We propose a completely automated algorithm for the detection of the spinal centreline and the centres of vertebral bodies and intervertebral discs in images acquired by computed tomography (CT) and magnetic resonance (MR) imaging. The developed methods are based on the analysis of the geometry of spinal structures and the characteristics of CT and MR images and were evaluated on 29 CT and 13 MR images of lumbar spine. The overall mean distance between the obtained and the ground truth spinal centrelines and centres of vertebral bodies and intervertebral discs were 1.8 +/- 1.1 mm and 2.8 +/- 1.9 mm, respectively, and no considerable differences were detected among the results for CT, T(1)-weighted MR and T(2)-weighted MR images. The knowledge of the location of the spinal centreline and the centres of vertebral bodies and intervertebral discs is valuable for the analysis of the spine. The proposed method may therefore be used to initialize the techniques for labelling and segmentation of vertebrae.

In the past, a number of methods were proposed for quantitative assessment of vertebral rotation from three-dimensional (3D) images. However, these methods were based on manual identification of distinctive anatomical landmarks, required manual determination of cross-sections from 3D images, and measured only axial vertebral rotation instead of the rotation in 3D. In this paper, we propose an automated method for quantitative assessment of vertebral rotation in 3D that is based on finding the planes of vertebral symmetry by matching image intensity gradients on both sides of each plane. The method was evaluated on 28 images of normal and pathological vertebrae, obtained by computed tomography (CT) and magnetic resonance (MR). For each vertebra, final angle displacements of 200 initial angle displacements, uniformly distributed within 30 degrees from manually obtained reference angles, were obtained. The results show that by the proposed method, vertebral rotation can be successfully estimated in 3D with an average accuracy of 1.0 degrees and precision of 0.5 degrees.

The purpose of this study is to present a framework for quantitative analysis of spinal curvature in 3D. In order to study the properties of such complex 3D structures, we propose two descriptors that capture the characteristics of spinal curvature in 3D. The descriptors are the geometric curvature (GC) and curvature angle (CA), which are independent of the orientation and size of spine anatomy. We demonstrate the two descriptors that characterize the spinal curvature in 3D on 30 computed tomography (CT) images of normal spine and on a scoliotic spine. The descriptors are determined from 3D vertebral body lines, which are obtained by two different methods. The first method is based on the least-squares technique that approximates the manually identified vertebra centroids, while the second method searches for vertebra centroids in an automated optimization scheme, based on computer-assisted image analysis. Polynomial functions of the fourth and fifth degree were used for the description of normal and scoliotic spinal curvature in 3D, respectively. The mean distance to vertebra centroids was 1.1 mm (+/-0.6 mm) for the first and 2.1 mm (+/-1.4 mm) for the second method. The distributions of GC and CA values were obtained along the 30 images of normal spine at each vertebral level and show that maximal thoracic kyphosis (TK), thoracolumbar junction (TJ) and maximal lumbar lordosis (LL) on average occur at T3/T4, T12/L1 and L4/L5, respectively. The main advantage of GC and CA is that the measurements are independent of the orientation and size of the spine, thus allowing objective intra- and inter-subject comparisons. The positions of maximal TK, TJ and maximal LL can be easily identified by observing the GC and CA distributions at different vertebral levels. The obtained courses of the GC and CA for the scoliotic spine were compared to the distributions of GC and CA for the normal spines. The significant difference in values indicates that the descriptors of GC and CA may be used to detect and quantify scoliotic spinal curvatures. The proposed framework may therefore improve the understanding of spine anatomy and aid in the clinical quantitative evaluation of spinal deformities.

A novel method for automated curved planar reformation (CPR) of magnetic resonance (MR) images of the spine is presented. The CPR images, generated by a transformation from image-based to spine-based coordinate system, follow the structural shape of the spine and allow the whole course of the curved anatomy to be viewed in individual cross-sections. The three-dimensional (3D) spine curve and the axial vertebral rotation, which determine the transformation, are described by polynomial functions. The 3D spine curve passes through the centres of vertebral bodies, while the axial vertebral rotation determines the rotation of vertebrae around the axis of the spinal column. The optimal polynomial parameters are obtained by a robust refinement of the initial estimates of the centres of vertebral bodies and axial vertebral rotation. The optimization framework is based on the automatic image analysis of MR spine images that exploits some basic anatomical properties of the spine. The method was evaluated on 21 MR images from 12 patients and the results provided a good description of spine anatomy, with mean errors of 2.5 mm and 1.7 degrees for the position of the 3D spine curve and axial rotation of vertebrae, respectively. The generated CPR images are independent of the position of the patient in the scanner while comprising both anatomical and geometrical properties of the spine.

