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.

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.

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.

Traditional techniques for visualizing anatomical structures are based on planar cross-sections from volume images, such as images obtained by computed tomography (CT) or magnetic resonance imaging (MRI). However, planar cross-sections taken in the coordinate system of the 3D image often do not provide sufficient or qualitative enough diagnostic information, because planar cross-sections cannot follow curved anatomical structures (e.g. arteries, colon, spine, etc). Therefore, not all of the important details can be shown simultaneously in any planar cross-section. To overcome this problem, reformatted images in the coordinate system of the inspected structure must be created. This operation is usually referred to as curved planar reformation (CPR). In this paper we propose an automated method for CPR of 3D spine images, which is based on the image transformation from the standard image-based to a novel spine-based coordinate system. The 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 proposed method was qualitatively and quantitatively evaluated on five CT spine images. The method performed well on both normal and pathological cases and was consistent with manually obtained ground truth data. The proposed spine-based CPR benefits from reduced structural complexity in favour of improved feature perception of the spine. The reformatted images are diagnostically valuable and enable easier navigation, manipulation and orientation in 3D space. Moreover, reformatted images may prove useful for segmentation and other image analysis tasks.

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.

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.

A new method for rapidly tailoring molecular properties is presented in which the three-dimensional shape of a malleable framework is controlled by heating with a template molecule.

This paper presents a novel 3D reconstruction method of the scoliotic spine using prior vertebra models with image-based information taken from biplanar X-ray images. We first propose a global modeling approach by exploiting the 3D scoliotic curve reconstructed from a coronal and sagittal X-ray image in order to generate an approximate statistical model from a 3D database of scoliosis patients based on a transformation algorithm which incorporates intuitive geometrical properties. The personalized 3D reconstruction of the spine is then achieved with a novel segmentation method which takes into account the variable appearance of scoliotic vertebrae (rotation, wedging) from standard quality images in order to segment and isolate individual vertebrae on the radiographic planes. More specifically, it uses prior 3D models regulated from 2D image level set functionals to identify and match corresponding bone structures on the biplanar X-rays. An iterative optimization procedure integrating similarity measures such as deformable vertebral contours regulated from high-level anatomical primitives, morphological knowledge and epipolar constraints is then applied to globally refine the 3D anatomical landmarks on each vertebra level of the spine. This method was validated on twenty scoliotic patients by comparing results to a standard manual approach. The qualitative evaluation of the retro-projection of the vertebral contours confirms that the proposed method can achieve better consistency to the X-ray image's natural content. A comparison to synthetic models and real patient data also yields good accuracy on the localization of low-level primitives such as anatomical landmarks identified by an expert on each vertebra. The experiments reported in this paper demonstrate that the proposed method offers a better matching accuracy on a set of landmarks from biplanar views when compared to a manual technique for each evaluated cases, and its precision is comparable to 3D models generated from magnetic resonance images (MRI), thus suitable for routine 3D clinical assessment of spinal deformities.

This investigation was aimed at the evaluation of the borders of individual variability of the human lumbar spine lordosis. 224 nuclear magnetic tomograms of persons of mature age were analyzed using morphometric, statistical methods, method of three-dimensional (3D) computer modeling and finite-element analysis. During the investigation, a hardware-software complex for morphometric research was created together with the new method of development of 3D computer models of the lumbar spine. The application of 3D modeling allowed to extend the knowledge of human spine biomechanics. Tensions and deformations were calculated in all lumbar vertebrae and intervertebral disks on the basis of spine 3D models developed. Finite-element analysis proved that a normal angle of lumbar lordosis was optimal for the transmission of the adequate compression loads, while the extreme forms of individual variability (high degrees of hyper- and hypolordosis), by changing the geometry of the vertebral column, result in the decrease of the functionality of this system.

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.

