Entropy of an image

juriguen · 2009-08-06 21:37:09

Hi all!

I am trying to figure out a problem more related to Image Processing or Computer Graphics, but from a mathematical point of view... So I would be very happy with any little help!

The thing is the following. I have a set of images (from 1 to P) that I want to merge in a certain way, using what is called an Image Fusion algorithm. It works doing the next steps:

i) First it splits the image into N = 2^n "chunks" of roughly equal energy (being this a simplification, and simply the sum of the grey scale values).
ii) Then it compares the Entropy of each subdivision with that of the other images for the same subdivision, and chooses the photo that provides the maximum.
iii) Finally it combines all the "chunks" and checks if the merged image has maximum Entropy. Otherwise, increments n and goes to i).

To do so, the entropy of a grey scale image is defined as follows:

where p_k is the probability of a certain grey level (obtained from the histogram), and the images are assumed to be 8 bits, so there are 256 possible grey level values.

So far, so good. My question is: can anybody find a way to relate the Entropy of the subdivisions with that of the merged image?

My only idea about this would be to consider that each "chunk" is characterized by a random variable Xk, which can take values x = [0..255], and the total image by a rv XT, over the same x.

Then,

Ok, even if it is correct, the relation becomes really complex... But at least I would like to know if it is a good point to start...

Does anybody know is there's a similar expression to relate Entropies?

Thanks a lot in advance for any comment or suggestion,
Jose

PS: please, anything will be helpful, even a comment saying: "all your probabilistic assumptions are wrong"... I have to admit I am not very good with probabilities!

PS2: I uploaded a splitted image as an example

Last edited by juriguen (2009-08-06 21:38:23)

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#1 2009-08-06 21:37:09

Entropy of an image

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