A new generic model-based segmentation scheme is presented, which can be trained from examples akin to the Active Shape Model (ASM) approach in order to acquire knowledge about the shape to be segmented and about the gray-level appearance of the object in the image. Because in the ASM approach the intensity and shape models are typically applied alternately during optimizing as first an optimal target location is selected for each landmark separately based on local gray-level appearance information only to which the shape model is fitted subsequently, the ASM may be misled in case of wrongly selected landmark locations. Instead, the proposed approach optimizes for shape and intensity characteristics simultaneously. Local gray-level appearance information at the landmark points extracted from feature images is used to automatically detect a number of plausible candidate locations for each landmark. The shape information is described by multiple landmark-specific statistical models that capture local dependencies between adjacent landmarks on the shape. The shape and intensity models are combined in a single cost function that is optimized non-iteratively using dynamic programming which allows to find the optimal landmark positions using combined shape and intensity information, without the need for initialization.

An automatic procedure for detecting and segmenting anatomical objects in 3-D images is necessary for achieving a high level of automation in many medical applications. Since today's segmentation techniques typically rely on user input for initialization, they do not allow for a fully automatic workflow. In this work, the generalized Hough transform is used for detecting anatomical objects with well defined shape in 3-D medical images. This well-known technique has frequently been used for object detection in 2-D images and is known to be robust and reliable. However, its computational and memory requirements are generally huge, especially in case of considering 3-D images and various free transformation parameters. Our approach limits the complexity of the generalized Hough transform to a reasonable amount by (1) using object prior knowledge during the preprocessing in order to suppress unlikely regions in the image, (2) restricting the flexibility of the applied transformation to only scaling and translation, and (3) using a simple shape model which does not cover any inter-individual shape variability. Despite these limitations, the approach is demonstrated to allow for a coarse 3-D delineation of the femur, vertebra and heart in a number of experiments. Additionally it is shown that the quality of the object localization is in nearly all cases sufficient to initialize a successful segmentation using shape constrained deformable models.

Models of geometry or appearance of three-dimensional objects may be used for locating and specifying object instances in 3D image data. Such models are necessary for segmentation if the object to be segmented is not separable based on image information only. They provide a-priori knowledge about the expected shape of the target structure. The success of such a segmentation task depends on the incorporated model knowledge. We present an automatic method to generate such a model for a given target structure. This knowledge is created in the form of a 3D Stable Mass-Spring Model (SMSM) and can be computed from a single sample segmentation. The model is built from different image features using a bottom-up strategy, which allows for different levels of model abstraction. We show the adequacy of the generated models in two practical medical applications: the anatomical segmentation of the left ventricle in myocardial perfusion SPECT, and the segmentation of the thyroid cartilage of the larynx in CT datasets. In both cases, the model generation was performed in a few seconds.

Active Shape Models (ASM) are widely employed for recognizing anatomic structures and for delineating them in medical images. In this paper, we present a novel strategy called Oriented Active Shape Models (OASM) in an attempt to overcome the following three major limitations of ASM: (1) poor delineation accuracy, (2) the requirement of a large number of landmarks, (3) the problem of sensitivity to search range to recognize the object boundary. OASM effectively combines the rich statistical shape information embodied in ASM with the boundary orientedness property and the globally optimal delineation capability of the live wire methodology of boundary segmentation. The latter allow live wire to effectively separate an object boundary from other non object boundaries with similar properties that come very close in the image domain. Our approach leads us to a 2-level dynamic programming method, wherein the first level corresponds to boundary recognition and the second level corresponds to boundary delineation. Our experiments in segmenting breast, liver, bones of the foot, and cervical vertebrae of the spine in MR and CT images indicate the following: (1) The accuracy of segmentation via OASM is considerably better than that of ASM. (2) The number of landmarks can be reduced by a factor of 3 in OASM over that in ASM. (3) OASM becomes largely independent of search range. All three benefits of OASM ensue mainly from the severe constraints brought in by the boundary-orientedness property of live wire and the globally optimal solution of dynamic programming.

This paper presents a new image segmentation algorithm using surface-to-image registration. The algorithm employs multi-level transformations and multi-resolution image representations to progressively register atlas surfaces (modeling anatomical structures) to subject images based on weighted external forces in which weights and forces are determined by gradients and local intensity profiles obtained from images. The algorithm is designed to prevent atlas surfaces converging to unintended strong edges or leaking out of structures of interest through weak edges where the image contrast is low. Segmentation of bone structures on MR images of rat knees analyzed in this manner performs comparably to technical experts using a semi-automatic tool.

Magnetic resonance (MR) imaging is frequently used to diagnose abnormalities in the spinal intervertebral discs. Owing to the non-isotropic resolution of typical MR spinal scans, physicians prefer to align the scanner plane with the disc in order to maximize the diagnostic value and to facilitate comparison with prior and follow-up studies. Commonly a planning scan is acquired of the whole spine, followed by a diagnostic scan aligned with selected discs of interest. Manual determination of the optimal disc plane is tedious and prone to operator variation. A fast and accurate method to automatically determine the disc alignment can decrease examination time and increase the reliability of diagnosis. We present a validation study of an automatic spine alignment system for determining the orientation of intervertebral discs in MR studies. In order to measure the effectiveness of the automatic alignment system, we compared its performance with human observers. 12 MR spinal scans of adult spines were tested. Two observers independently indicated the intervertebral plane for each disc, and then repeated the procedure on another day, in order to determine the inter- and intra-observer variability associated with manual alignment. Results were also collected for the observers utilizing the automatic spine alignment system, in order to determine the method's consistency and its accuracy with respect to human observers. We found that the results from the automatic alignment system are comparable with the alignment determined by human observers, with the computer showing greater speed and consistency.

Ankylosing Spondylitis is a disease of the vertebra where abnormal bone structures (syndesmophytes) grow at intervertebral disk spaces. Because this growth is so slow as to be undetectable on plain radiographs taken over years, it is necessary to resort to computerized techniques to complement qualitative human judgment with precise quantitative measures on 3-D CT images. Very fine segmentation of the vertebral body is required to capture the small structures caused by the pathology. We propose a segmentation algorithm based on a cascade of three level set stages and requiring no training or prior knowledge. First, the noise inside the vertebral body that often blocks the proper evolution of level set surfaces is attenuated by a sigmoid function whose parameters are determined automatically. The 1st level set (geodesic active contour) is designed to roughly segment the interior of the vertebra despite often highly inhomogeneous and even discontinuous boundaries. The result is used as an initial contour for the 2nd level set (Laplacian level set) that closely captures the inner boundary of the cortical bone. The last level set (reversed Laplacian level set) segments the outer boundary of the cortical bone and also corrects small flaws of the previous stage. We carried out extensive tests on 30 vertebrae (5 from each of 6 patients). Two medical experts scored the results at intervertebral disk spaces focusing on end plates and syndesmophytes. Only two minor segmentation errors at vertebral end plates were reported and two syndesmophytes were considered slightly under-segmented.

