This paper presents two new expressions for estimating registration accuracy in point-based rigid-body registration and points out a danger in using the traditional measure of registration accuracy. In this work we present two major results: we first derive an approximate expression for (TRE²), and we then use this to calculate the expected squared alignment error for individual fiducials. This leads to a surprising conclusion--the registration accuracy is generally worst near the fiducials which are most closely aligned. This should demonstrate the danger of relying on the traditional accuracy measure, namely fiducial registration error, to judge the quality of a registration.

In this contribution, we are concerned with the detection and refined localization of 3D point landmarks. We propose multi-step differential procedures which are generalizations of an existing two-step procedure for subpixel localization of 2D point landmarks. This two-step procedure combines landmark detection by applying a differential operator with refined localization through a differential edge intersection approach. In this paper, we theoretically analyze the localization performance of this procedure for analytical models of a Gaussian blurred L-corner as well as a Gaussian blurred ellipse. By varying the model parameters differently tapered and curved structures are represented. The results motivate the use of an analogous procedure for 3D point landmark localization. We generalize the edge intersection approach to 3D and, by combining it with 3D differential operators for landmark detection, we propose three multi-step procedures for subvoxel localization of 3D point landmarks. The multi-step procedures are experimentally tested for 3D synthetic images and 3D MR images of the human head. We show that the multi-step procedures significantly improves the localization accuracy in comparison to applying a 3D detection operator alone.

During an interventional neuroradiology exam, knowing the exact location of the catheter tip with respect to the patient can dramatically help the physician. An image registration between digital subtracted angiography (DSA) images and a volumic pre-operative image (magnetic resonance or computed tomography volumes) is a way to infer this important information. This mono-patient multimodality matching can be reduced to finding the projection matrix that transforms any voxel of the volume onto the DSA image plane. This modelization is unfortunately not valid in the case of distorted images, which is the case for DSA images. A classical angiography room can now generate 3D X-ray angiography volumes (3DXA). Since the DSA images are obtained with the same machine, it should be possible to deduce the projection matrix from the sensor data indicating the current machine position. We propose an interpolation scheme, associated to a pre-operative calibration of the machine that allows us to correct the distortions in the image at any position used during the exam with a precision of one pixel. Thereafter, we describe some calibration procedures and an associated model of the machine that can provide us with a projection matrix at any position of the machine. Thus, we obtain a machine-based 2D DSA/3DXA registration. The misregistration error can be limited to 2.5 mm if the patient is well centered within the system. This error is confirmed by a validation on a phantom of the vascular tree. This validation also yields that the residual error is a translation in the 3D space. As a consequence, the registration method presented in this paper can be used as an initial guess to an iterative refining algorithm.

Longitudinal magnetic resonance spectroscopy (MRS) studies require accurate repositioning of the volume of interest (VOI) over which measurements are made. In this work we present and evaluate a method for the image-guided repositioning of brain volumes of interest. The point-based registration technique we developed allows the repositioning to be performed on-line (i.e., while the patient is in the scanner). MR image volumes were acquired from six subjects, three scans each over the course of a month. During the first scan, two spectroscopy VOIs are visually selected: one in the frontal white matter, the other in the superior cerebellar vermis. The coordinates of 13 internal brain landmarks were also identified. During both subsequent scans, the same 13 landmarks were also identified, and the transformation that registers the first set of landmarks to the subsequent set is compared. This result is used to automatically map the position of the spectroscopy. VOIs from the first volume to the current volume. For the six subjects evaluated to date, we show an average repositioning error of the spectroscopy VOIs in the order of 1 mm. This accuracy allows us to conclude that any variation in the MR spectra are unlikely to be due to repositioning error.

Inter-subject coregistration is a powerful neuroimaging technique that enables comparison and detection of morphological differences across groups of subjects. The present study uses digital phantoms to evaluate errors in two widely employed approaches to inter-subject coregistration of structural MR images of the brain: the manual step-wise approach and the automated method provided with the software package SPM96. Phantoms were constructed by deforming a high resolution T1-weighted MR image in which we have embedded 12 landmarks. For the manual method the accuracy ranged from 0.8 mm in quadrigeminal plate to 2.4 mm in superior central sulcus and occipital lobe. The average error was 1.5 mm. For the automated SPM96 method and the 9 parameter model, the accuracy ranged from 0.8 mm to 2.1 mm and averaged 1.1 mm. Error of the manual method correlated strongly with the distance from the center of the image (r equals 0.77, slope equals .020, p equals .003). The linear correlation of the error obtained with the automated method with the distance was poor (r equals 0.39, slope equals .008, p > 0.2). The results suggest that the inferior performance of the manual method is due to its step-wise approach and to a relatively large rotational error.

We recently reported a hybrid registration technique that uses a weighted combination of multiple geometrical feature shapes. In this study we use the weighted geometrical feature (WGF) algorithm to register CT images of the head to physical space using the skin surface only, the bone surface only, and various weighted combinations of these surfaces and one fiducial point (centroid of a bone-implanted marker). We use data acquired from six patients that underwent temporal lobe craniotomies for the resection of cerebral lesions. Each patient had four external markers attached to transcutaneous posts screwed into the outer table of the skull. We evaluate and compare the accuracy of the registrations obtained using these various approaches by using as a gold standard the registration obtained using three of the four bone-implanted markers (the remaining marker is used in the various combinations). The results demonstrate that a combination of geometrical features can improve the accuracy of CT-to-physical space registration. The WGF algorithm might thus be useful in various image- guided surgical systems.