We present a novel method for curved planar reformation (CPR) of spine images obtained by magnetic resonance (MR) imaging. CPR images, created via a transformation from image-based to spine-based coordinate system, follow the structural shape of the spine and allow the whole course of the curved structure to be viewed in a single image. The spine-based coordinate system is defined on the 3D spine curve and on the axial vertebral rotation, both described by polynomial models. The 3D spine curve passes through the centers of vertebral bodies, and the axial vertebral rotation determines the rotation of vertebral spinous processes around the spine. The optimal polynomial parameters are found in an optimization framework, based on image analysis. The method was evaluated on 19 MR images of the spine from 10 patients.

Traditional techniques for analyzing tortuous anatomical structures (e.g. arteries, colon, spine) in the coordinate system of the 3D image generally do not provide sufficient or qualitative enough diagnostic information, because planar cross-sections do not follow curved paths along the structures. To overcome this shortcoming, images in the coordinate system of the structure must be created. We propose a transformation from standard image-based to a novel spine-based coordinate system. The origin and axes of the proposed spine-based coordinate system are determined on the curve that represents the vertebral column, and the rotation of the vertebrae around the spine curve, both of which are described by polynomial models. The optimal polynomial parameters are obtained in an image analysis based optimization framework. The method has been evaluated on five CT spine images.

In this paper, a novel method for EEG to MRI registration is proposed. Initial registration is achieved by extracting and matching symmetry planes of MRI and EEG data, followed by iterative registration based on minimizing a cost function. Comparison of the intensity distributions of the whole MR image and MRI voxels around a head surface point yields global similarities, while the comparison of intensity distributions of MRI voxels around corresponding EEG points, which reflects the head's sagittal symmetry, yields local similarities. Therefore, when the EEG points are registered to the MR image, maximal global and local similarities should be obtained. The cost function, incorporating global and local similarities, was the sum of Kullback-Leibler divergences between corresponding intensity distributions. The proposed method was evaluated on clinical MRI data with simulated EEG data, yielding mean registration error of 0.48 +/- 0.33 mm, while with real EEG data an average root-mean-square point-to-surface error of 2.27 +/- 0.02 mm was obtained.

An important part of image-guided radiation therapy or surgery is registration of a three-dimensional (3D) preoperative image to two-dimensional (2D) images of the patient. It is expected that the accuracy and robustness of a 3D/2D image registration method do not depend solely on the registration method itself but also on the number and projections (views) of intraoperative images. In this study, we systematically investigate these factors by using registered image data, comprising of CT and X-ray images of a cadaveric lumbar spine phantom and the recently proposed 3D/2D registration method. The results indicate that the proportion of successful registrations (robustness) significantly increases when more X-ray images are used for registration.

Image registrations that are based on similarity measures simply adjust the parameters of an appropriate spatial transformation model until the similarity measure reaches an optimum. The numerous similarity measures that have been proposed in the past are differently sensitive to imaging modality, image content and differences in the image content, selection of the floating and target image, partial image overlap, etc. In this paper, we evaluate and compare 12 similarity measures for the rigid registration. To study the impact of different imaging modalities on the behavior of similarity measures, we have used 16 CT/MR and 6 PET/MR image pairs with known 'gold standard' registrations. The results for the PET/MR registration and for the registration of CT to both rectified and unrectified MR images indicate that mutual information, normalized mutual information and the entropy correlation coefficient are the most accurate similarity measures and have the smallest risk of being trapped in a local optimum. The results of an experiment on the impact of exchanging the floating and target image indicate that, especially in MR/PET registrations, the behavior of some similarity measures, such as mutual information, significantly depends on which image is the floating and which is the target.

Medical image acquisition devices provide a vast amount of anatomical and functional information, which facilitate and improve diagnosis and patient treatment, especially when supported by modern quantitative image analysis methods. However, modality specific image artifacts, such as the phenomena of intensity inhomogeneity in magnetic resonance images (MRI), are still prominent and can adversely affect quantitative image analysis. In this paper, numerous methods that have been developed to reduce or eliminate intensity inhomogeneities in MRI are reviewed. First, the methods are classified according to the inhomogeneity correction strategy. Next, different qualitative and quantitative evaluation approaches are reviewed. Third, 60 relevant publications are categorized according to several features and analyzed so as to reveal major trends, popularity, evaluation strategies and applications. Finally, key evaluation issues and future development of the inhomogeneity correction field, supported by the results of the analysis, are discussed.