Rheumatoid Arthritis is one of the most common chronic diseases. Joint space width in hand radiographs is evaluated to assess joint damage in order to monitor progression of disease and response to treatment. Manual measurement of joint space width is time-consuming and highly prone to inter- and intra-observer variation. We propose a method for automatic extraction of finger bone boundaries using fast marching methods for quantitative evaluation of joint space width. The proposed algorithm includes two stages: location of hand joints followed by extraction of bone boundaries. By setting the propagation speed of the wave front as a function of image intensity values, the fast marching algorithm extracts the skeleton of the hands, in which each branch corresponds to a finger. The finger joint locations are then determined by using the image gradients along the skeletal branches. In order to extract bone boundaries at joints, the gradient magnitudes are utilized for setting the propagation speed, and the gradient phases are used for discriminating the boundaries of adjacent bones. The bone boundaries are detected by searching for the fastest paths from one side of each joint to the other side. Finally, joint space width is computed based on the extracted upper and lower bone boundaries. The algorithm was evaluated on a test set of 8 two-hand radiographs, including images from healthy patients and from patients suffering from arthritis, gout and psoriasis. Using our method, 97% of 208 joints were accurately located and 89% of 416 bone boundaries were correctly extracted.

Respiratory motion degrades image quality in PET and SPECT imaging. Patient specific information on the motion of structures such as the heart if obtained from CT slices from a dual-modality imaging system can be employed to compensate for motion during emission reconstruction. The CT datasets may not be contrast enhanced. Since each patient may have 100-120 coronal slices covering the heart, an automated but accurate segmentation of the heart is important. We developed and implemented an algorithm to segment the heart in non-contrast CT datasets. The algorithm has two steps. In the first step we place a truncated-ellipse curve on a mid-slice of the heart, optimize its pose, and then track the contour through the other slices of the same dataset. During the second step the contour points are drawn to the local edge points by minimizing an distance measure. The segmentation algorithm was tested on 10 patients and the boundaries were determined to be accurate to within 2 mm of the visually ascertained locations of the borders of the heart. The segmentation was automatic except for initial placement of the first truncated-ellipse and for having to re-initialize the contour for 3 patients for less than 3% (1-3 slices) of the coronal slices of the heart. These end-slices constituted less than 0.3% of the heart volume.

Segmentation of the left myocardium in four-dimensional (space-time) cardiac MRI data sets is a prerequisite of many diagnostic tasks. We propose a fully automatic method based on global minimization of an energy functional by means of the graphcut algorithm. Starting from automatically obtained segmentations of the left and right ventricles and a cardiac region of interest, a spatial model is constructed using simple and plausible assumptions. This model is used to learn the appearance of different tissue types by non parametric robust estimation. Our method does not require previously trained shape or appearance models. Processing takes 30-40s on current hardware. We evaluated our method on 11 clinical cardiac MRI data sets acquired using cine balanced fast field echo. Linear regression of the automatically segmented myocardium volume against manual segmentations (performed by a radiologist) showed an RMS error of about 12ml.

In the diagnosis of coronary artery disease, 3D-multi-slice computed tomography (MSCT) has recently become more and more important. In this work, an anatomical-based method for the segmentation of atherosclerotic coronary arteries in MSCT is presented. This technique is able to bridge severe stenosis, image artifacts or even full vessel occlusions. Different anatomical structures (aorta, blood-pool of the heart chambers, coronary arteries and their orifices) are detected successively to incorporate anatomical knowledge into the algorithm. The coronary arteries are segmented by a simulated wave propagation method to be able to extract anatomically spatial relations from the result. In order to bridge segmentation breaks caused by stenosis or image artifacts, the spatial location, its anatomical relation and vessel curvature-propagation are taken into account to span a dynamic search space for vessel bridging and gap closing. This allows the prevention of vessel misidentifications and improves segmentation results significantly. The robustness of this method is proven on representative medical data sets.

Osteoporosis is a metabolic bone disease leading to de-mineralization and increased risk of fracture. The two major factors that determine the biomechanical competence of bone are the degree of mineralization and the micro-architectural integrity. Today, modern imaging modalities exist that allow to depict structural details of trabecular bone tissue. Recently, non-linear techniques in 2D and 3D based on the scaling vector method (SVM) and the Minkowski functionals (MF) have been introduced, which show excellent performance in predicting bone strength and fracture risk. However, little is known about the performance of the various parameters with respect to monitoring structural changes due to progression of osteoporosis or as a result of medical treatment. We test and compare the two methodologies using realistic two-dimensional simulations of bone structures, which model the effect of osteoblasts and osteoclasts on the local change of relative bone density. Different realizations with slightly varying control parameters are considered. Our results show that even small changes in the trabecular structures, which are induced by variation of a control parameter of the system, become discernible by applying both the MF and the locally adapted scaling vector method. The results obtained with SVM are superior to those obtained with the Minkowski functionals. An additive combination of both measures drastically increases the sensitivity to slight changes in bone structures. These findings may be especially important for monitoring the treatment of patients, where the early recognition of (drug-induced) changes in the trabecular structure is crucial.

Stroke is the third leading cause of death in the western world and the major cause of disability in adults. The type and stenosis of extracranial carotid artery disease is often responsible for ischemic strokes, transient ischemic attacks (TIAs) or amaurosis fugax (AF). The identification and grading of stenosis can be done using gray scale ultrasound scans. The appearance of B-scan pictures containing various granular structures makes the use of texture analysis techniques suitable for computer assisted tissue characterization purposes. The objective of this study is to investigate the usefulness of variogram analysis in the assessment of ultrasound plague morphology. The variogram estimates the variance of random fields, from arbitrary samples in space. We explore stationary random field models based on the variogram, which can be applied in ultrasound plaque imaging leading to a Computer Aided Diagnosis (CAD) system for the early detection of symptomatic atherosclerotic plaques. Non-parametric tests on the variogram coefficients show that the cofficients coming from symptomatic versus asymptomatic plaques come from distinct distributions. Furthermore, we show significant improvement in class separation, when a log point-transformation is applied to the images, prior to variogram estimation. Model fitting using least squares is explored for anisotropic variograms along specific directions. Comparative classification results, show that variogram coefficients can be used for the early detection of symptomatic cases, and also exhibit the largest class distances between symptomatic and asymptomatic plaque images, as compared to over 60 other texture features, used in the literature.

