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Partial Differential Equations in Image Processing

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Book cover Mathematical Image Processing

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Our first encounter with a partial differential equation is this book was Application 3.23 on edge detection according to Canny: we obtained a smoothed image by solving the heat equation. The underlying idea was that images contain information on different spatial scales and one should not fix one scale a priori.

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Notes

  1. 1.

    Of course, we could also stack the columns into a vector, and indeed, some software packages have this as a default operation. The only difference between these two approaches is the direction of the x 1 and x 2 coordinates.

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Authors and Affiliations

  1. Institute for Mathematics and Scientific, University of Graz, Graz, Austria

    Kristian Bredies

  2. Braunschweig, Germany

    Dirk Lorenz

Authors
  1. Kristian Bredies
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  2. Dirk Lorenz
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Bredies, K., Lorenz, D. (2018). Partial Differential Equations in Image Processing. In: Mathematical Image Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01458-2_5

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