We present two visualization techniques for curve-centric volume reformation with the aim to create compelling comparative visualizations. A curve-centric volume reformation deforms a volume, with regards to a curve in space, to create a new space in which the curve evaluates to zero in two dimensions and spans its arc-length in the third. The volume surrounding the curve is deformed such that spatial neighborhood to the curve is preserved. The result of the curve-centric reformation produces images where one axis is aligned to arc-length, and thus allows researchers and practitioners to apply their arc-length parameterized data visualizations in parallel for comparison. Furthermore we show that when visualizing dense data, our technique provides an inside out projection, from the curve and out into the volume, which allows for inspection what is around the curve. Finally we demonstrate the usefulness of our techniques in the context of two application cases. We show that existing data visualizations of arc-length parameterized data can be enhanced by using our techniques, in addition to creating a new view and perspective on volumetric data around curves. Additionally we show how volumetric data can be brought into plotting environments that allow precise readouts. In the first case we inspect streamlines in a flow field around a car, and in the second we inspect seismic volumes and well logs fromdrilling.

This paper presents a novel self-calibration method of an X-ray sceneapplied for the 3D reconstruction of the scoliotic spine. Current calibration techniques either use a cumbersome calibration apparatus or depend on manually identified landmarks to determine the geometric configuration, thus limiting routine clinical evaluation. The proposed approach uses high level information automatically extracted from biplanar X-rays to solve the radiographic scene parameters. We first present a segmentation method which takes into account the variable appearance and geometry of a scoliotic spine in order to isolate and extract the silhouettes of the anterior vertebral body. By incorporating prior anatomical information through a Bayesian formulation of the morphological distribution, a multi-scale spine segmentation framework is proposed for scoliotic patients. An iterative non-linear optimization procedure, integrating a 3D visual hull reconstruction and geometrical torsion properties of the spine, is then applied to globally refine the geometrical parameters of the 3D viewing scene and obtain the optimal 3D reconstruction. An experimental comparison to data provided from reference synthetic models yields similar accuracy on the retro-projection of low-level primitives such as anatomical landmarks identified on each vertebra (2.2 mm). Results obtained from a clinical validation on 60 pairs of uncalibrated digitized Xrays of adolescents with scoliosis show that the 3D reconstructions from the new system offer geometrically accurate models with insignificant differences for 3D clinical indices commonly used in the evaluation of spinal deformities. The reported experiments demonstrate a viable and accurate alternative to previous reconstruction techniques, offering the first automatic approach for routine 3D clinical assessment in radiographic suites.

Serial block face imaging is a microscopy technique in which the top of a specimen is cut or ground away and a mosaic of images is collected of the newly revealed cross-section. Images collected from each slice are then digitally stacked to achieve 3D images. The development of fully automated image acquisition devices has made serial block face imaging more attractive by greatly reducing labour requirements. The technique is particularly attractive for studies of biological activity within cancellous bone as it has the capability of achieving direct, automated measures of biological and morphological traits and their associations with one another. When used with fluorescence microscopy, serial block face imaging has the potential to achieve 3D images of tissue as well as fluorescent markers of biological activity. Epifluorescence-based serial block face imaging presents a number of unique challenges for visualizing bone specimens due to noise generated by sub-surface signal and local variations in tissue autofluorescence. Here we present techniques for processing serial block face images of trabecular bone using a combination of non-uniform illumination correction, precise tiling of the mosaic in each cross-section, cross-section alignment for vertical stacking, removal of sub-surface signal and segmentation. The resulting techniques allow examination of bone surface texture that will enable 3D quantitative measures of biological processes in cancellous bone biopsies.

Recently, marginal space learning (MSL) was proposed as a generic approach for automatic detection of 3D anatomical structures in many medical imaging modalities [1]. To accurately localize a 3D object, we need to estimate nine pose parameters (three for position, three for orientation, and three for anisotropic scaling). Instead of exhaustively searching the original nine-dimensional pose parameter space, only low-dimensional marginal spaces are searched in MSL to improve the detection speed. In this paper, we apply MSL to 2D object detection and perform a thorough comparison between MSL and the alternative full space learning (FSL) approach. Experiments on left ventricle detection in 2D MRI images show MSL outperforms FSL in both speed and accuracy. In addition, we propose two novel techniques, constrained MSL and nonrigid MSL, to further improve the efficiency and accuracy. In many real applications, a strong correlation may exist among pose parameters in the same marginal spaces. For example, a large object may have large scaling values along all directions. Constrained MSL exploits this correlation for further speed-up. The original MSL only estimates the rigid transformation of an object in the image, therefore cannot accurately localize a nonrigid object under a large deformation. The proposed nonrigid MSL directly estimates the nonrigid deformation parameters to improve the localization accuracy. The comparison experiments on liver detection in 226 abdominal CT volumes demonstrate the effectiveness of the proposed methods. Our system takes less than a second to accurately detect the liver in a volume.

