Differences between revisions 6 and 7

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.

latex error! exitcode was 2 (signal 0), transscript follows:

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

latex error! exitcode was 2 (signal 0), transscript follows:

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

-  ⇤ ← Revision 6 as of 2008-12-08 12:50:12 → 
  Size: 1323
  Editor: anonymous
  Comment:
+   ← Revision 7 as of 2008-12-08 13:15:56 → ⇥
  Size: 1323
  Editor: anonymous
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 41:
-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 lie in this grey level interval.
+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.