I wasn't going to post this, but I guess I will anyway.
I went and grabbed a paper on a "haziness" metric.
... and I reimplemented the proposed (and most of the reference contrast metrics) in MATLAB. Some of the code does depend on MIMT, though I did make some effort to make sure everything would all run in a period-correct version (R2015b). The individual demos are sections within haziness_ws.m, one of which is replicated here:
density = [0 5 10 15 20 25 30 35];
F = {@(x) haziness_vitor(x);
@(x) contrast_michelson(x)};
titles = {'Vitor','Gautam','Histogram Spread','RMS','Michelson'};
K = zeros(nd,3,numel(F));
fname = sprintf('recorte_leite_%02d.jpg',density(k));
CT = [1 0 0; 0 1 0; 0 0 1];
xlabel('contaminant amount (mL)')
inpict = imread('recorte_leite_00.jpg');
I included @Gautam's proposed method as well, though I inverted it as a reluctant compromise. Since all the other metrics were treated as "contrast" rather than "haziness", I felt the comparison was easier if they all had the same general behavior. By themselves, I would think that a "haziness" metric would follow Gautam's intended behavior. That's especially true for something like Vitor, which is ostensibly a proxy for the physical medium density (as opposed to the perceptual aspects). This answer isn't a recommendation for any particular method. I just grabbed the first clear paper and ran with it. There are countless papers on contrast metrics, and I'm sure there are plenty specifically on measures of haze. If this one isn't what you want, pick another.
I don't have academic access anymore, and in the last 15 years, I've wasted way too many hours trying to implement crap in papers only to figure out that there are gross errors in the equations or entire chunks of the process which were left completely undescribed. Like I said, first clear paper. I'm not going to keep digging.
EDIT: FWIW, I thought I had posted a technique similar to Gautam's, but I don't see it. It might have been an unused demo for docs. Regarding MIMT imstats() has an 'edginess' metric that's derived from the gradient estimate without the effects of binarization and thinning. It also has a rough local contrast metric, but you can do the mean-normalized standard deviation too.
function K = haziness_gautam_dgm(inpict)
stats = imstats(inpict,'edginess','std','mean','normalized');
K = [stats(1,:); stats(2,:)./stats(3,:)];
The result is very similar to the included haziness_gautam(). There's no huge benefit to doing it this way, though it might be easier to write if you're used to it. The one thing imstats() does is that it will automagically return stats for all channels. It also does a bunch to safeguard against letting NaNs ruin the summary statistics.