High resolution MR-scanners working with magnetic field strengths of 3 Tesla are clinically available nowadays. They offer the possibility to obtain 3D images with unprecedented spatial resolution and/or signal-to-noise-ratio (SNR) allowing for an accurate visualization of the trabecular bone structure. It has been demonstrated that scaling indices are well suited to quantify these structures, especially to discriminate between plate-like and rod-like structural elements, which is crucial for the diagnosis of osteoporosis. Until now image quality has mainly been assessed by visual impression or by measures based on the SNR. In this work we present a methodology to assess different MR-sequences with respect to the texture measure that is used later in the image analysis. We acquired for a bone specimen HR-MR-sequences with different spatial resolution and signal to noise ratio. For these data sets we selected two volumes of interest (VOI) of same size located in the trabecular bone and in the background of the image. For both VOIs the scaling indices are calculated for different scale parameters. Subsequently the 'texture contrast' between structure and background is calculated by comparing the probability distributions of the scaling indices using a quadratic distance measure. By means of the contrast the optimal set of scale parameters is determined. By comparing the contrast for the different MR sequences the best suited ones are determined. It turns out that sequences with slightly lower spatial resolution but better signal to noise ration yield a better texture contrast than sequences with the best spatial resolution. The presented methodology offers the possibility to optimize simultaneously texture measures and MR-sequences, which will allow for an adapted and thus optimized analysis of image structures, e.g. trabecular bone, in the HR-MR data.

Automatic classification of the density of breast parenchyma is shown using a measure that is correlated to the human observer performance, and compared against the BI-RADS density rating. Increasingly popular in the United States, the Breast Imaging Reporting and Data System (BI-RADS) is used to draw attention to the increased screening difficulty associated with greater breast density; however, the BI-RADS rating scheme is subjective and is not intended as an objective measure of breast density. So, while popular, BI-RADS does not define density classes using a standardized measure, which leads to increased variability among observers. The adaptive thresholding technique is a more quantitative approach for assessing the percentage breast density, but considerable reader interaction is required. We calculate an objective density rating that is derived using a measure of local feature salience. Previously, this measure was shown to correlate well with radiologists' localization and discrimination of true positive and true negative regions-of-interest. Using conspicuous spatial frequency features, an objective density rating is obtained and correlated with adaptive thresholding, and the subjectively ascertained BI-RADS density ratings. Using 100 cases, obtained from the University of South Florida's DDSM database, we show that an automated breast density measure can be derived that is correlated with the interactive thresholding method for continuous percentage breast density, but not with the BI-RADS density rating categories for the selected cases. Comparison between interactive thresholding and the new salience percentage density resulted in a Pearson correlation of 76.7%. Using a four-category scale equivalent to the BI-RADS density categories, a Spearman correlation coefficient of 79.8% was found.

Numerous studies have investigated the relation between mammographic density and breast cancer risk. These studies indicate that women with high breast density have a four to six fold risk increase. An investigation of whether or not this relation is causal is important for, e.g., hormone replacement therapy (HRT), which has been shown to actually increase the density. No gold standard for automatic assessment of mammographic density exists. Manual methods such as Wolfe patterns and BI-RADS are helpful for communication of diagnostic sensitivity, but they are both time consuming and crude. They may be sufficient in certain cases and for single measurements, but for serial, temporal analysis it is necessary to be able to detect more subtle changes and, in addition, to be more reproducible. In this work an automated method for measuring the effect of HRT w.r.t. changes in biological density in the breast is presented. This measure is a novel measure, which provides structural information orthogonal to intensity-based methods. Hessian eigenvalues at different scales are used as features and a clustering of these is employed to divide a mammogram into four structurally different areas. Subsequently, based on the relative size of the areas, a density score is determined. In the experiments, two sets of mammograms of 50 patients from a double blind, placebo controlled HRT experiment were used. The change in density for the HRT group, measured with the new method, was significantly higher (p = 0.0002) than the change in the control group.

Early detection of structural damage to the optic nerve head (ONH) is critical in diagnosis of glaucoma, because such glaucomatous damage precedes clinically identifiable visual loss. Early detection of glaucoma can prevent progression of the disease and consequent loss of vision. Traditional early detection techniques involve observing changes in the ONH through an ophthalmoscope. Stereo fundus photography is also routinely used to detect subtle changes in the ONH. However, clinical evaluation of stereo fundus photographs suffers from inter- and intra-subject variability. Even the Heidelberg Retina Tomograph (HRT) has not been found to be sufficiently sensitive for early detection. A semi-automated algorithm for quantitative representation of the optic disc and cup contours by computing accumulated disparities in the disc and cup regions from stereo fundus image pairs has already been developed using advanced digital image analysis methodologies. A 3-D visualization of the disc and cup is achieved assuming camera geometry. High correlation among computer-generated and manually segmented cup to disc ratios in a longitudinal study involving 159 stereo fundus image pairs has already been demonstrated. However, clinical usefulness of the proposed technique can only be tested by a fully automated algorithm. In this paper, we present a fully automated algorithm for segmentation of optic cup and disc contours from corresponding stereo disparity information. Because this technique does not involve human intervention, it eliminates subjective variability encountered in currently used clinical methods and provides ophthalmologists with a cost-effective and quantitative method for detection of ONH structural damage for early detection of glaucoma.

We present a new algorithm for automatic detection of bright tubular structures and its performance for automatic segmentation of vessels in breast MR sequences. This problem is interesting because vessels are the main type of false positive structures when automatically detecting lesions as regions that enhance after injection of the contrast agent. Our algorithm is based on the eigenvalues of what we call the shape tensor. It is new in that it does not rely on image derivatives of either first order, like methods based on the eigenvalues of the mean structure tensor, or second order, like methods based on the eigenvalues of the Hessian. It is therefore more precise and less sensitive to noise than those methods. In addition, the smoothing of the output which is inherent to approaches based on the Hessian or structure tensor is avoided. The output of our filter does not present the typical over-smoothed look of the output of the two differential filters that affects both their precision and sensitivity. The scale selection problem appears also less difficult in our approach compared to the differential techniques. Our algorithm is fast, needing only a few seconds per sequence. We present results of testing our method on a large number of motion-corrected breast MR sequences. These results show that our algorithm reliably segments vessels while leaving lesions intact. We also compare our method to the differential techniques and show that it significantly out-performs them both in sensitivity and localization precision and that it is less sensitive to scale selection parameters.

