Image.noiseMRS bias

[mschuster]

I've measured a small, systematic bias in noiseMRS results. In the plot the noiseMRS values (blue dots) are about 2.5% smaller than the actual noise in the images. These are all synthetic, white-noise images with fixed mean and varying standard deviation of Gaussian noise. The Starch-Murtagh paper mentions a correctable bias of about this magnitude. IMO it is likely noiseMRS lacks this correction. If so the fix is easy. This is a low priority nit, but I thought I'd mention it anyway, as the ImageIntegration documentation claims a 1% accuracy. The purple squares are measurements from a different algorithm. The paper does not mention it, but I found the bias value depends on the number of levels used in the estimation.
Thanks,
Mike

[Juan Conejero]

Hi Mike,

This is now fixed in 1.8.0 RC2 and PCL 2.0.1. When I first implemented the MRS noise evaluation algorithm (back in 2005), my intention was just to have accurate estimates of relative image quality, i.e. noise estimates for image comparison/grading purposes. I neglected the 1/0.974 empirical factor that the authors mention in the original paper for this reason. Now I have added this correction to the PCL implementation, so the systematic bias has been removed.

This should not have any practical consequences for the tools using this algorithm. However, ImageIntegration's cache should be reset for safety, and comparisons of newly produced noise estimates with existing ones must take this correction into account. I'll post a note about this when I release RC2. Thank you for pointing out this problem.

[mschuster]

Thanks Juan,
Regarding the convergence issue which you mentioned is fixed in 1.8. The paper gives an iterative algorithm. Because the underlying function is discrete and not continuous (i.e. it involves thresholding), there is no guarantee that the iteration won't cycle amongst a set of values and hence not converge. A solution to this problem is obvious: keep a list of all solutions, and if the next solution is a member of the list then a cycle is detected, and so terminate, otherwise append the new solution to the list and keep going.
Thanks,
Mike