Machine Vision pp 369-464 | Cite as

Image Signals

  • Jürgen BeyererEmail author
  • Fernando Puente León
  • Christian Frese


An image signal g(x) acquired by the methods described in Chap.7 is a function g : \({{\mathbb{R}}^{2}}\to {{\mathbb{R}}^{Q}}\), which—in the general case—maps the whole image plane to vectorial values, where Q denotes the number of channels (cf. Sec. 1.3). At first, both the domain and the range of the image signal are considered to be continuous. In this case, g(x) is called a continuous image signal or an analog image signal.


Probability Density Function Power Spectral Density Discrete Fourier Transform Image Signal Dirac Delta Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Richard Bamler. Mehrdimensionale lineare Systeme. Springer, 1989.Google Scholar
  2. [2]
    Jürgen Beyerer. Analyse von Riefentexturen. PhD thesis, Universität Karlsruhe (TH), 1994.Google Scholar
  3. [3]
    Ronald Bracewell. The Fourier transform and its applications. McGraw-Hill, 3rd edition, 2000.Google Scholar
  4. [4]
    Elbert Oran Brigham. The fast Fourier transform and its applications. Prentice Hall, 1988.Google Scholar
  5. [5]
    Ilja Bronshtein, Konstantin Semendyayev, Gerhard Musiol, and Heiner Mühlig. Handbook of Mathematics. Springer, 6th edition, 2015.Google Scholar
  6. [6]
    Ward Cheney. Analysis for applied mathematics. Springer, 2001.Google Scholar
  7. [7]
    Ole Christensen. Frames and Bases – An Introductory Course. Birkhäuser, 2008.Google Scholar
  8. [8]
    James Cooley and John Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297–301, 1965.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Eberhard Hänsler. Statistische Signale: Grundlagen und Anwendungen. Springer, 3rd edition, 2001.Google Scholar
  10. [10]
    Harro Heuser. Funktionalanalysis – Theorie und Anwendung. Teubner, 4th edition, 2006.Google Scholar
  11. [11]
    Harro Heuser. Lehrbuch der Analysis, volume 2. Vieweg+Teubner, 14th edition, 2008.Google Scholar
  12. [12]
    Bernd Jähne. Digital image processing. Springer, 6th edition, 2005.Google Scholar
  13. [13]
    Karl-Dirk Kammeyer and Kristian Kroschel. Digitale Signalverarbeitung – Filterung und Spektralanalyse. Vieweg+Teubner, 7th edition, 2009.Google Scholar
  14. [14]
    Uwe Kiencke, Michael Schwarz, and ThomasWeickert. Signalverarbeitung – Zeit-Frequenz-Analyse und Schätzverfahren. Oldenbourg, 2008.Google Scholar
  15. [15]
    Robert Lalla. Verfahren zur Auswertung von Moiréaufnahmen technischer Oberflächen. PhD thesis, Universität Karlsruhe (TH), 1993.Google Scholar
  16. [16]
    Alan Oppenheim and Ronald Schafer. Discrete-time signal processing. Pearson, 3rd edition, 2010.Google Scholar
  17. [17]
    Athanasios Papoulis and Unnikrishna Pillai. Probability, random variables and stochastic processes. McGraw-Hill, 4th edition, 2002.Google Scholar
  18. [18]
    Fernando Puente León and Holger Jäkel. Signale und Systeme. De Gruyter Oldenbourg, Berlin, 6th edition, 2015.Google Scholar
  19. [19]
    Fernando Puente León and Uwe Kiencke. Messtechnik – Systemtheorie für Ingenieure und Informatiker. Springer, 9th edition, 2012.Google Scholar
  20. [20]
    Fernando Puente León and Norbert Rau. Detection of machine lead in ground sealing surfaces. Annals of the CIRP, 52(1):459–462, 2003.CrossRefGoogle Scholar
  21. [21]
    Alan Stuart and J. Keith Ord. Kendall’s advanced theory of statistics, volume 1, Distribution theory. Arnold, 6th edition, 2004.Google Scholar
  22. [22]
    Ulrich Tietze, Christoph Schenk, and Eberhard Gamm. Halbleiter-Schaltungstechnik. Springer, 13th edition, 2010.Google Scholar
  23. [23]
    Scott Tyo and Richard Olsen. PC-based display strategy for spectral imagery. In IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, pages 276–281, 2003.Google Scholar
  24. [24]
    Wolfgang Walter. Einführung in die Theorie der Distributionen. Bibliographisches Institut, 3rd edition, 1994.Google Scholar
  25. [25]
    Bernard Widrow, István Kollár, and Ming-Chang Liu. Statistical theory of quantization. IEEE Transactions on Instrumentation and Measurement, 45(2):353–361, April 1996.CrossRefGoogle Scholar
  26. [26]
    HellmuthWolf. Nachrichtenübertragung: eine Einführung in die Theorie. Springer, 2nd edition, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jürgen Beyerer
    • 1
    Email author
  • Fernando Puente León
    • 2
  • Christian Frese
    • 3
  1. 1.Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung and The Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Fraunhofer-Institut für Optronik, Systemtechnik und BildauswertungKarlsruheGermany

Personalised recommendations