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Transforms and Operators for Directional Bioimage Analysis: A Survey

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Focus on Bio-Image Informatics

Part of the book series: Advances in Anatomy, Embryology and Cell Biology ((ADVSANAT,volume 219))

Abstract

We give a methodology-oriented perspective on directional image analysis and rotation-invariant processing. We review the state of the art in the field and make connections with recent mathematical developments in functional analysis and wavelet theory. We unify our perspective within a common framework using operators. The intent is to provide image-processing methods that can be deployed in algorithms that analyze biomedical images with improved rotation invariance and high directional sensitivity. We start our survey with classical methods such as directional-gradient and the structure tensor. Then, we discuss how these methods can be improved with respect to robustness, invariance to geometric transformations (with a particular interest in scaling), and computation cost. To address robustness against noise, we move forward to higher degrees of directional selectivity and discuss Hessian-based detection schemes. To present multiscale approaches, we explain the differences between Fourier filters, directional wavelets, curvelets, and shearlets. To reduce the computational cost, we address the problem of matching directional patterns by proposing steerable filters, where one might perform arbitrary rotations and optimizations without discretizing the orientation. We define the property of steerability and give an introduction to the design of steerable filters. We cover the spectrum from simple steerable filters through pyramid schemes up to steerable wavelets. We also present illustrations on the design of steerable wavelets and their application to pattern recognition.

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Notes

  1. 1.

    Software available at http://bigwww.epfl.ch/demo/orientation/.

  2. 2.

    Plugin available at http://fiji.sc/Frangi/.

  3. 3.

    Available at http://eeweb.poly.edu/iselesni/WaveletSoftware/.

  4. 4.

    Available at http://www.curvelet.org/.

  5. 5.

    Available at http://www.shearlab.org/.

  6. 6.

    Available at http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/.

  7. 7.

    Available at http://www.math.uh.edu/~dlabate/software.html.

  8. 8.

    Available at http://bigwww.epfl.ch/demo/monogenic/.

  9. 9.

    Available at http://www-m6.ma.tum.de/Mamebia/MonogenicWaveletToolbox/.

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Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement \(\mbox{ n}^{\circ }\) 267439. The work was also supported by the Hasler Foundation, and the Swiss National Foundation (grant number: 200020-162343).

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Authors and Affiliations

  1. Biomedical Imaging Group, École polytechnique fédérale de Lausanne (EPFL), Station 17, 1015, Lausanne VD, Switzerland

    Zsuzsanna Püspöki, Martin Storath, Daniel Sage & Michael Unser

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  1. Zsuzsanna Püspöki
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  2. Martin Storath
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  3. Daniel Sage
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  4. Michael Unser
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Correspondence to Zsuzsanna Püspöki .

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Editors and Affiliations

  1. Dept. of Veterinary Sciences, University of Antwerp, Antwerpen, Antwerpen, Belgium

    Winnok H. De Vos

  2. Dept. of Human Genetics, KU Leuven, Leuven, Belgium

    Sebastian Munck

  3. University of Antwerp, Antwerp, Belgium

    Jean-Pierre Timmermans

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Püspöki, Z., Storath, M., Sage, D., Unser, M. (2016). Transforms and Operators for Directional Bioimage Analysis: A Survey. In: De Vos, W., Munck, S., Timmermans, JP. (eds) Focus on Bio-Image Informatics. Advances in Anatomy, Embryology and Cell Biology, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-28549-8_3

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