Structural, functional, and clinical studies in schizophrenia have, for several decades, consistently implicated dysfunction of the prefrontal cortex in the etiology of the disease. Functional and structural imaging studies, combined with clinical, psychometric, and genetic analyses in schizophrenia have confirmed the key roles played by the prefrontal cortex and closely linked "prefrontal system" structures such as the striatum, amygdala, mediodorsal thalamus, substantia nigra-ventral tegmental area, and anterior cingulate cortices. The nodal structure of the prefrontal system circuit is the dorsal lateral prefrontal cortex (DLPFC), or Brodmann area 46, which also appears to be the most commonly studied and cited brain area with respect to schizophrenia.^{1, 2, 3, 4} In 1986, Weinberger et. al. tied cerebral blood flow in the DLPFC to schizophrenia.¹ In 2001, Perlstein et. al. demonstrated that DLPFC activation is essential for working memory tasks commonly deficient in schizophrenia. 2 More recently, groups have linked morphological changes due to gene deletion and increased DLPFC glutamate concentration to schizophrenia.^{3, 4} Despite the experimental and clinical focus on the DLPFC in structural and functional imaging, the variability of the location of this area, differences in opinion on exactly what constitutes DLPFC, and inherent difficulties in segmenting this highly convoluted cortical region have contributed to a lack of widely used standards for manual or semi-automated segmentation programs. Given these implications, we developed a semi-automatic tool to segment the DLPFC from brain MRI scans in a reproducible way to conduct further morphological and statistical studies. The segmenter is based on expert neuroanatomist rules (Fallon-Kindermann rules), inspired by cytoarchitectonic data and reconstructions presented by Rajkowska and Goldman-Rakic.⁵ It is semi-automated to provide essential user interactivity. We present our results and provide details on our DLPFC open-source tool.

The hippocampus (Hc) and the amygdala (Am) are two cerebral structures that play a central role in main cognitive processes. Their segmentation allows atrophy in specific neurological illnesses to be quantified, but is made difficult by the complexity of the structures. In this work, a new algorithm for the simultaneous segmentation of Hc and Am based on competitive homotopic region deformations is presented. The deformations are constrained by relational priors derived from anatomical knowledge, namely probabilities for each structure around automatically retrieved landmarks at the border of the objects. The approach is designed to perform well on data from diseased subjects. The segmentation is initialized by extracting a bounding box and positioning two seeds; total execution time for both sides is between 10 and 15 minutes including initialization for the two structures. We present the results of validation based on comparison with manual segmentation, using volume error, spatial overlap and border distance measures. For 8 young healthy subjects the mean volume error was 7% for Hc and 11% for Am, the overlap: 84% for Hc and 83% for Am, the maximal distance: 4.2mm for Hc and 3.1mm for Am; for 4 Alzheimer's disease patients the mean volume error was 9% for Hc and Am, the overlap: 83% for Hc and 78% for Am, the maximal distance: 6mm for Hc and 4.4mm for Am. We conclude that the performance of the proposed method compares favourably with that of other published approaches in terms of accuracy and has a short execution time.

The definition of regions of interests (ROIs), such as suspect cancer nodules or lymph nodes in 3D CT chest images, is often difficult because of the complexity of the phenomena that give rise to them. Manual slice tracing has been used widely for years for such problems, because it is easy to implement and guaranteed to work. But the manual method is extremely time-consuming, especially for high-solution 3D images which may have hundreds of slices, and it is subject to operator biases. Numerous automated image-segmentation methods have been proposed, but they are generally strongly application dependent, and even the "most robust" methods have difficulty in defining complex anatomical ROIs. To address this problem, the semi-automatic interactive paradigm referred to as "live wire" segmentation has been proposed by researchers. In live-wire segmentation, the human operator interactively defines an ROI's boundary guided by an active automated method which suggests what to define. This process in general is far faster, more reproducible and accurate than manual tracing, while, at the same time, permitting the definition of complex ROIs having ill-defined boundaries. We propose a 2D live-wire method employing an improved cost over previous works. In addition, we define a new 3D live-wire formulation that enables rapid definition of 3D ROIs. The method only requires the human operator to consider a few slices in general. Experimental results indicate that the new 2D and 3D live-wire approaches are efficient, allow for high reproducibility, and are reliable for 2D and 3D object segmentation.

Accurate segmentation of small pulmonary nodules (SPNs) on thoracic CT images is an important technique for volumetric doubling time estimation and feature characterization for the diagnosis of SPNs. Most of the nodule segmentation algorithms that have been previously presented were designed to handle solid pulmonary nodules. However, SPNs with ground-glass opacity (GGO) also affects a diagnosis. Therefore, we have developed an automated volumetric segmentation algorithm of SPNs with GGO on thoracic CT images. This paper presents our segmentation algorithm with multiple fixed-thresholds, template-matching method, a distance-transformation method, and a watershed method. For quantitative evaluation of the performance of our algorithm, we used the first dataset provided by NCI Lung Image Database Consortium (LIDC). In the evaluation, we employed the coincident rate which was calculated with both the computerized segmented region of a SPN and the matching probability map (pmap) images provided by LIDC. As the result of 23 cases, the mean of the total coincident rate was 0.507 +/- 0.219. From these results, we concluded that our algorithm is useful for extracting SPNs with GGO and solid pattern as well as wide variety of SPNs in size.

The pulmonary lobes are the five distinct anatomic divisions of the human lungs. The physical boundaries between the lobes are called the lobar fissures. Detection of lobar fissure positions in pulmonary X-ray CT images is of increasing interest for the early detection of pathologies, and also for the regional functional analysis of the lungs. We have developed a two-step automatic method for the accurate segmentation of the three pulmonary fissures. In the first step, an approximation of the actual fissure locations is made using a 3-D watershed transform on the distance map of the segmented vasculature. Information from the anatomically labeled human airway tree is used to guide the watershed segmentation. These approximate fissure boundaries are then used to define the region of interest (ROI) for a more exact 3-D graph search to locate the fissures. Within the ROI the fissures are enhanced by computing a ridgeness measure, and this is used as the cost function for the graph search. The fissures are detected as the optimal surface within the graph defined by the cost function, which is computed by transforming the problem to the problem of finding a minimum s-t cut on a derived graph. The accuracy of the lobar borders is assessed by comparing the automatic results to manually traced lobe segments. The mean distance error between manually traced and computer detected left oblique, right oblique and right horizontal fissures is 2.3 ± 0.8 mm, 2.3 ± 0.7 mm and 1.0 ± 0.1 mm, respectively.

In this paper, we present a pseudo wavelet-based tagline detection method. The tagged MR image is transformed to the wavelet domain, and the prominent tagline coefficients are retained while others are eliminated. Significant stripes are extracted via segmentation, which are mixtures of tags and anatomical boundary that resembles line. A refinement step follows such that broken lines or isolated points are grouped or eliminated. Without assumption on tag models, our method extracts taglines automatically regardless their width and spacing. In addition, founded on the multi-resolution wavelet analysis, our method reconstructs taglines precisely and shows great robustness to various types of taglines.