We describe a new method for rigid registration of a pre- operative CT-scan image to a set of intra-operative x-ray fluoroscopic images, for guiding a surgical robot to its trajectory planned from CT. Our goal is to perform the registration, i.e. compute a rotation and translation of one data set with respect to the other to within a prescribed accuracy, based upon bony anatomy only, without external fiducial markers.

More than 250,000 lumbar spin operations are performed annually in the United States. Because of this large number of projected surgeries, improvements in surgical procedures can have a tremendous practical impact. We are developing a method to quickly and accurately register surface points extracted from ultrasound images of a vertebra to surfaces extracted from computed tomography images. Identification of surface points in ultrasound images is a challenging task, since points must be extracted in real time and sine large portions of the vertebral surface are invisible in the ultrasound image.

In this study we have examined errors in measurements of vertebral heights and vertebral area resulting from spin rotation and projection effects in x-ray images. Measurement errors were evaluated with phantom images, and simulated rotations of a 3D spine model. An active contour model (snake) was used for measurements of vertebral area. The model contained two pressure parameters which were needed to obtain good fits of the snake to upper and lower edges (endplates) of rotated vertebral bodies. Details of the snake model are included in this report. The results of this study indicate that six point vertebral morphometry can result to significant measurement errors, representing an overestimation of vertebral height and area, in cases showing projection effects and concealed endplate contours. In serial studies, such errors could produce the erroneous appearance of `growing' vertebral bodies. One can improve the accuracy of the morphometric analysis by using additional fiducial points placed on corresponding endplate contours. Additional useful information on fracture and vertebral deformity can be obtained by accurately tracking edge contours, using an active contour model, or comparable techniques.

A reliable and accurate registration technique is a critical requirement for computerized analysis of temporal changes of suspicious lesions in mammograms. Temporal mammographic changes manifest as `neodensities' and may, sometimes, be the only finding carcinoma. Because of the elasticity of the breast tissue, the absence of obvious landmarks, and the large variability in the relative position of the breast tissue projected on to the mammogram from one examination to the other, conventional registration techniques are not applicable to registration of breast images. We are developing an automated regional registration technique to simulate the method used by radiologists for identifying corresponding lesions on mammograms.

Automated multi-modality 3D medical image alignment has been an active area of research for many years. There have been a number of recent papers proposing and investigating the use of entropy derived measures of brain image alignment. Any registration measure must allow us to choose between transformation estimates based on the similarity of images within their volume of overlap. Since 3D medical images often have a limited extent and overlap, the similarity measure for the two transformation estimates may be derived from two very different regions within the images. Direct measures of information such as the joint entropy and mutual information will therefore be a function of, not only image similarity in the region of overlap, but also of the local image content within the overlap. In this paper we present a new measure, normalized mutual information, which is simply the ratio of the sum of the marginal entropies and the joint entropy. The effect of changing overlap on current entropy measures and this normalized measure are compared using a simple image model and experiments on clinical MR-PET and MR-CT image data. Results indicate that the normalized entropy measure provides significantly improved behavior over a range of imaged fields of view.

Recent studies indicate that maximizing the mutual information of the joint histogram of two images is an accurate and robust way to rigidly register two mono- or multimodal images. Using mutual information for registration directly in a local manner is often not admissible owing to the weakened statistical power of the local histogram compared to a global one. We propose to use a global joint histogram based on optimized mutual information combined with a local registration measure to enable local elastic registration.

Previous image registration schemes based on mutual information use Shannon's entropy measure, and they have been successfully applied for mono- and multimodality registration. There are cases, however, where maximization of mutual information does not lead to the correct spatial alignment of a pair of images. Some failures are due to the presence of local or spurious global maxima. In this paper we explore whether the normalization of mutual information via the use of a weight based on the size of region of overlap, improves the rate of successful alignments by reducing the presence of suboptimal extrema. In addition, we examine the utility of a deterministic entropy measure. The results of the present study indicate that: (1) the normalized mutual information provides a larger capture range and is more robust, with respect to optimization parameters, than the non-normalized mutual information, and (2) the optimization of mutual information with the deterministic entropy measure takes, on average, fewer iterations than when using Shannon's entropy measure. We conclude that the normalized mutual information using the deterministic entropy measure is a faster and more robust function for registration than the traditional mutual information.

Although a large variety of image registration methods have been described in the literature, only a few approaches have attempted to address the rigid registration of medical images showing gross dissimilarities (due for instance to lesion evolution). In the present paper, we develop driven registration algorithms, relying on robust pixel similarity metrics, that enable an accurate (subvoxel) rigid registration of dissimilar single or multimodal 2D/3D images. In the proposed approach, gross dissimilarities are handled by considering similarity measures related to robust M-estimators. A `soft redescending' estimator (the Geman- McClure p-function) has been adopted to reject gross image dissimilarities during the registration. The registration parameters are estimated using a top down stochastic multigrid relaxation algorithm. Thanks to the stochastic multigrid strategy, the registration is not affected by local minima in the objective function and a manual initialization near the optimal solution is not necessary. The proposed robust similarity metrics compare favorably to the most popular standard similarity metrics, on patient image pairs showing gross dissimilarities. Two case studies are considered: the registration of MR/MR and MR/SPECT image volumes of patients suffering from multiple sclerosis and epilepsy.

MRI has been proposed as an alternative method to mammography for detecting and staging breast cancer. Recent studies have shown that architectural features of breast masses may be useful in improving specificity. Since fractal dimension (fd) has been correlated with roughness, and border roughness is an indicator of malignancy, the fd of the mass border is a promising architectural feature for achieving improved specificity. Previous methods of estimating the fd of the mass border have been unreliable because of limited data or overlay restrictive assumptions of the fractal model. We present preliminary results of a statistical approach in which a sample space of fd estimates is generated from a family of self-affine fractal models. The fd of the mass border is then estimated from the statistics of the sample space.

