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Estimation of affine transformations directly from tomographic projections in two and three dimensions

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Abstract

This paper presents a new approach to estimate two- and three-dimensional affine transformations from tomographic projections. Instead of estimating the deformation from the reconstructed data, we introduce a method which works directly in the projection domain, using parallel and fan beam projection geometries. We show that any affine deformation can be analytically compensated, and we develop an efficient multiscale estimation framework based on the normalized cross correlation. The accuracy of the approach is verified using simulated and experimental data, and we demonstrate that the new method needs less projection angles and has a much lower computational complexity as compared to approaches based on the standard reconstruction techniques.

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Author notes

  1. René Mooser

    Present address: swissQuant Group AG, Kuttelgasse 7, 8001, Zurich, Switzerland

  2. Fredrik Forsberg

    Present address: LKAB R&D, P.O. Box 952, 97128, Luleå, Sweden

Authors and Affiliations

  1. Electronic/Metrology/Reliability Laboratory, Swiss Federal Laboratories for Materials Testing and Research (EMPA), Ueberlandstr. 129, 8600, Duebendorf, Switzerland

    René Mooser, Erwin Hack & Urs Sennhauser

  2. Division of Experimental Mechanics, Luleå University of Technology, 97187, Luleå, Sweden

    Fredrik Forsberg

  3. Computer Vision Laboratory, ETH Zurich, Sternwartstr. 7, 8092, Zurich, Switzerland

    Gábor Székely

Authors
  1. René Mooser
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  2. Fredrik Forsberg
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  3. Erwin Hack
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  4. Gábor Székely
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  5. Urs Sennhauser
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Correspondence to René Mooser.

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Mooser, R., Forsberg, F., Hack, E. et al. Estimation of affine transformations directly from tomographic projections in two and three dimensions. Machine Vision and Applications 24, 419–434 (2013). https://doi.org/10.1007/s00138-011-0376-2

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  • DOI: https://doi.org/10.1007/s00138-011-0376-2

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