Re: Manipulate Histogram to get specified mean, stddev

From: Martin Leese (please_at_see.Web.for.e-mail.INVALID)
Date: 11/26/04 

Date: Thu, 25 Nov 2004 19:22:27 -0700
To:  sbernoeg@vexcel.co.at

Piotr Stanczyk wrote:
> You will find quite a good treatment of this in the book by Gonzalez and
> Woods, Digital Image Processing.
>
> I'm going by memory on this, but this can be viewed as a histogram
> matching problem. So, this is usually explained in 2 steps.
>
>
> Let T(x) be the cumulative probablity distribution function of the input
> image. Get this by summing up the pdf, ~historgram, to x
>
> -- x
> \ hist(x) = T(x)
> /
> -- 0
>
> Applying just T(x) gets you just the histogram equalisation process,
> from here you can apply the mapping that will give you the
> charactersitics you require ...
>
> Let G(y) be the cumulative probablity distribution function of the
> output image. Since you have the pdf given to you via the mean and
> stddev, you can construct a Gaussian pdf with these values
>
> Then the tranformation you want is:
>
> inv{G} (T)

This will not only change the mean and stddev, but
will also force the shape of the histogram to be
Gaussian. My guess is that this is not what the
original poster wanted.

Jon Campbell's post contains a formula which
changes the mean and stddev, and also preserves
the shape of the histogram. Please ignore the
formula in my previous post to this thread as it
is wrong.

The original poster asked for a look-up table. To
create this, simply apply Jon's formula to values
from 0 to 255 and store the result. 

-- 
Regards,
Martin Leese
E-mail: please@see.Web.for.e-mail.INVALID
Web: http://members.tripod.com/martin_leese/

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