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Techniques for Computing Fabric Tensors: A Review

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Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

The aim of this chapter is to review different approaches that have been proposed to compute fabric tensors with emphasis on trabecular bone research. Fabric tensors aim at modeling through tensors both anisotropy and orientation of a material with respect to another one. Fabric tensors are widely used in fields such as trabecular bone research, mechanics of materials and geology. These tensors can be seen as semi-global measurements since they are computed in relatively large neighborhoods, which are assumed quasi-homogeneous. Many methods have been proposed to compute fabric tensors. We propose to classify fabric tensors into two categories: mechanics-based and morphology-based. The former computes fabric tensors from mechanical simulations, while the latter computes them by analyzing the morphology of the materials. In addition to pointing out advantages and drawbacks for each method, current trends and challenges in this field are also summarized.

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Notes

  1. 1.

    We thank Prof. Osman Ratib from the Service of Nuclear Medicine at the Geneva University Hospitals for providing the μCT scan of the vertebra; Andres Laib from SCANCO Medical AG and Torkel Brismar from the Division of Radiology at the Karolinska University Hospital for providing the μCT scan of the radius.

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  1. Department of Medical and Health Sciences (IMH), Center for Medical Image Science and Visualization (CMIV), Linköping University, Campus US, 58185, Linköping, Sweden

    Rodrigo Moreno & Örjan Smedby

  2. Department of Biomedical Engineering (IMT), Center for Medical Image Science and Visualization (CMIV), Linköping University, Campus US, 58185, Linköping, Sweden

    Magnus Borga

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  1. Dept. of Radiology, Harvard Medical School, Brigham, and Women's Hospital, Boston, Massachusetts, USA

    Carl-Fredrik Westin

  2. Technical University of Delft, Dept of Computer Graphics and Visualization, Delft, The Netherlands

    Anna Vilanova

  3. Universität des Saarlandes, Dept. of Mathematics, Saarbrücken, Germany

    Bernhard Burgeth

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Moreno, R., Borga, M., Smedby, Ö. (2014). Techniques for Computing Fabric Tensors: A Review. In: Westin, CF., Vilanova, A., Burgeth, B. (eds) Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54301-2_12

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