Skip to main content
SpringerLink
Log in
Book cover

Mathematical Image Processing pp 55–108Cite as

Birkhäuser

Basic Tools

  • Chapter
  • First Online:

  • 2514 Accesses

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

Abstract

In this book we regard, admittedly slightly arbitrarily, as basic tools histograms and linear and morphological filters. These tools belong to the oldest methods in mathematical image processing and are discussed in early books on digital image processing as well (cf. [67, 114, 119]).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   49.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. V. Aurich, J. Weule, Non-linear gaussian filters performing edge preserving diffusion, in Proceedings 17. DAGM-Symposium, Bielefeld (Springer, Heidelberg, 1995), pp. 538–545

    Google Scholar 

  2. T. Brox, O. Kleinschmidt, D. Cremers, Efficient nonlocal means for denoising of textural patterns. IEEE Trans. Image Process. 17(7), 1083–1092 (2008)

    Article  MathSciNet  Google Scholar 

  3. A. Buades, J.-M. Coll, B. Morel, A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  Google Scholar 

  4. J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)

    Article  Google Scholar 

  5. R.C. Gonzalez, P.A. Wintz, Digital Image Processing (Addison-Wesley, Reading, 1977)

    MATH  Google Scholar 

  6. F. Guichard, J.-M. Morel, Partial differential equations and image iterative filtering, in The State of the Art in Numerical Analysis, ed. by I.S. Duff, G.A. Watson. IMA Conference Series (New Series), vol. 63 (Oxford University Press, Oxford, 1997)

    Google Scholar 

  7. E.H. Lieb, M. Loss, Analysis. Graduate Studies in Mathematics, vol. 14, 2nd edn. (American Mathematical Society, Providence, 2001)

    Google Scholar 

  8. S. Paris, P. Kornprobst, J. Tumblin, F. Durand, Bilateral filtering: theory and applications. Found. Trends Comput. Graph. Vis. 4(1), 1–73 (2009)

    Article  Google Scholar 

  9. W.K. Pratt, Digital Image Processing (Wiley, New York, 1978)

    MATH  Google Scholar 

  10. J.M.S. Prewitt, Object enhancement and extraction, in Picture Processing and Psychopictorics, ed. by B.S. Lipkin, A. Rosenfeld (Academic, New York, 1970)

    Google Scholar 

  11. T.W. Ridler, S. Calvard, Picture thresholding using an iterative selection method. IEEE Trans. Syst. Man Cybern. 8(8), 630–632 (1978)

    Article  Google Scholar 

  12. A. Rosenfeld, A.C. Kak, Digital Picture Processing (Academic, New York, 1976)

    MATH  Google Scholar 

  13. S.M. Smith, J.M. Brady, SUSAN—A new approach to low level image processing. Int. J. Comput. Vis. 23(1), 45–78 (1997)

    Article  Google Scholar 

  14. I.E. Sobel, Camera models and machine perception. PhD thesis, Stanford University, Palo Alto (1970)

    Google Scholar 

  15. P. Soille, Morphological Image Analysis - Principles and Applications (Springer, Berlin, 1999)

    Book  Google Scholar 

  16. C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in International Conference of Computer Vision (1998), pp. 839–846

    Google Scholar 

  17. M. Welk, J. Weickert, F. Becker, C. Schnörr, C. Feddern, B. Burgeth, Median and related local filters for tensor-valued images. Signal Process. 87(2), 291–308 (2007)

    Article  Google Scholar 

  18. L.P. Yaroslavsky, Digital Picture Processing, An Introduction (Springer, Berlin, 1985)

    Book  Google Scholar 

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dirk Lorenz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bredies, K., Lorenz, D. (2018). Basic Tools. In: Mathematical Image Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01458-2_3

Download citation

Publish with us

Policies and ethics

Search

Navigation