Texture is an important attribute which is widely used in various image analysis applications. Among texture features, morphological texture features are least utilized in medical image analysis. From a computational standpoint, extracting morphological texture features from an image is a challenging task. The computational problem is made even greater in medical imaging applications where large images such as mammograms are to be analyzed. This paper discusses an efficient method to compute morphological texture features for any geometry of a structuring element corresponding to a texture type. A benchmarking of the code on three machines (Sun SPARC 20, Pentium II based Dell 400 workstation, and SGI Power Challenge 10000XL) as well as a parallel processing implementation was performed to obtain an optimum processing configuration. A sample processed mammogram is shown to illustrate the code outcome.

This paper describes a method of distinguishing between early malignant melanoma and benign moles by examining skin pattern texture on an image of the lesion. Skin patterning is a macroscopic texture composed of fine linear elements. This texture is poorly described by standard definitions of texture and poorly detected by existing techniques. Skin line patterning is detected through a new method which looks at small patches spaced equally across the image and constructs a profile of their linear self-similarity over a range of angles. Regions which exhibit skin patterning result in similar profiles for neighboring patches whereas no such similarity is found in areas where the patterning is disrupted. Interpretation of the profile images for the classification of the lesions is then addressed.

Various researchers have used texture analysis to perform ultrasound tissue characterization with mixed results. Others have used spectral parameters to classify tissue. Several groups have used a feature attributed to the mean scatterer spacing (MSS) as a discriminating feature for tissue classification. We have previously shown that the locations of peaks in the complex cepstrum (PCEP) provide a good estimate of MSS in phantom and simulation studies. In this work, we show that by combining PCEP with texture-based features, we are able to distinguish between normal and hepatitis patients with a high degree of accuracy.

Texture feature extraction is a fundamental stage in texture analysis. Therefore, the reduction of its computational time and memory requirements should be an aim of continuous research. The Spatial Gray Level Dependence Method (SGLDM) is one of the most significant statistical texture description methods, especially in medical image analysis. However, the co-occurrence matrix is inefficient in terms of time and memory requirements. This is due to its dependency on the number of grey levels in the entire image. Its inefficiency puts up barriers to the wider utilization of the SGLDM in a real application environment. This paper investigates the space and time efficiency of self-adjusting binary search trees, in replacing the co-occurrence matrix. These dynamic data structures store only the significant textural information extracted from an image region by the SGLDM. Furthermore, they have the ability to restructure themselves in order to adapt to the co-occurrence distribution of the grey levels in the analyzed region. This results in a better time performance for texture feature extraction. The proposed approach is applied to a number of magnetic resonance images of the human brain and the human femur. A comparison with the co-occurrence matrix, in terms of space and computational time, is performed.

The objective of this research was to develop a method for measuring small differences in diagnostic task performance between two imaging modalities. In the proposed Differential Receiver Operating Characteristic (DROC) method, the observer is shown a pair of images of the same patients, one from each modality A and B. The patient can be normal or abnormal but this information is not known to the observer. The observer selects the image that is preferred for the specified diagnostic task and assigns a rating. Analysis of this experiment yields the area under the DROC curve (A_d). If A_d is greater than 0.5, then modality B is superior to modality A and conversely, if it is less than 0.5, then A is superior to B. With a plausible assumption it can be shown that the result of the paired image presentation DROC experiment will track the difference in A_z's obtained from two single image presentation ROC experiments. A proof-of-concept experiment was conducted to test this idea. Both DROC and ROC studies were conducted using 6 readers. The DROC method was found to track the conventional ROC method and to yield far greater sensitivity, on the average about a factor of 3.46 greater. This work suggests a new paradigm for differential observer performance experiments. The DROC method has the potential for detecting extremely suitable differences in image quality, much smaller than is detectable by the present ROC method. This should allow rapid optimization of imaging systems, without the need for expensive and often inconclusive ROC studies.

A decision model is presented to increase the specificity of breast biopsy directly optimized on the receiver operating characteristic (ROC) area index. ROC area has higher clinical significance as a performance measure than the traditional metric mean-squared error (MSE). Excisional biopsy as practiced is highly sensitive to cancer but nonspecific; only one in three biopsies is malignant. Data for this study consists of 500 cases randomly selected from patients who underwent excisional biopsy for definitive diagnosis of breast cancer. For each case, inputs to the model consist of mammographic findings and patient history features. Outputs from the model built may be thresholded to correspond to the decision to biopsy a suspicious breast lesion. While clinically relevant, ROC area is a discontinuous function which cannot be optimized directly so a genetic algorithm approach is used to train a nonlinear artificial neural network. Performance using the genetic algorithm method of training was similar to that of a decision model trained using the traditional approach for this data set. ROC areas were obtained after training using three different approaches: genetic algorithm training optimized on ROC area produced an ROC area of 0.845 +/- 0.039, genetic algorithm training optimized on MSE produced an ROC area of 0.845 +/- 0.039, and traditional training using backpropagation produced an ROC area of 0.848 +/- 0.039. Despite the similar performance measures for models trained on this data, it is possible that with different data sets, training on ROC instead of MSE will produce models with significantly different performance. In this case, the genetic algorithm approach will prove useful.

