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= Image statistics =


The image is characterised by a '''probability density function''' (PDF). The PDF describes the probability of the occurrence of the discrete grey levels.


== Example ==
{{attachment:landsat_b80.png}}


The following code calculates the PDF {{{pdf(q)}}} for a ''byte'' image {{{img}}} in the intervall {{{[0,255]}}}

{{{#!python
h=histogram(img,bins=256,range=[0,255],normed=True)
pdf,x=h[0],h[1]
}}}

The expression {{{normed=True}}} is used for the normalization of the PDF. 
{{{#!latex
$\sum_{q=0}^{255}pdf(q)=1$
}}}

The anti-derivative of the PDF is the  '''cumulative density function''' (CDF). 
{{{#!latex
$cdf(q)=\sum_{q'=0}^{q}pdf(q')$
}}}

The cumulative sum can be calculated using
{{{#!python
cdf=pdf.cumsum()
}}}

{{attachment:landsat_b80_pdfcdf.png}}

The probability of the occurence of grey levels in the interval {{{[a,b]}}} can be calculated from the CDF. In the example shown, the probability of grey levels to occur in the interval {{{[12,25]}}} according to the first peak is 0.068. So roughly 7% of the image pixels are in this grey level interval.

{{{#!python
cdf[25]-cdf[12]
0.068
}}}