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 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.

After researching the forming principle of X-ray beam hardening and analyzing the usual methods of beam hardening correction, a beam hardening correction model was established, in which the independent variable was the projection gray, and so the computing difficulties in beam hardening correction can be reduced. By considering the advantage and disadvantage of fitting beam hardening curve to polynomial, a new expression method of the subsection beam hardening curves based on polynomial was proposed. In the method, the beam hardening data were fitted firstly to a polynomial curve which traverses the coordinate origin, then whether the got polynomial curve surged in the fore-part or back-part of the fitting range was judged based on the polynomial curvature change. If the polynomial fitting curve surged, the power function curve was applied to replace the surging parts of the polynomial curve, and the C1 continuity was ensured at the joints of the segment curves. The experimental results of computed tomography (CT) simulation show that the method is well stable in the beam hardening correction for the ideal CT images and CT images with added noises, and can mostly remove the beam hardening artifact at the same time.

The computing method for orthogonal Fourier-Mellin moments in a polar coordinate system is presented in detail. The image expressed in a Cartesian system has to be transformed into a polar coordinate system first when we calculate the orthogonal Fourier-Mellin moments of the image in a polar coordinate system, which will increase both computational complexity and error. To solve the problem, a new direct computing method for orthogonal Fourier-Mellin moments in a Cartesian coordinate system is proposed, which can avoid the image transformation between two coordinate systems and eliminate the rounding error in coordinate transformation and decrease the computational complexity.

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.

Introduction: The scope of transesophageal echocardiography (TEE) is increasing as it is becoming a standard imaging tool in the intensive care unit, and intraoperatively in cardiac and non cardiac surgery. Anesthesiologists therefore have a need for training in conducting and interpreting a TEE exam. To assist with this training, we have created a new online teaching aid for TEE and incorporated it in a Web site. The primary challenge in learning TEE is translating the two dimensional (2D) echocardiographic image into a visualization of the three-dimensional (3D) structure of the heart. This Web site provides a learning environment where users can view all of the 20 standard TEE positions with a 3D heart model showing a representation of the plane of the echocardiographic image. The student is able to rotate the 3-D heart model and echo plane to view it from any perspective, helping them to relate the echocardiographic image to the structures of the heart. Users are also able to remove the part of the 3D image above the echo plane, revealing the internal structures of the heart that correspond to the TEE image in the video clip of that view as shown in Figure 1. This resource can be used by educators for teaching small group sessions and by students for self-study. METHODS: A digital 3D model of the heart was constructed that provides an accurate representation of the exterior and interior structures of the heart. The 3D model allowed sections of the heart to be created along the plane of the TEE image. The cross section revealed when the portion of the model above the echo plane is removed represents the structures seen in the TEE image. Iterative adjustment of the 3D model was used until there was a good match between the video images for all 20 standard diagnostic TEE views and the corresponding cross sections of the model. The TEE images thus acted as a "reality check" on the 3D model, ensuring its accuracy. RESULTS: Figure 1 shows the 3D heart model on the left with the portion above the echo plane removed for the mid esophageal right ventricle inflow/outflow view, and the corresponding TEE video clip on the right. Face and content validity was assessed with 3 staff anesthesiologists and 2 cardiologists, and usability was assessed using 5 anesthesia residents. Iterative changes to the model and the navigation were based on this evaluation. Construct validity will be carried out with anesthesia and cardiology Fellows, assessing their improvement in knowledge of the 20 standard views with a pre-test/post-test design.Discussion: This free online teaching aid will provide a unique resource that will be valuable for both educators and trainees learning to interpret TEE images nationally and around the world.References: None.

The 3D reconstruction of the spine in upright posture can be obtained by bi-planar radiographic methods, developed since the 1970s. The principle is to identify 4-25 anatomical landmarks per vertebrae and per images. This identification time is hardly manageable in clinical practice. A semi-automated method is used: 3D standard vertebral models are positioned along with a 3D curve (identified all the way through the vertebral bodies). The silhouettes of the models of C7 and L5 vertebrae are first adjusted and the positions of the other vertebrae are interpolated and optimised. The inter- and intra-operator variabilities and the errors between the semi-automated method and the manual identification of six anatomical landmarks per vertebra are evaluated on 20 pairs of X-ray images of subjects with different spinal deformities. The identification time for the semi-automated method is 5 min. For scolitic subjects, the precision is under 2.2 degrees and the accuracy is under 3.2 degrees for all lateral, sagittal and axial rotations.

The detection and extraction of complex anatomical structures usually involves a trade-off between the complexity of local feature extraction and classification, and the complexity and performance of the subsequent structural inference from the viewpoint of combinatorial optimization. Concerning the latter, computationally efficient methods are of particular interest that return the globally-optimal structure. We present an efficient method for part-based localization of anatomical structures which embeds contextual shape knowledge in a probabilistic graphical model. It allows for robust detection even when some of the part detections are missing. The application scenario for our statistical evaluation is spine detection and labeling in magnetic resonance images.

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 develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the IFGT. Using the IFGT, we derive the ordinary differential equations (ODEs) that describe image flowlines. We study the diagonalization of the ODEs of multidimensional frequency modulation on the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. We illustrate these new methods of image pattern analysis on textured and fingerprint images. We envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity. Examples of such textures abound in nature.

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.