Measure distance between images

Question

Regarding my question about Gaussian noise reduction, I would like to know of a simple method to quantify the success of a noise reduction filter.

I've attempted a few methods of noise reduction and I want some method to determine which one works best. I have the original image, a noisy version and a few versions created from attempts to reduce the noise. I thought about trying some matrix distance measurement from the enhanced image and the original image, in order to compare the methods of noise reduction. Will this work okay or is there some other common method other than just looking at the pictures?

Answer 1

The problem with the mean-square error metric is that it doesn't represent well the visual quality of the restored image. To address that, some other metrics have been developed. One that is quite popular now is called Structural Similarity. The source code for it can be found here.

Answer 2

My colleagues working on noise redution always use Signal To Noise Ratio (SNR) to compare the quality of the denoising: http://en.wikipedia.org/wiki/Signal-to-noise_ratio

Here are some scientific articles of my colleague Julien Mairal doing state-of-the-art noise reduction: http://www.di.ens.fr/~mairal/index.php

Answer 3

The obvious distance to use is the sum of the squares of the pixel errors. The squared pixel error would be (p1 - p2)^2 for a grayscale image (the intensity of the two pixels are p1 and p2), or (r1 - r2)^2 + (g1 - g2)^2 + (b1 - b2)^2 if you have a RGB image (the colors of the two pixels are (r1, g1, b1) and (r2, g2, b2)). You can refine this a bit by scaling the RGB components differently to compensate for the fact that the human eye responds to blue less strongly than green and red.