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.

The aim of this paper is to provide a complete overview of the existing methods for quantitative evaluation of spinal curvature from medical images, and to summarize the relevant publications, which may not only assist in the introduction of other researchers to the field, but also be a valuable resource for studying the existing methods or developing new methods and evaluation strategies. Key evaluation issues and future considerations, supported by the results of the overview, are also discussed.

Quantitative evaluation of axial vertebral rotation is essential for the determination of reference values in normal and pathological conditions and for understanding the mechanisms of the progression of spinal deformities. However, routine quantitative evaluation of axial vertebral rotation is difficult and error-prone due to the limitations of the observer, characteristics of the observed vertebral anatomy and specific imaging properties. The scope of this paper is to review the existing methods for quantitative evaluation of axial vertebral rotation from medical images along with all relevant publications, which may provide a valuable resource for studying the existing methods or developing new methods and evaluation strategies. The reviewed methods are divided into the methods for evaluation of axial vertebral rotation in 2D images and the methods for evaluation of axial vertebral rotation in 3D images. Key evaluation issues and future considerations, supported by the results of the overview, are also discussed.

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.

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.