Probabilities, Greyscales, and Histograms

[Pages:50]Probabilities, Greyscales, and Histograms:

Chapter 3a G&W

Ross Whitaker (modified by Guido Gerig)

School of Computing University of Utah

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Goal

? Image intensity transformations ? Intensity transformations as mappings ? Image histograms ? Relationship btw histograms and

probability density distributions ? Repetition: Probabilities

? Image segmentation via thresholding

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Intensity transformation example

g(x,y) = log(f(x,y))

g(x1,y1) = log ( f(x1,y1) )

f(x1,y1)

g(x1,y1)

f(x2,y2)

g(x2,y2)

g(x2,y2) = log ( f(x2,y2) )

?We can drop the (x,y) and represent this kind of filter as an intensity

transformation s=T(r). In this case s=log(r)

-s: output intensity

-r: input intensity

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Intensity transformation

s T (r)

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? 1992?2008 R. C. Gonzalez & R. E. Woods

Gamma correction

? 1992?2008 R. C. Gonzalez & R. E. Woods

s cr

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Gamma transformations

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? 1992?2008 R. C. Gonzalez & R. E. Woods

Gamma transformations

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? 1992?2008 R. C. Gonzalez & R. E. Woods

Piecewise linear intensity transformation

?More control ?But also more parameters for user to specify

?Graphical user interface can be useful

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? 1992?2008 R. C. Gonzalez & R. E. Woods

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