estimating parameters of Gaussian mixture model by Genetic Algorithms (Gas) and Expectation Maximization (EM). It has been shown that Gas is independent of initialization parameters. In this work we propose combination of Gas and EM algorithms (GA-EM) for learning Gaussian mixture components to achieve accurate parameter estimation independent of initial values. To assess the performance of the proposed method, a series of Gaussian phantoms, based on modified Shepp-Logan method, were created. In this phantom, each tissue segment presents a Gaussian density function that its mean and variance can be controlled. EM, Gas and GAs-EM were employed to estimate the tissue parameters in each phantom. The results indicate that EM algorithm, as expected is heavily impacted by the initial values. Coupling Gas with EM not only improves the overall accuracy, it also provides estimates that are independent of initial seed values. The proposed method offers a solution for accurate and stable solution for parameter estimation in for Gaussian mixture models, with higher likelihood of achieving global optimal. Obtaining such accurate parameter estimation is a key requirement for several image segmentation approaches, which rely on a priori knowledge of tissue distribution.

This paper presents the results of applying the modified deterministic annealing (DA) algorithm to simulated and clinical magnetic resonance (MR) brain data with multiple sclerosis (MS) lesions. Modified deterministic annealing algorithm is a very efficient segmentation algorithm for isolating MS lesions in the MR images when utilizing all the information contained in all modalities. To fully utilize the information contained in all the modalities, vector segmentation is carried out instead of unimodal segmentation. The vectors to be clustered are formed by multi-modal MR brain data. Through some arithmetic manipulations synthesized image data can be obtained which greatly alleviate the effect of noise and intensity inhomogeneity. Isolated multiple sclerosis lesions are outliers to the brain tissues. Even with noise level up to 7% the MS MR brain data can still be satisfactorily segmented. This method does not need a prior model, and is conceptually very simple. It delineates not only large lesions but small ones as well. The whole process is completely automated without any intervention by an operator, which can be a very promising tool for MS follow-up studies. Comparison between the segmentation results from the simulated MS brain data and from the clinical MS brain data shows that with the current high quality MRI facilities, images with noise above 3% and intensity inhomogeneity above 20% will usually not be produced. Segmentation results for the clinical data are much better and easier to obtain than the simulated noisy data. To get even better results for the MS lesions, inverse problem techniques have to be applied. Noise model and intensity inhomogeneity model have to be established and improved using the given MRI data during iteration.

Three-dimensional (3-D) vessel trees can provide useful visual and quantitative information during interventional procedures. To calculate the 3-D vasculature from biplane images, the transformation relating the imaging systems (i.e., the rotation matrix R and the translation vector t) must be determined. We have developed a technique to calculate these parameters, which requires only the identification of approximately corresponding vessel regions in the two images. Initial estimates of R and t are generated based on the gantry angles, and then refined using an optimization technique. The objective function to be minimized is determined as follows. For each endpoint of each vessel in the first image, an epipolar line in the second image is generated. The intersection points between these two epipolar lines and the corresponding vessel centerline in the second image are determined. The vessel arclength between these intersection points is calculated as a fraction of the entire vessel region length in the image. This procedure is repeated for every vessel in each image. The value of the objective function is calculated from the sum of these fractions, and is smallest when the total fractional arclength is greatest. The 3-D vasculature is obtained from the optimal R and t using triangulation, and vessel curvature is then determined. This technique was evaluated using simulated curves and vessel centerlines obtained from clinical images, and provided rotational, magnification and relative curvature errors of 1 degree(s), 1% and 14% respectively. Accurate 3-D and curvature measures may be useful in clinical decision making, such as in assessing vessel tortuousity and access, during interventional procedures.

Thinning on binary images is widely discussed in the past three decades. A binary image can be obtained by thresholding a gray-level image. For preventing possible information losses in the thresholding process, it may be natural to design thinning algorithms directly on the original gray-level images. This paper proposes a two-step template-based thinning algorithm on gray-level images. The first step of the algorithm is to extract 4-connected gray-level skeletons from gray-level objects. The second step is to extract 8-connected gray-level skeletons from the consequent result of the first step.

