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On the Use of Low-Pass Filters for Image Processing with Inverse Laplacian Models

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Abstract

A novel signal processing-oriented approach to solving problems involving inverse Laplacians is introduced. The Monogenic Signal is a powerful method of computing the phase of discrete signals in image data, however it is typically used with band-pass filters in the capacity of a feature detector. Substituting low-pass filters allows the Monogenic Signal to produce approximate solutions to the inverse Laplacian, with the added benefit of tunability and the generation of three equivariant properties (namely local energy, local phase and local orientation), which allow the development of powerful numerical solutions for a new set of problems. These principles are applied here in the context of biological cell segmentation from brightfield microscopy image data. The Monogenic Signal approach is used to generate reduced noise solutions to the Transport of Intensity Equation for optical phase recovery, and the resulting local phase and local orientation terms are combined in an iterative level set approach to accurately segment cell boundaries. Potential applications of this approach are discussed with respect to other fields.

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Authors and Affiliations

  1. Department of Radiation Physics, Stanford University, 875 Blake Wilbur Drive, CC-G206, Stanford, CA, 94305, USA

    Rehan Ali

  2. FRS FREng FMedSci Wolfson Medical Vision Lab, Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

    Tunde Szilagyi & Michael Brady

  3. Mirada Medical Ltd, Innovation House, Mill Street, Oxford, OX2 0JX, UK

    Mark Gooding

  4. Gray Institute for Radiation Oncology and Biology, University of Oxford, Old Road Campus Research Building, Oxford, OX3 7QD, UK

    Martin Christlieb

Authors
  1. Rehan Ali
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  2. Tunde Szilagyi
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  3. Mark Gooding
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  4. Martin Christlieb
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  5. Michael Brady
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Correspondence to Rehan Ali.

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Ali, R., Szilagyi, T., Gooding, M. et al. On the Use of Low-Pass Filters for Image Processing with Inverse Laplacian Models. J Math Imaging Vis 43, 156–165 (2012). https://doi.org/10.1007/s10851-011-0299-6

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  • DOI: https://doi.org/10.1007/s10851-011-0299-6

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