Detection of abnormalities is critical to the success of mammogram screening and represents a perceptual problem even for experienced radiologists. This perceptual problem makes the development of reliable automated methods for detection of abnormalities very important. The present work demonstrates improvements in the existing techniques for detection of masses by using an evidential approach to mammogram segmentation. A method of partitioning mammograms into homogeneous regions by using `generic' label is presented. This method assigns the same label to regions based on similarity between regions in the feature space and does not require estimation of model parameters from specific region samples. The features best suited to represent the difference between tissue and masses texture are selected and combined within the framework of the Dempster-Shafer Theory of Evidence. Utilization of the Dempster-Shafer Theory of Evidence has improved the accuracy of detection by allowing to incorporate any number of different features and deal with the uncertainty inherent in these types of problems. Exploitation of constraints, representing domain knowledge, to forbid certain configuration of regions during segmentation results in an improved partitioning of the mammograms. A constrained stochastic relaxation algorithm is used for building an optimal label map to separate tissue and masses.

The fidelity of the reconstructed image in an image coding/decoding scheme and the lowest transmission bit rate from rate-distortion theory can be predicted provided the image statistics are known. Currently popular subband image coding assumes Gaussian source with memory for optimal performance. However, most images do not follow the ideal distribution. The advantage of subband coding lies in the fact that the wavelet coefficients in decomposed subimages have probability distribution functions (pdf's) that can be modeled as a generalized Gaussian when proper parameters are chosen experimentally. However, the filter length chosen for digital implementation of a specific wavelet is crucial in shaping the pdf characteristics and hence in the ability to predict the achievable bit rate at minimum distortion in a quantization scheme. We have analyzed the pdf's of a number of wavelets and chosen filter lengths providing the best fit to a generalized Gaussian distribution for encoding an image by vector quantization of multiresolution wavelet subimages using an adaptive clustering. Our results demonstrate that the performance of the adaptive vector quantizer improves significantly when wavelet filter lengths are chosen to fit the generalized Gaussian distribution.

The classification of brain PET volumes is carried out in three main steps: (1) registration, (2) feature extraction and (3) classification. The PET images were already smoothed with a 16 mm isotropic Gaussian kernel and registered within the Talairach and Tournoux reference system. To make the registration more accurate over a single reference, a method based on optical flow was applied. Feature extraction is carried out by principal component analysis (PCA). Support vector machines (SVM) are then used for classification, because they are better controlled than neural networks (NN) and well adapted to small sample size problems. SVM are constructed by a training algorithm that maximizes the margin between the training vectors and the decision boundary. The algorithm is simple quadratic programming under linear constraints, which leads to global optimum. The decision boundary is expressed as a linear combination of supporting vectors which are a subset of the training vectors closest to the decision boundary. After registration, NN and SVM were trained with the features extracted by PCA from the training set. The estimate error rate is 7.1% for SVM and 14.3% for NN.

In 1996, the University of Iowa launched a multiphase project for the development of a well-structured interdisciplinary image systems engineering curriculum with both depth and breadth in its offerings. This project has been supported by equipment grants from the Hewlett Packard Company. The new teaching approach that we are currently developing is very dissimilar to that we used in previous years. Lectures consist of presentation of concepts, immediately followed by examples, and practical exploratory problems. Six image processing classes have been offered in the new collaborative learning environment during the first two academic years. This paper outlines the employed educational approach we are taking and summarizes our early experience.

More and more often, undergraduate students express the desire to take a course on image processing. These students will learn the most if the theory and algorithms covered in class can be not only illustrated through examples shown by the instructor during class but also coded, tested, and evaluated by the class participants. In the past, the major hurdle to developing a hands-on approach to image processing instruction has been the amount of programming required to implement relatively simple applications. Typical undergraduate students lack experience with low level programming languages and time is spent teaching the language itself rather than experimenting with the algorithms. High level and interpreted programming languages such as Matlab permit to address this question. Even with very little practical exposure to the language, students can rapidly develop the level of skills required to implement a range of image processing algorithms. This presentation will go over the material covered in a senior level introductory course in image processing taught at Vanderbilt University. The course itself is taught in a traditional way but it is supported by laboratories during which students are asked to implement algorithms ranging from connected component labeling to image deblurring. The students are also assigned projects that span several weeks. Examples of such assignments and projects are presented.

This paper gives a comparative overview of ten of the currently available computer vision and image processing textbooks. These texts differ significantly in their coverage, scope, approach, and target audience. Because of the multi-disciplinary nature of this field, it is important to select a textbook that takes advantage of students' backgrounds and gives them the foundation necessary to integrate diverse concepts. This comparative review provides computer vision and image processing educators with a starting point from which they can select a textbook appropriate for their students' needs.

We are developing computerized methods to distinguish between malignant and benign lesions in contrast-enhanced magnetic resonance images of the breast. In this study, we compare 2D spatial analysis of lesions with 3D spatial analysis. Our database consists of 28 lesions: 15 malignant and 13 benign. At 90 s intervals, 4 to 6 scans are obtained, and the spatial uptake of contrast agent is analyzed. Computer-extracted features quantify the inhomogeneity of uptake, sharpness of the margins, and shape of the lesion. Stepwise multiple regression is employed to obtain a subset of features, followed by linear discriminant analysis to estimate the likelihood of malignancy. Cross-validation and ROC analysis are used to evaluate the performance of the method in distinguishing between benign and malignant lesions. The procedures are performed in 3D, and in 2D from single and multiple slices. Shape and sharpness of the lesion were the most effective features. ROC analysis yielded an A_z value of 0.96 for 3D features, between 0.67 and 0.92 for single slices, and 0.88 for 2D features from multiple slices. The performance of 2D analysis on single slices depends strongly on the selected plane and may be significantly lower than the accuracy of full 3D analysis.