During the last years, three-dimensional X-ray imaging has become a well-established imaging modality, setting the golden standard for spatial resolution in three-dimensional X-ray imaging. Firstly introduced on a motorized C-arm system, it gained benefit from the high spatial resolution of the image intensifier. Using cone-beam reconstruction, it provided fast access to truly three-dimensional imaging with isotropic voxel dimensions. However, the non-rigid mechanics and the image distortion in the image intensifier required dedicated calibration processes and obligated the developers to use the most stable and reliable system in the C-arm device family. The need for system calibration also required the system to be able to reproducibly adjust the C-arm to the pre-calibrated positions, which seemed only possible with the motorized movement of a high-end system. On mobile, non-motorized C-arm systems, which are often used for guiding surgical procedures, however, 3D application has not been feasible due to the non-reproducibility of the mechanical movement. In this paper, first results regarding the feasibility of this approach are presented. The data were acquired on a Philips BV 26 surgical C-arm. This device is fully movable. The C arc is adjusted manually.

Before a retrospective registration algorithm can be used routinely in the clinic, methods must be provided for distinguishing between registration solutions that are clinically satisfactory and those that are not. One approach is to rely on a human observer. Here, we present an algorithmic procedure for assessing quality that discriminates between badly misregistered pairs and those that are clinically useful.

Non-rigid image registration is a prerequisite for many medical imaging applications such as change analysis in image-based diagnosis and therapy assessment. Nonlinear interpolation methods may be used to recover the deformation if the correspondence of the extracted feature points is available. However, it may be very difficult to establish such correspondence at an initial stage when confronted with large and complex deformation. In this paper, a mixture of principal axes registration (mPAR) is proposed to tackle the correspondence problem using a neural computation method. The feature is to align two point sets without needing to establish the explicit point correspondence. The mPAR aligns two point sets by minimizing the relative entropy between their probability distributions resulting in a maximum likelihood estimate of the transformation mixture. The neural computation for the mPAR is developed using a committee machine to obtain a mixture of piece-wise rigid registrations. The complete registration process consists of two steps: (1) using the mPAR to establish an improved point correspondence and (2) using a multilayer perceptron (MLP) neural network to recover the nonlinear deformation. The mPAR method has been applied to register a contrast-enhanced magnetic resonance (MR) image sequence. The experimental results show that our method not only improves the point correspondence but also results in a desirable error-resilience property for control point selection errors.

Nonrigid registration of medical images is an important procedure in many aspects of current biomedical and bioengineering research. For example, it is a necessary step for studying the variation of biological tissue properties, such as shape or diffusion properties across population, compute population averages, or atlas-based segmentation. Recently we have introduced the Adaptive Bases registration algorithm as a general method for performing nonrigid registration of medical images and we have shown it to be faster and more accurate than existing algorithms of the same class. The overall properties of the Adaptive Bases algorithm are reviewed here and the method is validated on applications that include the computation of average images, atlas based segmentation, and motion correction of video images. Results show the Adaptive Bases algorithm to be capable of producing high quality nonrigid matches for the applications above mentioned.

This paper provides initial analysis of a new consistent, large-deformation elastic image registration (CLEIR) algorithm that jointly estimates a consistent set of forward and reverse transformations between two images. The estimated transformations are able to accommodate large deformations while constraining the forward and reverse transformations to be inverses of one another. The algorithm assumes that the two N-dimensional images to be registered contain topologically similar objects and were collected using the same imaging modality. The image registration problem is formulated in a (N+1)-dimensional space where the additional dimension is referred to as the temporal or time dimension. A periodic-in-time, nonlinear, (N+1)-dimensional transformation is estimated that deforms one image into the shape of the other and back again. Large deformations from one image to the other are accommodated by concatenating the small-deformation incremental transformations from one time instant to the next. An inverse consistency constraint is placed on the incremental transformations to enforce within a specified tolerance that the forward and reverse transformations between the two images are inverses of each other. The feasibility of the algorithm for accommodating nonlinear deformations was demonstrated using 2D synthesized phantom images and CT inner ear images. The effect of varying the number of intermediate templates was studied for these data sets.

