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Automated Determination of the Spine-Based Coordinate System for an Efficient Cross-Sectional Visualization of 3D Spine Images

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Spinal Imaging and Image Analysis

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 18))

Abstract

The most common and straightforward visualization of three-dimensional (3D) images of the spine and vertebrae, usually obtained by computed tomography (CT) or magnetic resonance (MR) imaging techniques, is based on multi-planar cross-sections that are positioned in the coordinate system of the 3D image. However, such multi-planar cross-sections may not provide sufficient or qualitative enough diagnostic information, because they cannot follow the curvature of the spine. As a result, not all of the important details can be shown simultaneously in any cross-section. To overcome this problem, cross-sections have to be generated in the coordinate system of the spine, which can be achieved by curved-planar 3D image reformation that reduces the structural complexity in favor of an improved feature perception of anatomical structures. The parameters for such cross-sectional image reformation are determined from the spine-based coordinate system, which is defined by the curve representing the vertebral column and by the rotation of vertebrae about the spine curve. This chapter is focused on the techniques for automated determination of the spine-based coordinate system for an efficient cross-sectional visualization of 3D spine images, acquired by the CT and MR imaging techniques. The reformatted cross-sections are diagnostically valuable, enable easier navigation, manipulation and orientation in 3D space, and are useful for initializing segmentation and other automated image analysis tasks.

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Notes

  1. 1.

    It is assumed that point \({\mathbf{p}} = [x,y,z]\) is a column vector. If \({\mathbf{p}}\) is a row vector, vector transpose operation is required, therefore the equation \({\mathbf{p}^{\prime}} = (x^{\prime},y^{\prime},z^{\prime}) = R{\kern 1pt} [x,y,z] = R{\kern 1pt} {\mathbf{p}}\) turns into \({\mathbf{p}^{\prime}} = (x^{\prime},y^{\prime},z^{\prime}) = \left( {R{\kern 1pt} [x,y,z]^{T} } \right)^{T} = \left( {R{\kern 1pt} {\mathbf{p}}^{T} } \right)^{T}\).

  2. 2.

    It is assumed that \({\mathbf{p}}\) is a column vector. If \({\mathbf{p}}\) is a row vector, vector transpose operation is required, therefore Eq. 56 turns into \({\mathbf{p}^{\prime}} = (x^{\prime},y^{\prime},z^{\prime}) = \left( {R(\alpha ,\beta ,\gamma ) [x,y,z]^{T} } \right)^{T} = \left( {R(\alpha ,\beta ,\gamma ) {\mathbf{p}}^{T} } \right)^{T}\).

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Acknowledgements

The author would like to thank B. Ibragimov (University of Ljubljana, Faculty of Electrical Engineering, Slovenia) for manually segmenting the spine from a CT image that was used for rendering purposes.

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  1. Faculty of Electrical Engineering, University of Ljubljana, Tržaška cesta 25, SI-1000, Ljubljana, Slovenia

    Tomaž Vrtovec

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  1. GE Healthcare and University of Western Ontario, London, Ontario, Canada

    Shuo Li

  2. Clinical Center, National Institutes of Health, Bethesda, Maryland, USA

    Jianhua Yao

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Vrtovec, T. (2015). Automated Determination of the Spine-Based Coordinate System for an Efficient Cross-Sectional Visualization of 3D Spine Images. In: Li, S., Yao, J. (eds) Spinal Imaging and Image Analysis. Lecture Notes in Computational Vision and Biomechanics, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-12508-4_8

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