You can use one of ASTM Standards, for example

https://www.astm.org/Standards/C1649.htm

or

https://www.stellarnet.us/systems/color-measurement-systems/?gclid=Cj0KCQjwzunmBRDsARIsAGrt4mtExahnSm4nUiSykwjT2wUtSLSobmxiMCMRqO0XXlaXqTUDTByI1v8aAiz9EALw_wcB

Hi Jun,

If I understand your question, you want to know how to predict the perceived color of an area that is composed of a large quantity of small stimuli, such as in a mosaic. I'm not certain of reseach "specific" to the question, but here are things to point you in the correct direction.

ICAM (Appearance Modeling):

First off, I suggest you take a look at ICAM, the image appearance model developed by Mark Fairchild at RIT.

Stimulus Size:

The size of stimulus has a direct impact at which point perception goes from integration (perceiving a continuous tone) to individual stimuli. This is predicted partially by Michaelson Contrast:

(La - Lb) / (La + Lb)

Which essentially determines when a stimuli reaches a spatial frequency and becomes.a continuous tone. See also "minimum circle of confusion".

Metamerism:

Metamerism refers to the eye sensing a specific color even though the color is created by a different set of wavelengths. The effect is caused by the eye's cones being stimulated to the same degree, but with stimuli of different wavelengths and intensities.

For instance, in normal vision the pure wavelength of 585nm is perceived as yellow. But you can make yellow on your compute monitor by specifying red and green, such as #FFFF00. This causes the monitor to emit maximum RED and maximum GREEN, but these colors DO NOT mix to form a pure wavelength of 585nm. The red light stimulates the red cones and the green light stimulates the green cones in the same way that 585nm stimulates the red and green cones.

COLOR PAIRS & MULTICOLOR MATH

The math to add two colors in a linear colorspace is trivial, for instance if you just want to predict the color of a field of small stimuli where:

• All stimuli are the same size.
• All stimuli are one of only two colors, C1 and C2.
• The stimuli are equally dispersed (normal distribution)
• There is an equal number of stimuli.
• And you have measurements of both C1 and C2 as linear light values

THEN:

Cpredicted = (C1_LinearValue + C2_LinearValue) / 2

Note: You must work with linear values! Linear RGB or CIEXYZ which is linear. You cannot use CIELAB. L*a*b* is perceptually uniform, using L* (Lstar) the perceptual lightness curve, and thus non-linear. CIELAB must be converted to a linear colorspace before using this simple math.

Light is linear, so if you have a linear light environment, the math is surprisingly simple. For instance if you are using a linear RGB color model, (with no gamma curve, i.e. gamma 1.0) with normalized color values from 0 to 1, and you have these colors:

Linear RGB values:

C1 as R 0.0 G 0.334 B 0.548 (Cerulean Blue)

C2 as R 1.0 G 0.995 B 0.0. (Yellow)

Then add each channel, and divide each channel by 2

R1 + R2 = 1.0

G1 + G2 = 1.3294

B1 + B2 = 0.5478

1.0 / 2 = R 0.5

1.3294 / 2 = G 66.47

0.5478 / 2 = B 27.39

To display on an sRGB monitor, the sRGB gamma needs to be applied, the exact curve has a linearized section, but for discussion purposes we'll use the simple power function, 1/2.2 or 0.455:

0.50.455 = R´0.735 which rounds to 8bit 188 or Hex BC

66.470.455 = G´0.835 which rounds to 8bit 213 or Hex D5

27.390.455 = B´0.560 which rounds to 8bit 143 or Hex 8F

For reference, the gamma encoded (non-linear) hex values for the two sRGB colors that resulted in the perception of sRGB #BCD58F are:

sRGB #009CC3 (Cerulean Blue)

sRGB #FFFE00 (Yellow)

There is an example file using these values attached. You'll see the blue/yellow checkerboard of small, same-sized stimuli in equal quantities on the left, and on the right the solid color predicted by the math listed above.

MULTIPLE COLORS

But what about multiple colors, multiple size stimuli, and different distributions? As I hope the simple demonstration above shows, you can use fairly simple additive math when you are working with linear light values.

The Wikipedia page on CIEXYZ has useful math for mixing colors in CIE.xyY colorspace: https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram

Nevertheless, so long as the colorspace is linear relative to light, the math for combining tristimulus values is fairly straightforward.

SUMMARY:

So I'd think for a mosaic, you'd need to measure or calculate the total area of each color in the mosaic, measure each color sample with a spectrocolorimeter, then use the appropriate math to calculate the linear light value of the predicted color, and convert that to sRGB values for computer display.

Because light is linear, if 30% of the surface area is color C1 and 45% is color C2, and 25% is color C3, you can weight your average accordingly. To use the simple linear RGB math above, that indicates:

RGB1 * 0.3 + RGB2 * 0.45 + RGB3 * 0.25 = RGBpredicted

Which I believe would work assuming again a normal distribution of the mosaic tiles, though I'm not sure what practical limits there may be. Also, you need to calculate the grout around the tiles as that will affect perception if it represents more than 1% of the reflective surface area.

Cheers,

Andy

Dear Jun Tang, I succeeded in modelling the effect of texture detail on visual colour using cluster analysis and I have posted a PowerPoint presentation file for the relevant conference on RG. Go if you will to my posted set of PPT files and read Col Appearance. ppt

Regards

David.