This paper presents a technique for determining a tooth's pose given a dental plaster cast and a set of generic tooth models. The ultimate goal of pose estimation is to obtain information about the sizes and positions of the roots, which lie hidden within the gums, without the use of X-rays, CT or MRI. In our approach, the tooth of interest is first extracted from the 3D dental cast image through segmentation. 2D views are then generated from the extracted tooth and are matched against a target view generated from the generic model with known pose. Additional views are generated in the vicinity of the best view and the entire process is repeated until convergence. Upon convergence, the generic tooth is superimposed onto the dental cast to show the position of the root. The results of applying the technique to canines demonstrate the excellent potential of the algorithm for generic tooth fitting.

In the single-photon emission computed tomography (SPECT), it is highly desirable to provide physicians with a measure of the strength of the liver-heart cross talk as a means of assessing the quality of the images, so that appropriate actions can be taken to avoid false diagnosis. Liver-heart cross talk is an phenomenon in which the liver count interferes with the heart count in 3D reconstruction, which generates artifacts in the reconstructed images. In this paper, we propose an automatic method for quantification of such liver-heart cross talk. The system performs heart detection followed by non-heart organ segmentation and quantification of their activities. An appearance-based approach is applied to find the heart center in each image, with invariance to image intensity and contrast. Then heart and non-heart activities are quantified in each image. A measurement formula is proposed to compute the amount of liver-heart cross talk as a function of the size of the non-heart activity regions, of the strengths of the heart and non-heart activities, and of the distance of the non-heart regions to the heart. The method has been tested on 150 patient studies of different isotopes and acquisition types, with very promising results.

A novel figure-of-merit (FOM) for automatically quantifying the types of artifacts that appear in compressed images was investigated. This FOM is based on task specific linear combinations of magnitude, frequency and 'localized' structure information derived from difference images. For each elemental diagnostic task (e.g., detection of microcalcifications) a value is calculated as the weighted linear combination of the output of an array of filters, and the FOM is defined to be the maximum of these values, taken over all relevant diagnostic tasks. This FOM was tested by applying it to a previously assembled set of 60 mammograms that had been digitized and compressed at five different compression levels using our version of the original JPEG algorithm. The FOM results were compared to subjective assessments of image quality provided by nine radiologists. A subset consisting of 25 images was also processed with the JPEG 2000 algorithm and evaluated by the FOM. A significant correlation existed between readers' subjective ratings and FOMs for JPEG compressed images. A comparison between the results of the two compression algorithms reveals that, to achieve a comparable FOM level, the JPEG 2000 images were compressed at a bitrate that was typically 15% lower than that of images compressed with the original JPEG algorithm.

In this paper, a JPEG domain image watermarking method that utilizes spatial masking is presented. The watermarking algorithm works in the compressed domain, and can be implemented efficiently in real-time (only 50ms is required for a 512x512 24-bit color image on a 700MHz computer). In many applications, particularly those associated with delivering images over the Internet, the ability to watermark images in real-time is required. In order to achieve a real-time watermarking capability, the proposed technique avoids many of the computation steps associated with JPEG compression. Specifically, the forward and inverse DCT do not need to be calculated, nor do any of the computations associated with quantization. Robustness to JPEG compression and additive noise attacks is achieved with the proposed system, and the relationship between watermark robustness and watermark position is described. A further advantage of the proposed method is that it allows a watermark to be detected in an image without referencing to the original unwatermarked image, or to any other information used in the watermark embedding process.