Breast ultrasound can potentially increase the accuracy of computerized discrimination of malignant and benign masses. Newly developed 3D ultrasound techniques provide statistically richer information than conventional 2D ultrasound, and may therefore be better-suited for computerized statistical classification techniques. In this study, we investigated the feasibility of classifying solid breast masses using features extracted from 3D ultrasound images. Our data set consisted of seventeen biopsy-proven masses. Eight of the masses were malignant and nine were benign. The masses were identified by an experienced breast radiologist in the 3D volume, and a 3D ellipsoid containing the mass was defined. Spatial gray level dependence features were extracted from 2D slices in three regions, which were (1) the interior of the ellipse; (2) a disk-shaped region at the upper periphery of the ellipse; and (3) a disk-shaped region at the lower periphery of the ellipse. 2D analysis was performed by evaluating the classification accuracy of the features extracted from each slice. 3D analysis was performed by first averaging feature values from different slices into a single 3D feature, and then evaluating the classification accuracy. The best texture feature in this study achieved a classification accuracy of A_z equals 0.97 for both 3D and 2D analysis. Our results indicate that the performance of 3D analysis is comparable to that of 2D analysis using the best available slice. Since the best 2D slice for texture analysis may not be known a-priori, this preliminary study suggests that 3D ultrasound may be beneficial for computerized breast mass characterization.

We are developing computerized schemes to detect clustered microcalcifications in mammograms, and to classify malignant versus benign microcalcifications. The purpose of this study is to investigate the effects on the performance of computer classification when results of computer-detected true microcalcifications and computer detected false-positive signals are used as input to the computer classification scheme. We found that when trained using manually identified microcalcifications, the computer classification performance was not degraded significantly when up to 60% of true microcalcifications were missed, and when false-positive signals made up approximately one half of the computer detection.

A computer-aided diagnosis (CAD) scheme could improve radiologists' diagnostic performance in their detection of lung nodules on chest radiographs if the computer output were used as a `second opinion'. The current CAD scheme that we have developed achieved a performance of 70% sensitivity and 1.7 false positives per image for our database. This database consisted of two hundred PA chest radiographs, including 100 normals and 100 abnormals (containing 122 confirmed nodules). Our purpose in this study was to improve our scheme further by incorporating new features derived from analysis of the histogram of radial edge gradients on nodule candidates.

3D reconstruction of medical images is increasingly being used to diagnose disease and to direct therapy. Virtual bronchoscopy is a recently developed type of 3D reconstruction of the airways that may be useful for diagnosis of lesions of the airway. In this study, we compare two methods for computer-aided diagnosis of polypoid airway tumors: a parametric (`patch') and non-parametric ('grey-scale') algorithm. We found that both methods have comparable specificities. Although the non-parametric method is twelve times faster than the parametric method, we found that is sensitivity lags behind that of the parametric method by 3 to 16% when lesions of all sizes are considered. For lesions at least 5 mm in size, the sensitivities are comparable if a small convolution kernel is used.

One of the basic assumptions in the computed tomography (CT) is that the scanned object has constant attenuation characteristics across the thickness of the slice. In reality, however, this assumption is often violated. The projection data set of a head CT scan, for example, is often corrupted by bony structures partially intruded into the scanning plane. As a result, severe streaking and shading artifacts appear in the reconstructed images. This phenomenon is called partial volume. In this paper, we propose an iterative approach to the partial volume artifact reduction. CT images are first reconstructed with a filtered backprojection algorithm. The generated images subsequently undergo a fuzzy membership classification process to arrive at bone-only images, which in turn will be used to produce gradient images. The projection error is then calculated based on the gradient image. For better error estimation, the scan data is collected in a helical mode and highly overlapped images are reconstructed. The error term is filtered and back-projected to produce a partial volume error image, which is scaled and subtracted from the original image. Various phantom studies have demonstrated the effectiveness of our approach.

In this paper the reconstruction of SPECT images is explored using the Total-Variation method. The method is able to recover edge information of the image and is therefore suitable for `blocky' types of images. The paper provides a basic reconstruction algorithm with examples using synthetic and patient data.

Neural networks are applied to a Rayleigh discrimination task for simulated limited-view computed tomography with maximum-entropy reconstruction. Network performance is compared to that obtained using the best machine approximation to the ideal observer found in an earlier investigation. Results obtained on 2D subimage inputs are compared with those for 1D inputs and presented previously at this conference. Back-propagation neural networks significantly outperform the `best' standard nonadaptive linear machine observer and also the intuitively appealing `matched filter' obtained by averaging over the images in a large training data set. In addition, the back-propagation neural network operating on 2D subimages performs significantly better than that limited to 1D inputs. Finally, improved performance on this Rayleigh task is found for nonlinear (over linear, that is, simple perceptron) neural network decision strategies.

The detection of scattered photons affects both image quality and accuracy of quantitation accuracy in Single Photon Emission Computed Tomography (SPECT). The aim of this work was to evaluate three scatter correction methods: Jaszczak subtraction, the triple energy window method and an artificial neural network based approach. This evaluation was performed not only in terms of contrast and spatial resolution but also in terms of absolute and relative quantitation. A Monte Carlo simulation of an anthropomorphic cardiac phantom allowed us to obtain a realistic SPECT study while knowing the primary (non scattered) photon distribution. The knowledge of the primary activity made possible the study of the effect of scatter alone independently on all other phenomena affecting quantitation. The quantitative error propagation between the projections and the reconstructed slices due to scatter was studied as well as resolution, contrast and uniformity recoveries in the corrected images. The results show that an artificial neural network achieved the best scatter correction both in terms of relative (gives the same uniformity as in the primary distribution) and absolute quantitation (error < 4%) and resolution. The triple energy window method led to good quantitation (error < 8%) and contrast results but poorer resolution recovery than the artificial neural network based approach. Jaszczak subtraction yielded good quantitation (error < 7%) but introduced severe non uniformities in the image (decrease of the uniformity by 35%).

