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

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

   1 h=histogram(img,bins=256,range=[0,255],normed=True)
   2 pdf,x=h[0],h[1]

The expression normed=True is used for the normalization of the PDF.

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The anti-derivative of the PDF is the cumulative density function (CDF).

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The cumulative sum can be calculated using

   1 cdf=pdf.cumsum()

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.

   1 cdf[25]-cdf[12]
   2 0.068