Abstract
Noise in an image can be defined as the unwanted part of that image. The noise may be random in some way, as is the pepper-and-salt appearance on a television screen when the station goes off the air, or it may be systematic, as with the ghost seen when an echo of the wanted signal arrives with a time delay after reflection from a hill. When the television image responds independently to sparks in a faulty thermostat in the nearby refrigerator or to a faulty ignition system on a passing motorcycle, the noise exhibits both random and systematic features. In other cases, the wanted signal may be random; thermal microwave or infrared radiation used for mapping the ground is of this nature. As a result, one person’s noise may be another person’s signal and vice versa. Very often it does not matter much what the character of the noise is, only its magnitude is needed, an attitude that is reflected in the term signal-to-noise ratio. As the examples show, the noise in an image need not be independent of, but can be closely connected with, the wanted signal itself. In the latter case if the signal is removed, the noise will change. When the noise is independent, it may be studied on its own in the absence of any wanted signal.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature cited
R. J. Adler (1981), The Geometry of Random Fields, John Wiley & Sons, New York.
M. F. Barnsley (1988), “Fractal modelling of real world images,” in H-O Peitgen and D. Saupe, eds, The Science of Fractal Images, Springer-Verlag, New York.
M. S. Bartleti (1975), The Statistical Analysis of Spatial Pattern, Chapman and Hall, London.
B. Delaunay (1934), “Sur la sphère vide,” Bull. Acad. Sci. USSR, Classe des Sciences Mathérnatiques et Naturelles, Series 7, pp. 793–800.
G. L. Dirichlet (1850), “Uber die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen,” Journal für Reine und Angewandte Mathematik, vol. 40, pp. 209–227.
W. A. Gardner, (1988) Statistical Spectral Analysis. A Nonprobabilistic Approach, Prentice Hall, Englewood Cliffs, N.J.
P. J. Green AND R. Sibson (1978), “Computing Dirichlet tessellations in the plane,” The Computer Journal, vol. 21, pp. 168–173.
P. Holgate (1972), “The use of distance methods for the analysis of spatial distribution of points,” in P. A. W. Lewis, ed., Stochastic Point Processes, John Wiley & Sons, New York.
V. Icke AND VAN DER Weygaert (1991), “The galaxy distribution as a Voronoi foam,” Quarterly J. Roy. Astronom. Soc., vol. 32, pp. 85–112.
B. Julesz (1960), “Binocular depth perception of computer-generated patterns,” Bell Syst. Tech. J., vol. 39, pp. 1125–1162.
N. E. Thing (1993), “Magic Eye,” Viking Penguin, New York.
C. W. Tyler AND Clarke (1990), “The autostereogram,” Proc. Int. Soc. Opt. Eng., vol. 1256, pp. 182–197.
H. Larralde et al. (1992), “Territory covered by N diffusing particles,” Nature, vol. 355, pp. 423–426.
B. B. Mandelbrot (1982), The Fractal Geometry of Nature, W.H. Freeman, New York.
R. Morrison (1984), “Low cost computer graphics for micro computers,” Software— Practice and Experience, vol. 12, pp. 767–776.
A. Okabe, B. Boots, AND K. Sugihara (1992), Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, John Wiley & Sons, Chichester, U.K.
A. Papoulis (1965), Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York.
H-O Peitgen, H. Jurgens, AND D. Saupe (1992), Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York.
Lord Rayleigh (1905), “The problem of the random walk,” Nature, vol. 72, p. 318.
B. D. Ripley (1981), Spatial Tessellations, John Wiley & Sons, New York.
C. A. Rogers (1964), Packing and Covering, Cambridge University Press, Cambridge.
R. Samadani AND C. Han (1993), “Computer-assisted extraction of boundaries from images,” Conference Proceedings on Storage and Retrieval for Image and Video Databases, 2–3 February 1993, San Jose, California, Society of Photo-Optical Engineers, vol. 1908, pp. 219–224.
J. G. Skellam (1952), Biometrika, vol. 39, pp. 346–362.
R. T. Stevens (1990), Fractal Programming in Turbo Pascal, Redwood City, M&T Publishing.
D. Stoyan, W. S. Kendall AND J. Mecke (1987), Stochastic Geometry and Its Applications, Akademie-Verlag, Berlin.
G. Voronoï (1908), “Nouvelles applications des paramètres continus à la théorie des formes quadratiques, deuxième mémoire, recherches sur les paralleloèdres primitifs,” Journal für Reine und Angewandte Mathematik, vol. 134, pp. 198–287.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bracewell, R. (2003). Two-Dimensional Noise Images. In: Fourier Analysis and Imaging. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8963-5_17
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8963-5_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4738-5
Online ISBN: 978-1-4419-8963-5
eBook Packages: Springer Book Archive