The Markov Chain Monte Carlo (MCMC) technique provides a means to generate a random sequence of model realizations that sample the posterior probability distribution of a Bayesian analysis. That sequence may be used to make inferences about the model uncertainties that derive from measurement uncertainties. This paper presents an approach to improving the efficiency of the Metropolis approach to MCMC by incorporating an approximation to the covariance matrix of the posterior distribution. The covariance matrix is approximated using the update formula from the BFGS quasi-Newton optimization algorithm. Examples are given for uncorrelated and correlated multidimensional Gaussian posterior distributions.

A Maximum Likelihood estimation technique is proposed for optimal estimation of Magnetic Resonance (MR) T₂ maps from a set of magnitude MR images. Thereby, full use is made of the actual probability density function of the magnitude data, which is the Rician distribution. While equal in terms of precision, the proposed method is demonstrated to be superior in terms of accuracy compared to conventional relaxation parameter estimation techniques.

In most clinical MR images, global patient motion is predominantly interview (between readouts), and corrupts the phase of the received signal for that line of k-space. No information, however, is lost--if the original motion is known and appropriate phase corrections applied, the image can be perfectly restored. It is therefore possible to correct for motion given only the real and imaginary data from the scanner by simply trying different possible motion corrections and searching for the highest quality resulting image with a suitable evaluation function. Such an `autofocusing' algorithm was recently described, using image entropy as the cost function; however, very long computation times are required. If the corrupting motion is primarily 1D, much faster autofocusing might be possible by calculating only selected lines of the image. In this paper, we describe work on such an algorithm, implemented with both minimum entropy and maximum variance as the cost functions. Tests on several 256 X 256 magnitude images artificially corrupted by 1D motion indicate that evaluating only eight selected columns of the image (calculated with eight 1D FFT's) works very well--essentially as well as evaluating the whole image, which requires 2D FFT's. The run time dropped from several hours for 2D FFT's to less than ten minutes using 1D FFT's. One test image with little dark area was not well corrected, indicating the possible dependence of both cost functions on dark regions to be cleared of artifacts.

This paper presents a fast method for magnetic resonance imaging (MRI) based on discrete cosine transform (DCT). In the proposed method, DCT is used for phase encoding and discrete Fourier transform (DFT) is used for frequency encoding. Because of the superior information compression property of DCT compared to DFT, the proposed method requires a smaller portion of the k-space to generate acceptable MRI images. Thus, the new method reduces the imaging time and increases the patient throughput. The hardware modifications for generating DCT encoded free induction decay signals and reconstruction algorithms to generate tomographic images are presented. Capability of the method in generating MRI images is illustrated through computer simulations. Finally, the effect of MRI noise on the quality of the resulting images are shown by simulation studies.

When conventional techniques are employed in the quantitative analysis of phase contrast magnitude Magnetic Resonance (MR) data, the results obtained are biased. The bias is due to the contributions from inherent random noise. To remove this bias, knowledge of the actual shape of the data probability density function becomes essential. In the present work, the full knowledge of the probability distribution of the phase contrast magnitude MR data is exploited for optimal estimation of the underlying signal.

A new method for compensating motion artifacts in computerized tomography is presented. The algorithm operates on the raw data, that is, on the measured Radon transform. An edge detection is performed on the Radon transform image. Two curves are obtained from these edges, which are fitted by a polynomial. The pointwise differences between the edges of the Radon transform image and the fitted curves are used to determine the parameters for the motion compensation. The corresponding operations are performed on the rows of the Radon transform. Our method is independent of the image reconstruction algorithms like filtered backprojection, Fourier method, etc. since all transformations are performed on the raw data.

Acoustic shear waves of low frequency can be detected and measured using a phase contrast based magnetic resonance imaging technique called MR Elastography or correlation or phase measurement based echo ultrasound techniques. Spatio- temporal variations of displacements caused by the propagating waves can be used to estimate local values of the elasticity of the object being imaged. The currently employed technique for estimating the elasticity from the wave displacement maps, the local frequency estimator (LFE), has fundamental resolution limits and also has problems with shadowing and other refraction-related artifacts. These problems can be overcome with an inverse approach using Green's function integrals which directly solve the wave equation problem for the propagating wave. The complete measurements of wave displacements as a function of space and time over the object of interest obtained by the above techniques make possible an iterative approach to inversion of the wave equation to obtain elasticity and attenuation maps. The speed of convergence of such an iterative method can be improved by using LFE as the initial guess for the object function. This article describes the proposed and evaluates the improvements over the LFE for simulated data and in-vivo breast measurements.

