I'm glad my explanation for this puzzling effect was useful.
I didn't mention in my last post that the fundamental reason for the change in shape of the histogram (ie, from flat and wide to a narrow peak) is something called the "Central Limit Theorem" of probability theory ( http://en.wikipedia.org/wiki/Central_limit_theorem ). I've illustrated it below. It shows one of the many wonderful connections between math and art, and especially math and Photoshop. Even better, anyone who owns a copy of PS can do this for themselves.
First, I show uniformly distributed random noise -- what it looks like, and its histogram:
[ATTACH]40011[/ATTACH] [ATTACH]40012[/ATTACH]
I then took the noise (ie, first image above), and ran it through a Gaussian blur with a radius of 3 pixels, and show the resulting image and the histogram for it.
[ATTACH]40013[/ATTACH] [ATTACH]40014[/ATTACH]
Note the dramatic change in the shape of the histogram, and also notice that the standard deviation (shown in Photoshop's info panel) has been reduced by a factor of around 10x!
The narrowing up of the histogram illustrates perfectly what the Central Limit Theorem predicts - averaging large numbers of identically distributed random numbers produces new random numbers (ie, new pixel values) whose histogram (in the limit of very large numbers of terms in the average, ie, large blur radii) approaches a Gaussian centered on the average of the original distribution. BTW, the reason that the average in my little example is not at 0.5 is because the calculations were done in a gamma weighted color space. If I had taken the time to switch over to a linear gamma space, the resulting peak would be exactly at 0.5.
We would love to see more of your work, so, if you like, please come back to the forum and chat, show off more of your very nice work, etc.
Best regards,
Tom M
Moderator, Photography Section
PSG
