Re: Transforming a sparse histogram to a Gaussian histogram

On May 3, 1:58 am, Dev <gun...@xxxxxxxxx> wrote:
Hi All,

Thanks for all the replies. I am trying an algorithm on image
restoration which uses a Gaussian distribution. As natural images have
a sparse distribution rather than a gaussian distribution, I have to
convert the image to have a gaussian distribution which matches the
sparse distribution. I will go through the provided links in more
detail. Meantime if you have any other examples/code/documents, please
let me know.

Thanks,

Dev-
---------------------------------------------------------------------------------------------------
Dev:
This doesn't really answer the questions. All you added was that
you're trying an algorithm on image restoration. Let me see if I can
read between the lines and figure out what you're trying to say.
1. You have some images with a sparse distribution (only some bins
have pixels in them and most of the bins are completely empty).
2. Your images are degraded somehow and you want to restore them.
3. The image restoration algorithm that you want to try assumes that
the degraded images have a Gaussian histogram.
4. You want to transform your images so that they have a Gaussian
histogram because then you think that the algortihm will work better
with your input images.

Does that about sum it up?

OK, now for the second round of questions:
1. How was your image degraded? Blur, noise, quantization, color
shift?
2. Was it quantized, so THAT is the reason the histogram is now
sparse? Contrary to what you say, natural images DON'T have a
quantized histogram, except for some very special scenes (e.g. test
charts). If I go and take a snapshot of my backyard, I guarantee you
that it won't have a sparse histogram, nor will it have a Gaussian
histogram either for that matter.
3. Are you sure that the restoration algorithm really wants a Gaussian
IMAGE histogram? I really, really doubt this. I bet that what it
really expects is a Gaussian distribution for the NOISE (not the
underlying "true" image). Additive white Gaussian noise is a common
concept and I bet your algorithm is trying to get rid of that noise,
but the image itself can have whatever histogram it has. Or it
assumes a Gaussian point spread function and it wants to undo the blur
c aused by that.
4. You say "gaussian distribution which matches the sparse
distribution." This is inherently impossible. If it's Gaussian, it's
not sparse and if it's sparse it's not Gaussian. They can't match.
You can have two distributions (say, sparse and Gaussian) have the
same mean and standard deviation, but that doesn't mean the
"distributions" (which is the histogram) match, it simply means that
the first and second central moments match.
5. What provided links? Who provided links to whom? I didn't see
that you provided any links to us.
Regards,
ImageAnalyst
.

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