Digital image fusion is a useful technique that can be applied to achieve extended depth-of-field microscope imaging. The central idea is to incorporate from all input images the regions that contain most in-focus signals into a single composite image. The amount of signal content of a particular region is estimated by an activity measure in general. To our best knowledge, all existing approaches in the literatures rely on estimates based on the strength of high frequency signal components as the activity measure. However, such measure does not distinguish true image signals from noise. We propose to use a multiscale point-wise product as the activity measure, which does not amplify the effect of noise. The resulting scheme shows a significant improvement on imaging of cytological specimens in terms of both subjective and objective quality even under a noise-free environment. More importantly, the scheme has a significant advantage over existing methods in the presence of noise.

In magnetic resonance imaging (MRI), there are three bands of images ("MRI triplet") available, which are T1-, T2- and PD-weighted images. The three images of a MRI triplet provide complementary structure information and therefore it is useful for diagnosis and subsequent analysis to combine three-band images into one. We propose an advanced discrete wavelet transform (αDWT) for three-band MRI image fusion and the αDWT algorithm is further optimized utilizing two quantitative fusion metrics - the image quality index (IQI) and ratio spatial frequency error (rSFe). In the aDWT method, principle component analysis (PCA) and morphological processing are incorporated into a regular DWT fusion algorithm. Furthermore, the αDWT has two adjustable parameters - the level of DWT decomposition (L_d) and the length of the selected wavelet (L_w) that determinately affect the fusion result. The fused image quality can be quantitatively measured with the established metrics - IQI and rSFe. Varying the control parameters (L_d and L_w), an iterative fusion procedure can be implemented and running until an optimized fusion is achieved. We fused and analyzed several MRI triplets from the Visible Human Project^® female dataset. From the quantitative and qualitative evaluations of fused images, we found that (1) the αDWTi-IQI algorithm produces a smoothed image whereas the αDWTi-rSFe algorithm yields a sharpened image, (2) fused image "T1+T2" is the most informative one in comparison with other two-in-one fusions (PD+T1 and PD+T2), (3) for three-in-one fusions, no significant difference is observed among the three fusions of (PD+T1)+T2, (PD+T2)+T1 and (T1+T2)+PD, thus the order of fusion does not play an important role. The fused images can significantly benefit medical diagnosis and also the further image processing such as multi-modality image fusion (with CT images), visualization (colorization), segmentation, classification and computer-aided diagnosis (CAD).

In this paper, we evaluate different non-rigid image registration methodologies in the context of atlas-based brain image segmentation. Three non-rigid voxel-based registration regularization schemes (viscous fluid, elastic and curvature-based registration) combined with the mutual information similarity measure are compared. We conduct large-scale atlas-based segmentation experiments on a set of 20 anatomically labelled MR brain images in order to find the optimal parameter settings for each scheme. The performance of the optimal registration schemes is evaluated in their capability of accurately segmenting 49 different brain sub-structures of varying size and shape.

The importance of small animal imaging in fundamental and clinical research is growing rapidly. These studies typically involve micro PET, micro MR, and micro CT images as well as optical or fluorescence images. Histological images are also often used to complement and/or validate the in vivo data. As is the case for human studies, automatic registration of these imaging modalities is a critical component of the overall analysis process, but, the small size of the animals and thus the limited spatial resolution of the in vivo images present specific challenges. In this paper, we propose a series of methods and techniques that permit the inter-subject registration of micro MR and histological images. We then compare results obtained by registering directly MR volumes to each other using a non-rigid registration algorithm we have developed at our institution with results obtained by registering first the MR volumes to their corresponding histological volume, which we reconstruct from 2D cross-sections, and then registering histological volumes to each other. We show that the second approach is preferable.

During functional magnetic resonance imaging (fMRI) brain examinations, the signal extraction from a large number of images is used to evaluate changes in blood oxygenation levels by applying statistical methodology. Image registration is essential as it assists in providing accurate fractional positioning accomplished by using interpolation between sequentially acquired fMRI images. Unfortunately, current subvoxel registration methods found in standard software may produce significant bias in the variance estimator when interpolating with fractional, spatial voxel shifts. It was found that interpolation schemes, as currently applied during the registration of functional brain images, could introduce statistical bias, but there is a possible correction scheme. This bias was shown to result from the "weighted-averaging" process employed by conventional implementation of interpolation schemes. The most severe consequence of inaccurate variance estimators is the undesirable violation of the fundamental 'stationary' assumption required for many statistical methods and Gaussian random field analysis. Thus, this bias violates assumptions of the general linear model (GLM) and/or t-tests commonly used in fMRI studies. Using simulated data as well as actual human data in this, it was demonstrated that this artifact can significantly alter the magnitude and location of the resulting activation patterns/results. Further, the work detailed here introduces a bias correction scheme and evaluates the improved accuracy of its sample variance calculation and influence on fMRI results through comparison with traditional fMRI image registered data.

The endovascular repair of an abdominal aortic aneurysm is a minimal invasive therapy which has been established during the past 15 years. A stent-graft is placed inside the aorta in order to cover the weakened regions of its wall. During a time interval of one or more years the stent-graft can migrate and deform with the risk of the occlusion of one of its limbs or of the rupture of the aneurysm. In this work we developed several strategies to quantify the migration and deformation in order to assess the risk coming with these movements and especially to characterize appearing complications by them. We calculated the rigid movement of the stent-graft and the aorta relative to the spinal canal. For this purpose, firstly, we rigidly registered the spinal canals, extracted for the different points in time, in order to establish a fixed reference system. All objects have been segmented first and surface points have been determined before applying a rigid and non-rigid point set registration algorithm. The change in the residual error after registration of the stent-graft with an increasing number of degrees of freedom indicates the amount of change in the stent-graft's morphology. We investigated a sample of 9. Two cases could be clearly distinguished by the quantified parameters: a high global migration and a strong reduction of the residual error after non-rigid registration. In both cases, strong complications have been detected by the examination of clinical experts but only by means of the images acquired one year later.

One method of modelling respiratory motion of the abdomen is to acquire CT images at different points in the respiratory cycle and develop a deformation model that gives a mapping between corresponding anatomical points in the images. In this work, we use such a method, and the target application is radiosurgery, particularly radiosurgical treatment of lesions that move during respiration, for example those in the liver, lung, or pancreas. In order to accurately calculate the treatment dose, it is necessary to have a good deformation map both globally and locally (in the vicinity of the treatment target). We use a dual-resolution method in order to allow a more accurate deformation model to be computed in the region of interest. We also introduce a tissue stiffness constraint, along with an application of matrix algebra that allows this constraint to be applied in an effective way with respect to the control point values.

