[magick-developers] Kurtosis patch correction WAS Re: Patch to calculate kurtosis and skewness of image channels

[Anthony Thyssen]

On Fri, 16 Jan 2009 23:24:29 +0530
magick-developers-bounces at imagemagick.org wrote:

| While using ImageMagick patched with the original kurtosis patch, I
| realized I had made an error in magick/identify.c, where just like the
| mean and standard deviation, kurtosis and skewness were being divided
| by the values 'scale' and 'QuantumRange'.
| 
| While this makes sense for the mean and standard deviation, it does
| not in case of kurtosis and skewness. This is because the first two
| are dimensional numbers. They have units associated with them. So for
| the red channel the mean would be the mean amount of 'redness' as it
| were, etc.
| 
Looking at the changes as a result of this patch
http://www.imagemagick.org/Usage/compare/#type_bw

 Channel statistics:
    gray:
      min: 0 (0)
      max: 127 (0.498039)
      mean: 9.7071 (0.0380671)
      standard deviation: 23.4909 (0.0921213)
      kurtosis: 8.75478
      skewness: 3.02607
  Image statistics:
    OverAll:
      min: 0 (0)
      max: 127 (0.498039)
      mean: 7.28032 (0.0285503)
      standard deviation: 20.7734 (0.0814645)
      kurtosis: 13.032
      skewness: 3.60838


This is a gray scale image.  Actually a Black and White
image that has been 'solarized' so that the white half
has been negated, so  white -> black.
It is really a test of how much 'gray' is present in the
image.

But as it is gray. how can it be that we get a different
result for gray colors when compared to overall?

All that would happen in this case is that overall should have
the gray data repeated three times.  The results in that case
should be the same set of statistics.  But that is
obviously NOT the case!

Something is definitely not right here!


  Anthony Thyssen ( System Programmer )    <A.Thyssen at griffith.edu.au>
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  Clarke's Law:  Study what the most respected authorities agree can NOT
         be done - then do it.           --  Arthur C. Clark
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     Anthony's Home is his Castle     http://www.cit.gu.edu.au/~anthony/