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Algorithms for the Recovery of the 3-D Shape of Anatomical Structures from Single X-Ray Images

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Computational Methods in Biophysics, Biomaterials, Biotechnology and Medical Systems

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31.1 3.1 Introduction

The recovery of the three-dimensional (3-D) shape of anatomical structures is one of the most important problems in the field of medical imaging as the quantitative, computer-based assessment of such a shape and its changes plays an important role in clinical and research studies on a number of diseases.

A frequently studied class of solutions to this problem consists of performing the regional segmentation of a big enough sequence of tomographic (e.g. magnetic resonance (MR), computed tomography (CT) or echographic) images and stacking the segmented slices (sometimes with interpolation) to obtain volumetric representations of the 3-D shape of the imaged structures (Robb et al., 1983; Robb and Barillot, 1989; Higgins et al., 1990; Ylä-Jääski et al., 1991; Coppini et al., 1992a; Joliot and Mazoyer, 1993). Alternatively, detailed surface representations can be obtained from the boundaries of the structures of interest detected in each slice by means of surface...

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Notes

  1. 1.

    1 It should be noted that, under the hypothesis of a single structure in the scene, the reconstruction of an image representing the density of a structure is actually equivalent to the regional segmentation of a cross section of such a structure and, thus, the reconstruction of several parallel slices is equivalent to instantiating a3-D volumetric shape representation.

  2. 2.

    2 An alternative expression for the potential energy of S is , where k1 and k2 are the principal curvatures of the surface.

  3. 3.

    3 The section are “equatorial”, minimally constrained sections in which maximum recovery errors are to be expected.

  4. 4.

    4 The artifacts in the rendered images are due to corresponding artifacts in the original CT slices caused by lead tooth-fillings.

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  1. Cornelius T. Leondes
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Leondes, C.T. (2003). Algorithms for the Recovery of the 3-D Shape of Anatomical Structures from Single X-Ray Images. In: Leondes, C.T. (eds) Computational Methods in Biophysics, Biomaterials, Biotechnology and Medical Systems. Springer, Boston, MA. https://doi.org/10.1007/0-306-48329-7_3

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  • DOI: https://doi.org/10.1007/0-306-48329-7_3

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