In this paper, we propose a multi-modal non-rigid 2D-3D registration technique. This method allows a non-rigid alignment of a patient pre-operatively computed tomography (CT) to few intra operatively acquired fluoroscopic X-ray images obtained with a C-arm system. This multi-modal approach is especially focused on the 3D alignment of high contrast reconstructed volumes with intra-interventional low contrast X-ray images in order to make use of up-to-date information for surgical guidance and other interventions. The key issue of non-rigid 2D-3D registration is how to define the distance measure between high contrast 3D data and low contrast 2D projections. In this work, we use algebraic reconstruction theory to handle this problem. We modify the Euler-Lagrange equation by introducing a new 3D force. This external force term is computed from the residual of the algebraic reconstruction procedures. In the multi-modal case we replace the residual between the digitally reconstructed radiographs (DRR) and observed X-ray images with a statistical based distance measure. We integrate the algebraic reconstruction technique into a variational registration framework, so that the 3D displacement field is driven to minimize the reconstruction distance between the volumetric data and its 2D projections using mutual information (MI). The benefits of this 2D-3D registration approach are its scalability in the number of used X-ray reference images and the proposed distance that can handle low contrast fluoroscopies as well. Experimental results are presented on both artificial phantom and 3D C-arm CT images.

Most of the suggested image registration methods are based on the optimization of an objective function. Drawbacks of this approach are the problem of local minima and the need to initialize the transformation close to the true solution. This paper presents a method for N-dimensional rigid and similarity image registration that is not optimization-based and consequently it doesn't involve local minima and initialization. Instead of obtaining the transformation parameters implicitly through an iterative optimization process, they are obtained explicitly. The proposed method has advantages over existing explicit methods. The explicit expressions for transformation parameters involve image integrals and no image derivatives, which makes the method robust to noise. It is shown that the method has a few desired properties including symmetry and transitivity, and that it is invariant to initial alignment of the images. The method has been tested on simulated and real brain 2D and 3D MR image pairs and the achieved average registration error was one voxel.

The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has its benefits and is suitable for describing a range of medical structures in two dimensions. Delineations in medical applications often consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss a Euclidean alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding starting points, the alignment of one shape onto another consists of a single expression. If the starting points are arbitrary, we present a simple algorithm to bring a set of shapes into correspondence. Results are given for three different data sets; 62 outlines of the corpus callosum brain structure, 61 outlines of the brain ventricles, and 50 outlines of the right lung. The results show that even though starting points, translations, rotations and scales have been randomized, the alignment succeeds in all cases. As an application of the proposed method, we show how high-quality shape models represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects using the minimum description length criterion, producing ample correspondences. Results on this are also presented for all three data sets.

Image registration is the process of aligning separate images into a common reference frame so that they can be compared visually or statistically. In order for this alignment to be accurate and correct it is important to identify the correct anatomical correspondences between different subjects. We propose a new approach for a feature-based, inter-subject deformable image registration method using a novel displacement field interpolation. Among the top deformable registration algorithms in the literature today is the work of Shen et al. called HAMMER. This is a feature-based, hierarchical registration algorithm, which introduces the novel idea of fusing feature and intensity matching. The algorithm presented in this paper is an implementation of that method, where significant improvements of some important aspects have been made. A new approach to the algorithm will be introduced as well as clarification of some key features of the work of Shen et al. which have not been elaborated in previous publications. The new algorithm, which is referred to as Mjolnir (Thor's hammer), was validated on both synthesized and real T1 weighted MR brain images. The results were compared with results generated by HAMMER and show significant improvements in accuracy with reduction in computation time.

In this article, we propose a new registration method, based on a statistical analysis of deformation fields. At first, a set of MRI brain images was registered using a viscous fluid algorithm. The obtained deformation fields are then used to calculate a Principal Component Analysis (PCA) based decomposition. Since PCA models the deformations as a linear combination of statistically uncorrelated principal components, new deformations can be created by changing the coefficients in the linear combination. We then use the PCA representation of the deformation fields to non-rigidly align new sets of images. We use a gradient descent method to adjust the coefficients of the principal components, such that the resulting deformation maximizes the mutual information between the deformed image and an atlas image. The results of our method are promising. Viscous fluid registrations of new images can be recovered with an accuracy of about half a voxel. Better results can be obtained by using a more extensive database of learning images (we only used 84). Also, the optimization method used here can be improved, especially to shorten computation time.

Regularized nonrigid medical image registration algorithms usually estimate the deformation by minimizing a cost function, consisting of a similarity measure and a penalty term that discourages "unreasonable" deformations. Conventional regularization methods enforce homogeneous smoothness properties of the deformation field; less work has been done to incorporate tissue-type-specific elasticity information. Yet ignoring the elasticity differences between tissue types can result in non-physical results, such as bone warping. Bone structures should move rigidly (locally), unlike the more elastic deformation of soft issues. Existing solutions for this problem either treat different regions of an image independently, which requires precise segmentation and incurs boundary issues; or use an empirical spatial varying "filter" to "correct" the deformation field, which requires the knowledge of a stiffness map and departs from the cost-function formulation. We propose a new approach to incorporate tissue rigidity information into the nonrigid registration problem, by developing a space variant regularization function that encourages the local Jacobian of the deformation to be a nearly orthogonal matrix in rigid image regions, while allowing more elastic deformations elsewhere. For the case of X-ray CT data, we use a simple monotonic increasing function of the CT numbers (in HU) as a "rigidity index" since bones typically have the highest CT numbers. Unlike segmentation-based methods, this approach is flexible enough to account for partial volume effects. Results using a B-spline deformation parameterization illustrate that the proposed approach improves registration accuracy in inhale-exhale CT scans with minimal computational penalty.

Nonrigid registration is a technique commonly used in the field of medical imaging. A drawback of most current nonrigid registration algorithms is that they model all tissue as being nonrigid. When a nonrigid registration is performed, the rigid objects in the image, such as bony structures or surgical instruments, may also transform nonrigidly. Other consequences are that tumour growth between follow-up images may be concealed, or that structures containing contrast material in one image and not in the other may be compressed by the registration algorithm. In this paper we propose a novel regularisation term, which is added to the cost function in order to penalise nonrigid deformations of rigid objects. This regularisation term can be used for any representation of the deformation field capable of modelling locally rigid deformations. By using a B-spline representation of the deformation field, a fast algorithm can be devised. We show on 2D synthetic data, on clinical CT slices, and on clinical DSA images, that the proposed rigidity constraint is successful, thus improving registration results.

