Re: Usable Tones in Different Gammas
Re: Usable Tones in Different Gammas
- Subject: Re: Usable Tones in Different Gammas
- From: Robin Myers <email@hidden>
- Date: Sun, 10 Dec 2000 11:23:28 -0800
- Organization: Robin Myers Imaging
Dear Mr. Gierling,
I believe your L* calculations are in error. You are starting with the entire
range of RGB values and calculating the perceptable steps within that range.
Since the RGB values are quantized to 8-bits, you must start with the reduced
set of quantized 8-bit values and calculate the number of perceptable steps
from these. I performed my own calculations using this method and the results
are below. I also discovered that I had accidentally reversed the values in
my previous post. Below are the correct values and my calculation of the
number of perceptual steps using your number of 1 Delta-E.
Available Grayscale Values
Gamma 0-63 64-127 128-191 192-255 Total Values
------------------------------------------------------------------------------------
1.8 22 52 64 64 202
2.2 13 43 64 64 184
Perceivable Steps (assuming 1 Delta-E steps)
Gamma 0-63 64-127 128-191 192-255 Total Values
------------------------------------------------------------------------------------
1.8 19 21 18 16 74
2.2 13 21 20 19 73
As you can see from this, the 1.8 gamma has a slight edge over the 2.2 gamma.
Although, I would suggest that they should be considered to have the same
number of 1 Delta-E steps. What is interesting is the distribution. The 1.8
gamma has more steps in the shadows and the 2.2 has more steps in the
highlights.
For the gentleman that asked where I got the value of 0.5 as a JND (Just
Noticible Difference) for achromatic colors, I have been unable to find my
reference on this. However, if you put up a grayscale from 0-255 in RGB on a
monitor (in a darkened room) and look for the steps, you will easily come up
with more than 100 steps (the theoretical maximum for L* if 1 Delta-E steps
are involved). So the perceivable number of steps must be more than 100. My
own experiments suggest a 0.5 Delta-E (or smaller) for achromatic colors).
This is dependent on dark adaption, the surround, and numerous other factors.
But the 1 Delta-E as a JND has traditionally been used for chromatic colors,
not achromats. Also, if you will examine some of the charts used for
displaying JNDs, you will see that as the chroma increases, the JND increases
beyond 1 Delta-E. This suggests that as the color becomes more achromatic,
the JND decreases. There have also been several experiments that show the
surround has a large influence on a JND. Studies with a gray background close
to the reflectance of the test patches increases the sensitivity of the
visual system to differences, thus decreasing the JND.
I apologize for all the science here, but there have been many misleading
statements made on this forum that have shaky scientific foundations. My
intention here has been to show that a gamma of 2.2 has fewer gray values,
both realizible and perceptual than a gamma of 1.8. If anyone would like to
check my calculations, I will be happy to share my Excel spreadsheet that
performs these calculations. Please email my privately for the spreadsheet.
So, what do you get with a 2.2 gamma? You get more contrast in the image.
Studies have shown that higher contrast can influence the perception of
sharpness. There is a steeper step in lightness changes at the edges of
objects so the apparent sharpness increases. This is the same phenomenon that
makes unsharp masking work (it just works locally at the edges of the
objects, not globally on the entire image). So the image looks sharper, even
though you are showing fewer gray levels. You also use less correction in the
gamma lookup tables, so there may be some benefits in gradients showing less
Mach banding.
Thank you for your indulgence,
Robin Myers