Vascular disease is a leading cause of death and disability in the western world. Diagnosis and staging of atherosclerosis is a challenge, especially with regards to the identification of plaque vulnerability. We are developing imaging methods based upon MRI and intravascular microcoils. In order to rigorously validate our MRI imaging methods and algorithms, we have developed a new cryo-imaging system that allows one to alternately section and image the block face of tissue. We obtain 3D pathology of vessel segments excised from cadaver and we characterize the tissues of atheroma using episcopic autofluorescence and bright field microscopy images. After embedding the vessel, the block is frozen, and block face microscopic images are taken every 200microm with an image resolution of 30micromx30microm. The series of images is then corrected for uneven illumination, serially registered to one another, and the 3D vessel segment is reconstructed. Some sections are recovered and processed with histological staining for validation. Seven tissue types can be readily identified from the cryo-images: necrotic core, calcification, lipid pool, media, adventitia, fibrosis, thrombus, and normal intima. Since the whole vessel segment is available, we could register 3D data to images from MR, or other modalities, for validation. In addition, visualization tools such as multi-planar reformatting 3D rendering can be used to study 3D plaque morphology, in microscopic detail.

The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.

The variations in dendritic branch morphology and spine density provide insightful information about the brain function and possible treatment to neurodegenerative disease, for example investigating structural plasticity during the course of Alzheimer's disease. Most automated image processing methods aiming at analyzing these problems are developed for in vitro data. However, in vivo neuron images provide real time information and direct observation of the dynamics of a disease process in a live animal model. This paper presents an automated approach for detecting spines and tracking spine evolution over time with in vivo image data in an animal model of Alzheimer's disease. We propose an automated pipeline starting with curvilinear structure detection to determine the medial axis of the dendritic backbone and spines connected to the backbone. We, then, propose the adaptive local binary fitting (aLBF) energy level set model to accurately locate the boundary of dendritic structures using the central line of curvilinear structure as initialization. To track the growth or loss of spines, we present a maximum likelihood based technique to find the graph homomorphism between two image graph structures at different time points. We employ dynamic programming to search for the optimum solution. The pipeline enables us to extract dynamically changing information from real time in vivo data. We validate our proposed approach by comparing with manual results generated by neurologists. In addition, we discuss the performance of 3D based segmentation and conclude that our method is more accurate in identifying weak spines. Experiments show that our approach can quickly and accurately detect and quantify spines of in vivo neuron images and is able to identify spine elimination and formation.

Two-dimensional far-zone focusing lenses are designed using the coordinate transformation approach that feature minimized reflections from the lens boundaries. A flat lens of trapezoidal cross section completely converts incident waves with cylindrical wavefronts into transmitted waves with planar wavefronts. A rectangular lens with reduced non-magnetic material parameters that incorporates a nonlinear coordinate transformation features a significantly reduced amount of reflections compared with the non-magnetic lens based on a linear transformation. The improved reflection performance of each new lens design is verified using a full-wave finite-element analysis and compared with previously reported transformation optical lenses.

We address the 3D volume reconstruction problem from depth adjacent sub-volumes acquired by a confocal laser scanning microscope (CLSM). Our goal is to align the sub-volumes by estimating a set of optimal global transformations that preserve morphological continuity of medical structures, e.g., blood vessels, in the reconstructed 3D volume. We approach the problem by learning morphological characteristics of structures of interest in each sub-volume to understand global alignment transformations. Based on the observations of morphology, sub-volumes are aligned by connecting the morphological features at the sub-volume boundaries by minimizing morphological discontinuity. To minimize the discontinuity, we introduce three morphological discontinuity metrics: discontinuity magnitude at sub-volume boundary points, and overall and junction discontinuity residuals after polynomial curve fitting to multiple aligned sub-volumes. The proposed techniques have been applied to the problem of aligning CLSM sub-volumes acquired from four consecutive physical cross sections. Our experimental results demonstrated significant improvements of morphological smoothness of medical structures in comparison with the results obtained by feature matching at the sub-volume boundaries. The experimental results were evaluated by visual inspection and by quantifying morphological discontinuity metrics.