Respiratory motion is a significant source of error in radiotherapy treatment planning. 4D-CT data sets can be useful to measure the impact of organ motion caused by breathing. But modern CT scanners can only scan a limited region of the body simultaneously and patients have to be scanned in segments consisting of multiple slices. For studying free breathing motion multislice CT scans can be collected simultaneously with digital spirometry over several breathing cycles. The 4D data set is assembled by sorting the free breathing multislice CT scans according to the couch position and the tidal volume. But artifacts can occur because there are no data segments for exactly the same tidal volume and all couch positions. We present an optical flow based method for the reconstruction of 4D-CT data sets from multislice CT scans, which are collected simultaneously with digital spirometry. The optical flow between the scans is estimated by a non-linear registration method. The calculated velocity field is used to reconstruct a 4D-CT data set by interpolating data at user-defined tidal volumes. By this technique, artifacts can be reduced significantly. The reconstructed 4D-CT data sets are used for studying inner organ motion during the respiratory cycle. The procedures described were applied to reconstruct 4D-CT data sets for four tumour patients who have been scanned during free breathing. The reconstructed 4D data sets were used to quantify organ displacements and to visualize the abdominothoracic organ motion.

Modern MDCT and micro-CT scanners are able to produce high-resolution three-dimensional (3D) images of anatomical trees, such as the airway tree and the heart and liver vasculature. An important problem arising in many contexts is the matching of trees depicted in two different images. Three basic steps are used in order to match two trees: (1) image segmentation, to extract the raw trees from a given pair of 3D images; (2) axial-analysis, to define the underlying centerline structure of the trees; and (3) tree matching, to match the centerline structures of the trees. We focus on step (3). This task is complicated by several problems associated with current segmentation and axial-analysis methods, including missing branches, false branches, and other topological errors in the extracted trees. We propose a model-based approach in which the extracted trees are assumed to arise from an initially unknown common structure corrupted by a sequence of modelled topological deformations. We employ a novel mathematical framework to directly incorporate this model into the matching problem. Under this framework, it is possible to define the set of matches that are consistent with a given deformation model. The optimal match is the member of this set that maximizes a user-definable similarity measure. We present several such similarity measures based upon geometrical attributes (e.g., branch lengths, branching angles, and relative branchpoint locations as measured from the 3D image data). We locate the globally optimal match via an efficient dynamic programming algorithm. Our primary analytical result is a set of sufficient conditions on the user-definable similarity measure such that our dynamic programming algorithm is guaranteed to locate an optimal match. Experimental results have been generated for 3D human CT chest scans and micro-CT coronary arterial-tree images of mice. The resulting matches are in good agreement with correspondences defined by human experts.

Little work has been done on comparing the performance of statistical model-based approaches and nonrigid registration algorithms. This paper deals with the qualitative and quantitative comparison of active appearance models (AAMs) and a nonrigid registration algorithm based on free-form deformations (FFDs). AAMs are known to be much faster than nonrigid registration algorithms. On the other hand nonrigid registration algorithms are independent of a training set as required to build an AAM. To obtain a further comparison of the two methods, they are both applied to automatically register multi-slice myocardial perfusion images. The images are acquired by magnetic resonance imaging, from infarct patients. A registration of these sequences is crucial for clinical practice, which currently is subjected to manual labor. In the paper, the pros and cons of the two registration approaches are discussed and qualitative and quantitative comparisons are provided. The quantitative comparison is obtained by an analysis of variance of landmark errors, i.e. point to point and point to curve errors. Even though the FFD-based approach does not include a training phase it gave similar accuracy as the AAMs in terms of point to point errors. For the point to curve errors the AAMs provided higher accuracy. In both cases AAMs gave higher precision due to the training procedure.

Tagged Magnetic Resonance Imaging (MRI) is currently the reference modality for myocardial motion and strain analysis. Mutual Information (MI) based non rigid registration has proven to be an accurate method to retrieve cardiac motion and overcome many drawbacks present on previous approaches. In a previous work¹, we used Wavelet-based Attribute Vectors (WAVs) instead of pixel intensity to measure similarity between frames. Since the curse of dimensionality forbids the use of histograms to estimate MI of high dimensional features, k-Nearest Neighbors Graphs (kNNG) were applied to calculate α-MI. Results showed that cardiac motion estimation was feasible with that approach. In this paper, K-Means clustering method is applied to compute MI from the same set of WAVs. The proposed method was applied to four tagging MRI sequences, and the resulting displacements were compared with respect to manual measurements made by two observers. Results show that more accurate motion estimation is obtained with respect to the use of pixel intensity.

Three-dimensional (3D) stress echocardiography is a novel technique for diagnosing cardiac dysfunction, by comparing wall motion of the left ventricle under different stages of stress. For quantitative comparison of this motion, it is essential to register the ultrasound data. We propose an intensity based rigid registration method to retrieve two-dimensional (2D) four-chamber (4C), two-chamber, and short-axis planes from the 3D data set acquired in the stress stage, using manually selected 2D planes in the rest stage as reference. The algorithm uses the Nelder-Mead simplex optimization to find the optimal transformation of one uniform scaling, three rotation, and three translation parameters. We compared registration using the SAD, SSD, and NCC metrics, performed on four resolution levels of a Gaussian pyramid. The registration's effectiveness was assessed by comparing the 3D positions of the registered apex and mitral valve midpoints and 4C direction with the manually selected results. The registration was tested on data from 20 patients. Best results were found using the NCC metric on data downsampled with factor two: mean registration errors were 8.1mm, 5.4mm, and 8.0° in the apex position, mitral valve position, and 4C direction respectively. The errors were close to the interobserver (7.1mm, 3.8mm, 7.4°) and intraobserver variability (5.2mm, 3.3mm, 7.0°), and better than the error before registration (9.4mm, 9.0mm, 9.9°). We demonstrated that the registration algorithm visually and quantitatively improves the alignment of rest and stress data sets, performing similar to manual alignment. This will improve automated analysis in 3D stress echocardiography.

Cardiac interventional procedures such as myocardial stem cell delivery and radiofrequency ablation require a high degree of accuracy and efficiency. Real-time, 2-D MR technology is being developed to guide such procedures; the associated challenges include the relatively low resolution and image quality in real-time images. Real-time MR guidance can be enhanced by acquiring a 4-D (3-D + phase) volume prior to the procedure and aligning it to the 2-D real-time images, so that corresponding features in the prior volume can be integrated into the real-time image visualization. This technique provides spatial context with high resolution and SNR. A left ventricular (LV) myocardial wall contour tracking system was developed to maintain spatial alignment of prior volume images to real-time MR images. Over 9 test images sequences, each comprising 100 frames of simulated respiratory motion, the tracker maintained alignment with a mean displacement error of 1.61mm in a region of interest around the LV, as compared to a mean displacement error of 5.2mm without tracking.

