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Multi-scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization

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Abstract

Ridge and valley enhancing filters are widely used in applications such as vessel detection in medical image computing. When images are degraded by noise or include vessels at different scales, such filters are an essential step for meaningful and stable vessel localization. In this work, we propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a fourth-order diffusion tensor whose eigentensors and eigenvalues are determined from the local Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient implementation using a fast explicit diffusion scheme and demonstrate results on synthetic images and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters, as well as established second-order vessel enhancing filters, our newly proposed one better restores the centerlines in all cases.

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Authors and Affiliations

  1. Institute of Computer Science II, University of Bonn, Bonn, Germany

    Shekoufeh Gorgi Zadeh & Thomas Schultz

  2. Umwelt-Campus Birkenfeld, Hochschule Trier, Birkenfeld, Germany

    Stephan Didas

  3. Department of Ophthalmology, University of Bonn, Bonn, Germany

    Maximilian W. M. Wintergerst

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  1. Shekoufeh Gorgi Zadeh
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  2. Stephan Didas
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  3. Maximilian W. M. Wintergerst
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  4. Thomas Schultz
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Correspondence to Shekoufeh Gorgi Zadeh.

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Gorgi Zadeh, S., Didas, S., Wintergerst, M.W.M. et al. Multi-scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization. J Math Imaging Vis 59, 257–269 (2017). https://doi.org/10.1007/s10851-017-0729-1

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  • DOI: https://doi.org/10.1007/s10851-017-0729-1

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