Iterative methods for the reconstruction of PET images can produce results superior to filtered backprojection since they are able to explicitly model the Poisson statistics of photon pair coincidence detection. However, many implementations of these methods use simple forward and backward projection schemes based either on linear interpolation or on computing the volume of intersection of detection tubes with each voxel. Other important physical system factors, such as depth dependent geometric sensitivity and spatially variant detector pair resolution are often ignored. In this paper, we examine the effect of a more accurate system model on algorithm performance. A second factor that limits the performance of the iterative algorithms is the chosen objective function and the manner in which it is optimized. Here we compare performance of filtered backprojection (FBP) with the OSEM (ordered subsets EM) algorithm, which approximately maximizes the likelihood, and a MAP (maximum a posteriori) method using a Gibbs prior with convex potential functions. Using the contrast recovery coefficient (CRC) as a performance measure, we performed various phantom experiments to investigate how the choice of algorithm and projection matrix affect reconstruction accuracy. Plots of CRC versus background variance were generated by varying cut-off frequency in FBP, subset size and iteration number or post-smoothing kernel in OSEM, and smoothing parameter in the MAP reconstructions. The results of these studies show that all of the iterative methods tested produce superior CRCs than FBP at matched background variance. However, there is also considerable variation in performance within the class of statistical methods depending on the choice of projection matrix and reconstruction algorithm.

This paper describes a new image reconstruction method to reduce the presence of image artifacts in scintimammography. SPECT data are mathematically modified prior to conventional image processing, followed by an inverse transform, which permits the tomographic visualization of low signals in the presence of large background intensities observed in scintimammography. Images of Tc-99m sestamibi distribution were obtained in a modeled `breast tissue', with a high activity in the `myocardium' as compared to the `breast tissue' (i.e. 20:1). Image reconstruction with the modified algorithm were qualitatively correct and demonstrated the regions of enhanced uptake (lesions) with no evidence of artifacts from the background counts in the heart. Comparison with MRI demonstrated that the hot regions were properly located and correlated with the MRI data. In contrast, a standard (i.e. Filtered Back Projection) reconstruction resulted in streak artifacts in place of `breast tissue' which rendered them clinically useless. This new approach to scintimammography offers the prospect of significantly reducing image artifacts and improving imaging accuracy.

The MUSIC (Multiple Signal Classification) algorithm is a recently proposed method in solving multiple dipole localization problem from spatio-temporal magnetocardiograph (MCG) data. There are many factors that may effect the resolvability of MUSIC method in solving MCG inverse problem. For example, the number and space arrangement of sensors, the signal-noise ratio of measurement data, the relative position of dipole to the sensors, the direction of dipole. In the case of multiple dipoles are assumed, the distance and time correlation between the dipoles may take a great effect on the solution accuracy. We need a quantitative method of evaluate the resolvability of MUSIC algorithm. In this paper spherically symmetric conductor model is applied as the forward model. The statistical performance of the MUSIC algorithm is discussed by using the MUSIC error covariance matrix. The Cramer-Rao Lower Bound (CRLB) on localization errors for MCG current source dipole models is presented. The performance of MUSIC algorithm is compared with the ultimate performance corresponding to CRLB. The numerical studies with simulated MCG data are presented in two cases: one dipole is assumed and two dipoles are assumed.

This paper describes a modeller for building 3D anatomic atlases. The main contribution is the ability to incrementally learn inter-patient variations in structure, shape, and function; with support for variations in structure (topology) being of particular significance. The modeller uses graph theory as a mathematical base and is, in fact, quite general with possible applications in wider computer vision contexts. In this paper we describe the general modeller, and illustrate it specifically by showing how to use it to build a catalogue of vasculature and variations. We have used such a catalogue of vasculature for 3D reconstruction of x-ray angiograms, simulation of x-ray angiography, and interpretation of images and text combined; the first two of these are the most mature and are briefly outlined. We conclude by discussing the limitations of the model both generally and specifically.

In this paper we present an approach for 3D reconstruction of vascular skeletons from x-ray angiograms at arbitrary angles. The key to this problem is solving the correspondence problem; that is, determine a mapping between points in each image pair. This paper describes, in some detail, the two main steps in our approach: (1) we determine vessels that correspond between images to obtain a `coarse grained' solution that acts to focus our next step; (2) we determine the correspondence between points in corresponding vessels, this gives a `fine grained' solution enabling the 3D shape of the vessel to be computed. We use a model of a collection of vasculature during the first step, use the second step relies only on general assumptions about space- curves. There are several novelties: images can be at arbitrary angles; generalization from the collection to include new vasculature; and weak dependence on the kind of image data. Results show the approach is efficient in time and space, accurate and reliable, and robust to noise.

Segmentation and 3D reconstruction of vessel center lines from subtraction angiography is difficult because of noise, an uneven distribution of the contrast agent, and bone structures concealing the vessels. In biplane images, some ambiguities in segmentation in one of the images can be resolved using image information from the other image. Images are first processed separately. A-priori vessel probabilities are computed using the grey value in the image. Gradients and second derivatives are computed using gaussian derivatives. Subsequently, 3D reconstruction is carried out in a line-by-line fashion between user-specified base lines on both images. The user is asked to point out corresponding vessel cross-sections on the frontal and lateral image. 3D locations are computed. Between adjacent 3D locations, intermediate 3D locations are estimated iteratively using location, curvature and size of the previously computed 3D vessel cross-section. The estimates are optimized evaluating local attributes in the two projection images, such as the grey level, the gradient and the closeness to the initial estimate. WE applied the method for the reconstruction of artificial and real structures. The artificial object consisted of metal wires with sizes ranging between 1 and 5 mm. Various parts of the structure were extracted and reconstructed successfully. Reconstructing center lines from real images was more difficult because of the image degrading influences. Structures with a size of about 1 mm were extracted and reconstructed successfully even though they were barely visible. The amount of user interaction depended on the visibility of the structures in the two images.