In this paper we develop a new filtering framework for tensor signal processing using the theory of vector spaces. From this point of view, signals are regarded as elements of vector spaces and operators as mappings from the input space to the output space. Hence, it is possible to generalize the principle of superposition to any operator defined on the signal spaces. Systems that obey that generalization of the principle of superposition are referred to as homomorphic and they can be decomposed in a cascade of three homomorphic subsystems: the first one operates on the input signal space, the second one is a linear system in the usual sense and the third one operates on the output signal space. Thus, suitable input and output subsystems can be chosen to deal with input signals, which defines a whole family of homomorphic filters. To apply this idea for DT-MRI signals, which consist of positive semi-definite matrices, we identify input and output signal spaces as the set of those real symmetric positive semi-definite matrices. Our homomorphic filtering framework not only guarantees a positive-semidefinite output tensor field whatever linear filter is used to regularize the noisy input, but also reduces the swelling effect produced by a faster regularization of diffusivities rather than orientations, as demonstrate the encouraging results that have been obtained.

Reconstruction methods for MR imaging of dynamic objects have traditionally been analyzed using the projection slice theorem. In this paper, we present a new theoretical framework for analyzing MR imaging of dynamic objects. Our framework reinterprets the object stationarity assumption in the MR reconstruction techniques as a combination of filtering and downsampling operations performed on the acquired k-space data. We have analyzed our results in x-f (spatial coordinate - temporal frequency) space using a time-sequential analysis. While the projection slice theorem has only be used to analyze the Cartesian sampling pattern, the new framework can analyze any arbitrary sampling pattern with a given reconstruction algorithm. Further, the new theoretical framework can be used to analyze the effect of relaxing the object stationarity assumption over the reconstructed MR images. We have demonstrated the use of our framework by analyzing two popular image reconstruction techniques, namely view-sharing and UNFOLD. In the analysis of view-sharing, we have confirmed the fact that interleaved and bit reversed k-space sampling patterns provide better artifact suppression for dynamic MR imaging. We propose using a different filter to further reduce artifacts in the reconstructed images. In the case of UNFOLD, we have analyzed the effect of relaxing the object stationarity assumption and have shown that it leads to an increase in motion artifacts.

Magnetic resonance images are often corrupted by intensity inhomogeneity (i.e., bias field effects), which manifests itself as slow intensity variations over the image domain. Such shading artifacts must be corrected before performing computerized analyses such as intensity-based segmentation and quantitative analysis. In this paper, we present a novel strategy in the fuzzy c-means (FCM) framework that simultaneously estimates the bias field while segmenting the image. An additive field term that models the bias field is incorporated into the FCM objective function. We propose a new term based on the spectral parameterization (i.e., wavelet coefficients) of the bias field that serves as a regularizer to enforce the smoothness of the estimated bias field. We also introduce a second regularization term that causes the labeling of each pixel to be influenced by its immediate neighborhood pixels. The latter regularization term renders the algorithm less sensitive to noise. We show that the novel objective functional could be optimized efficiently using an iterative process. The efficacy of the algorithm is demonstrated on synthesized images as well as on clinical breast MR images. With the synthesize images, segmentation accuracy using standard FCM is 89.07% while segmentation accuracy with the proposed algorithm is 99.95%.

High angular resolution diffusion imaging (HARDI) has recently been of great interest to characterize non-Gaussian diffusion process. In the white matter of the brain, this occurs when fiber bundles cross, kiss or diverge within the same voxel. One of the important goal is to better describe the apparent diffusion process in these multiple fiber regions, thus overcoming the limitations of classical diffusion tensor imaging (DTI). In this paper, we design the appropriate mathematical tools to describe noisy HARDI data. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, we propose a new regularization algorithm to estimate a smoother and closer diffusivity profile to the true diffusivities without noise. We exploit properties of the spherical harmonics to define a smoothing term based on the Laplace-Beltrami for functions defined on the unit sphere. An additional contribution of the paper is the derivation of the general transformation taking the spherical harmonics coefficients to the high order tensor independent elements. This allows the careful study of the state of the art high order anisotropy measures computed from either spherical harmonics or tensor coefficients. We analyze their ability to characterize the underlying diffusion process. We are able to recover voxels with isotropic, single fiber anisotropic and multiple fiber anisotropic diffusion. We test and validate the approach on diffusion profiles from synthetic data and from a biological rat phantom.

The multiplicity of sensors used in medical imaging leads to different noises. Non informative noise can damage the image interpretation process and the performance of automatic analysis. The method proposed in this paper allows compensating highly noisy image data from non informative noise without sophisticated modeling of the noise statistics. This generic approach uses jointly a wavelet decomposition scheme and a non-isotropic Total Variation filtering of the transform coefficients. This framework benefits from both the hierarchical capabilities of the wavelet transform and the well-posed regularization scheme of the Total Variation. This algorithm has been tested and validated on test-bed data, as well as different clinical MR and 3D ultrasound images, enhancing the capabilities of the proposed method to cope with different noise models.

In this paper we seek to improve the standard method of assessing the degree of calcification in the lumbar aorta visualized on lateral 2-D X-rays. The semiquantitative method does not take density of calcification within the individual plaques into account and is unable to measure subtle changes in the severity of calcification over time. Both of these parameters would be desirable to assess, since they are the keys to assessing important information on the impact of risk factors and candidate drugs aiming at the prevention of atherosclerosis. As a further step for solving this task, we propose a pixelwise inpainting-based refinement scheme that seeks to optimize the individual plaque shape by maximizing the signal-to-noise ratio. Contrary to previous work the algorithm developped for this study uses a sorted candidate list, which omits possible bias introduced by the choice of starting pixel. The signal-to-noise optimization scheme will be discussed in different settings using TV as well as Harmonic inpainting and comparing these with a simple averaging process.

In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach.

We propose a multi-step approach for representing and classifying tree-like structures in medical images. Examples of such tree-like structures are encountered in the bronchial system, the vessel topology and the breast ductal network. We assume that the tree-like structures are already segmented. To avoid the tree isomorphism problem we obtain the breadth-first canonical form of a tree. Our approach is based on employing tree encoding techniques, such as the depth-first string encoding and the Prüfer encoding, to obtain a symbolic representation. Thus, the problem of classifying trees is reduced to string classification where node labels are the string terms. We employ the tf-idf text mining technique to assign a weight of significance to each string term (i.e., tree node label). We perform similarity searches and k-nearest neighbor classification of the trees using the tf-idf weight vectors and the cosine similarity metric. We applied our approach to the breast ductal network manually extracted from clinical x-ray galactograms. The goal was to characterize the ductal tree-like parenchymal structures in order to distinguish among different groups of women. Our best classification accuracy reached up to 90% for certain experimental settings (k=4), outperforming on the average by 10% that of a previous state-of-the-art method based on ramification matrices. These results illustrate the effectiveness of the proposed approach in analyzing tree-like patterns in breast images. Developing such automated tools for the analysis of tree-like structures in medical images can potentially provide insight to the relationship between the topology of branching and function or pathology.