Consistency of MR scan planning is very important for diagnosis, especially in multi-site trials and follow-up studies, where disease progress or response to treatment is evaluated. Accurate manual scan planning is tedious and requires skillful operators. On the other hand, automated scan planning is difficult due to relatively low quality of survey images ("scouts") and strict processing time constraints. This paper presents a novel method for automated planning of MRI scans of the spine. Lumbar and cervical examinations are considered, although the proposed method is extendible to other types of spine examinations, such as thoracic or total spine imaging. The automated scan planning (ASP) system consists of an anatomy recognition part, which is able to automatically detect and label the spine anatomy in the scout scan, and a planning part, which performs scan geometry planning based on recognized anatomical landmarks. A validation study demonstrates the robustness of the proposed method and its feasibility for clinical use.

In this study, a Method to segment ovary Magnetic Resonance (MR) images and distinguish healthy tissue from cysts has been described. Through the application of independent component analysis (ICA) to a set of perfusion MR images it was possible to extract the output independent components and their corresponding signal-time curves. After examining and analyzing this result, a polynomial approach was computed to represent the main features of each curve, and automated particular selection of independent components was obtained by applying a Bayesian information criterion able to show the most relevant components. The results shown in this work permit to conclude that the independent components with a step-like signal-time curve allow to distinguish healthy tissue from cysts, thus, giving very promising results for the application of ICA to ovary tissue segmentation of perfusion MR images.

Curved Planar Reformation (CPR) has proved to be a practical and widely used tool for the visualization of curved tubular structures within the human body. It has been useful in medical procedures involving the examination of blood vessels and the spine. However, it is more difficult to use it for large, tubular, structures such as the trachea and the colon because abnormalities may be smaller relative to the size of the structure and may not have such distinct density and shape characteristics.Our new approach improves on this situation by using volume rendering for hollow regions and standard CPR for the surrounding tissue. This effectively combines gray scale contextual information with detailed color information from the area of interest. The approach is successfully used with each of the standard CPR types and the resulting images are promising as an alternative to virtual endoscopy.Because the CPR and the volume rendering are tightly coupled, the projection method used has a significant effect on properties of the volume renderer such as distortion and isometry. We describe and compare the different CPR projection methods and how they affect the volume rendering process.A version of the algorithm is also presented which makes use of importance driven techniques; this ensures the users attention is always focused on the area of interest and also improves the speed of the algorithm.

Recently, extensions to curved planar reformation (CPR) were proposed to improve vascular visualization of medical images. While these projective transformations provide enhanced visualization of vascular trees, non-planar alignment and arbitrary topology can cause visualization artifacts. Vascular trees in medical images are not aligned to planar cross-sections of volumetric image slices and thus aggravate simultaneous visualization of diagnostic features. Complex tree topology and non-planar alignment requires the need for an adaptive projection scheme to prevent visualization artifacts while preserving correctness of anatomical information. In this paper, we present algorithmic details for topological and orientation invariant visualization of vascular trees. Vascular high-level description of the medial axis guides the reformation process by flattening the vascular tree interior to successive image planes for respective radial sampling angles. Tree orientations are estimated from intrinsic shape properties of the vascular tree for rotation invariant projection. Radial sampling planes perpendicular to the medial axis tangents are the basis for topological invariant visualization of complete vascular interiors. We present experimental results on two different vascular tree topologies and demonstrate that our method is able to produce artifact free visualization of vascular interiors.

This paper reports a study on correlation comparison of the vertebral axial rotation relative to curvature and torsion of scoliotic spine. The goal of this study is to understand whether the vertebral axial rotation is more correlated to the curvature or to the torsion of the scoliosis spinal deformity. For this purpose, the simplified 3D spine models are constructed on the randomly chosen images of scoliosis patients. The 3D spine model is based on two orthogonal spinal radiographic images taken from coronal and sagittal planes. Superimposed on these two images, the 3D Bezier curves are fitted interactively onto the center of the spine on both coronal and sagittal images. Upon the 3D Bezier Curve fitting, a series of simplified 3D vertebrae are implemented onto the 3D Bezier Curve proportional in size to its axis. The curvature and torsion then are obtained by difference quotients algorithm. In determining the vertebral axial rotation, the measurements are conducted directly on the coronal spine images. The lateral margins and centers of pedicles are used as landmarks for the rotation calculation. The correlation coefficients are calculated from both vertebral axial rotation relative to the curvature and to the torsion found on each vertebra. The strength of correlations from both cases is compared in the table.