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| = Random variables = | = Image statistics = |
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| The measurements that form an image show statistical fluctuations. The image is characterised by a probability density function (PDF). The PDF ''f'' describes the probability of the occurrence of a discrete grey level ''q'' in the range of grey levels ''Q''. | The image is characterised by a probability density function (PDF). The PDF ''f'' describes the probability of the occurrence of a discrete grey level ''q'' in the range of grey levels ''Q''. |
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| $\sum_{q=1}^Qf_q=1$ | $\sum_{q=0}^Qf_q=1$ |
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| == Probability density functions and histograms == | == Example == {{attachment:landsat_b80.png}} |
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| The PDF of an image can be calculated and displayed using the {{{pylab.hist}}} function or it can be calculated using the {{{scipy.histogram}}} function. |
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| [[attachment:landsat_b80.png]] | The following code calculates the PDF {{{pdf}}} 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). It can be approximated from the cumulative sum {{{#!python cdf=pdf.cumsum() }}} {{attachment:landsat_b80_pdfcdf.png}} |
Image statistics
The image is characterised by a probability density function (PDF). The PDF f describes the probability of the occurrence of a discrete grey level q in the range of grey levels Q.
latex error! exitcode was 2 (signal 0), transscript follows:
Example
The following code calculates the PDF pdf for a byte image img in the intervall [0,255]
The expression normed=True is used for the normalization of the PDF.
latex error! exitcode was 2 (signal 0), transscript follows:
The anti-derivative of the PDF is the cumulative density function (CDF). It can be approximated from the cumulative sum
1 cdf=pdf.cumsum()
