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I have applied Two different Image Enhancement Algorithm on a particular Image and got two resultant image , Now i want to compare the quality of those two image in order to find the effectiveness of those two Algorithms and find the more appropriate one based on the comparison of Feature vectors of those two images.So what Suitable Feature Vectors should i compare in this Case?

Iam asking in context of comparing the texture features of the images and which feature vector will be more suitable.

I need Mathematical support for verifying the effectiveness of any one algorithm based on the evaluation of Images for example using Constrast and Variance.So are there any more approaches do that?

Deepak kumar Jha
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    That's a very broad question. It is almost impossible to answer. – Eitan T Jun 27 '12 at 13:45
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    Show the pictures to a collection of people and ask them which one looks better. – slayton Jun 27 '12 at 14:33
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    More seriously, the problem is you need to define a metric for Image Quality and you have to figure out a way to calculate it from the image. Both are not trivial tasks. – slayton Jun 27 '12 at 14:34

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A better approach would be to do some Noise/Signal ratio by comparing image spectra ?

Joel Falcou
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Slayton is right, you need a metric and a way to measure against it, which can be an academic project in itself. However, i could think of one approach straightaway, not sure if it makes sense to your specific task at hand:

Metric: The sum of abs( colour difference ) across all pixels. The lower, the more similar the images are.

Method: For each pixel, get the absolute colour difference (or distance, to be precise) in LAB space between original and processed image and sum that up. Don't ruin your day trying to understand the full wikipedia article and coding that, this has been done before. Try re-using the methods getDistanceLabFrom(Color color) or getDistanceRgbFrom(Color color) from this PHP implementation.
It worked like a charm for me when i needed a way to match a color of pixels in a jpg picture - which basically is the same principle.

The theory behind it (as far as my limited understanding goes): It's doing a mathematical abstraction of rgb or (better) lab colour space as a three dimensional room, and then calculate the distance, that's why it works well - and hardly worked for me when looking at a color code from a one-dimensionional perspective.

Philzen
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The usual way is to start with a reference image (a good one), then add some noise on it (in a controlled way).

Then, your algorithm should remove as much as possible from the added noise. The results are easy to compare with a signal-to-noise ration (see wikipedia).

Now, the approach is easy to apply on simple noise models, but if you aim to improve more complex appearance issues, you must devise a way to apply the noise, which is not easy.

Another, quite common way to do it is the one recommended by slayton: take all your colleagues to appreciate the output of your algorithm, then average their impressions.

Sam
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If you have only the 2 images and no reference (higest quality) image, then you can see my rude solution/bash script there: https://photo.stackexchange.com/questions/75995/how-do-i-compare-two-similar-images-sharpness/117823#117823

It gets the 2 filenames and outputs the higher quality filename. It assumes the content of the images is identical (same source image). It can be fooled though.

A. Genchev
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