The 3D coronary vessels can be reconstructed by means of different cardiac imaging modalities. Two of the most widely used modalities for the purpose of coronary tree reconstruction are intravascular ultrasounds (IVUS) and biplane angiography. Current 3D vessel reconstruction based on IVUS pullback imaging is limited by the lack of information about the real vessel curvature, because the path of the catheter is assumed to be a straight line. This limitation can be overcome if information from an IVUS sequence is fused with a biplane X-ray image of the catheter acquired at the start of the pullback procedure. This work focuses on the reconstruction of the catheter path from biplane angiograms. This reconstruction represents the 3D path followed by the catheter inside the vessel of interest. While other approaches reconstruct the vessel after it has been segmented in both images independently, our approach, based on the snakes technique, allows us to segment and reconstruct the catheter trajectory merging information from both images simultaneously. The result is a more robust reconstruction since 3D constraints can be used and no correspondence of points between the projections is required. This reconstruction will allow a posterior more exact combination of IVUS and biplane angiography image modalities.

X-ray mammography is one of the most significant diagnosis methods in early detection of breast cancer. Usually two X- ray images from different angles are taken from each mamma to make even overlapping structures visible. X-ray mammography has a very high spatial resolution and can show microcalcifications of 50 - 200 micron in size. Clusters of microcalcifications are one of the most important and often the only indicator for malignant tumors. These calcifications are in some cases extremely difficult to detect. Computer assisted diagnosis of digitized mammograms may improve detection and interpretation of microcalcifications and cause more reliable diagnostic findings. We build a low-cost mammography workstation to detect and classify clusters of microcalcifications and tissue densities automatically. New in this approach is the estimation of the 3D formation of segmented microcalcifications and its visualization which will put additional diagnostic information at the radiologists disposal. The real problem using only two or three projections for reconstruction is the big loss of volume information. Therefore the arrangement of a cluster is estimated using only the positions of segmented microcalcifications. The arrangement of microcalcifications is visualized to the physician by rotating.

This paper presents reproducibility studies for the segmentation results obtained by our optimal MRI feature space method. The steps of the work accomplished are as follows. (1) Eleven patients with brain tumors were imaged by a 1.5 T General Electric Signa MRI System. Four T2- weighted and two T1-weighted images (before and after Gadolinium injection) were acquired for each patient. (2) Images of a slice through the center of the tumor were selected for processing. (3) Patient information was removed from the image headers and new names (unrecognizable by the image analysts) were given to the images. These images were blindly analyzed by the image analysts. (4) Segmentation results obtained by the two image analysts at two time points were compared to assess the reproducibility of the segmentation method. For each tissue segmented in each patient study, a comparison was done by kappa statistics and a similarity measure (an approximation of kappa statistics used by other researchers), to evaluate the number of pixels that were in both of the segmentation results obtained by the two image analysts (agreement) relative to the number of pixels that were not in both (disagreement). An overall agreement comparison was done by finding means and standard deviations of kappa statistics and the similarity measure found for each tissue type in the studies. The kappa statistics for white matter was the largest (0.80) followed by those of gray matter (0.68), partial volume (0.67), total lesion (0.66), and CSF (0.44). The similarity measure showed the same trend but it was always higher than kappa statistics. It was 0.85 for white matter, 0.77 for gray matter, 0.73 for partial volume, 0.72 for total lesion, and 0.47 for CSF.

A system that automatically segments and labels complete glioblastoma-multiform tumor volumes in magnetic resonance images of the human brain is presented. The magnetic resonance images consist of three feature images (T1- weighted, proton density, T2-weighted) and are processed by a system which integrates knowledge-based techniques with multispectral analysis and is independent of a particular magnetic resonance scanning protocol. Initial segmentation is performed by an unsupervised clustering algorithm. The segmented image, along with cluster centers for each class are provided to a rule-based expert system which extracts the intra-cranial region. Multispectral histogram analysis separates suspected tumor from the rest of the intra-cranial region, with region analysis used in performing the final tumor labeling. This system has been trained on eleven volume data sets and tested on twenty-two unseen volume data sets acquired from a single magnetic resonance imaging system. The knowledge-based tumor segmentation was compared with radiologist-verified `ground truth' tumor volumes and results generated by a supervised fuzzy clustering algorithm. The results of this system generally correspond well to ground truth, both on a per slice basis and more importantly in tracking total tumor volume during treatment over time.

The study presented in this paper tests the hypothesis that the combination of a global similarity transformation and local free form deformations can be used for the accurate segmentation of internal structures in MR images of the brain. To quantitatively evaluate our approach, the entire brain, the cerebellum and the head of the caudate have been segmented manually on one of the volumes and mapped back onto all the other volumes using the computed transformations. The contours so obtained have been compared to contours drawn manually around the structures of interest in each individual brain. Manual delineation was repeated to test intra-rater variability. Contours were quantitatively compared using a similarity index defined as 2 times the area encircled by both contours divided by the sum of the areas encircled by each contour. This index ranges from 0 to 1 with zero indicating zero overlap and one indicating a perfect agreement between two contours. It is sensitive to both displacement and differences in shape and it is thus preferable to a simple area comparison. Results indicate that the method we proposed can be used to segment accurately and fully automatically large and small structures in high resolution 3D images of the brain. The average similarity indices between the manual and automatic segmentations are 0.96, 0.97, and 0.845 for the whole head, the cerebellum, and the head of the caudate respectively. These numbers are 0.97, 0.97, and 0.88 when two manual delineations are compared. Statistical analysis reveals that the differences in mean similarity indices between the two manual delineations and between the manual delineations and the automatic segmentation method are statistically significant for the whole head and the caudate but not for the cerebellum. It is shown, however, that similarity indices in the range of 0.85 correspond to contours that are virtually undistinguishable.