| | Ghostrider
Administrator
Posts: 43 |
C64 color comparison
So, I'm playing around with something that utilizes color differences, and I wanted my code to be as good as I could make it. That led me into a little research, resulting in the below table (and documentation) in my code. I have no idea whether others have done anything like this, I just thought I'd share it in case it could be useful for someone. (Tho I guess there could be someone who doesn't like the Pepto palette). The color-differences range from 0 to 100, as can be seen from the difference between black and white.
/* COLOR-DIFFERENCE TABLE, measuring how alike 2 colors look to the human eye.
*
* Created by translating the correct C64 RGB-palette (as thoroughly researched
* by Philip 'Pepto' Timmermann, and published in the "Commodore VIC-II Color
* Analysis"):
*
* Black White Red Cyan Purple Green Blue
* 00 00 00 ff ff ff 68 37 2b 70 a4 b2 6f 3d 86 58 8d 43 35 28 79
*
* Yellow Orange Brown Lt Red Dark Grey Med Grey Lt green
* b8 c7 6f 6f 4f 25 43 39 00 9a 67 59 44 44 44 6c 6c 6c 9a d2 84
*
* Lt Blue Lt Grey
* 6c 5e b5 95 95 95
*
*
* into the intended perceptually uniform CIE L*a*b* (CIELAB) color space via
* Photoshop CS5:
*
* Black White Red Cyan Purple Green Blue
* 0 0 0 100 0 0 29 21 18 64 -15 -13 35 32 -32 54 -29 33 22 25 -45
*
* Yellow Orange Brown Lt Red Dark Grey Med Grey Lt green
* 78 -15 42 36 10 30 24 0 33 49 20 17 29 0 0 46 0 0 79 -29 33
*
* Lt Blue Lt Grey
* 44 22 -45 62 0 0
*
* and finally, using the above CIE L*a*b* values, computing the
* color-differences between any two C64 colors. This was done using a Matlab
* implementation of the CIEDE2000 color-difference formula, published by
* Gaurav Sharma at the University of Rochester. As of 2016, this should be the
* best visual-color-difference algorithm available.
*/
float colordiff[16][16] = {
{0.00000, 100.00000, 27.29927, 53.26580, 33.36977, 46.54540, 27.91278,
71.32101, 30.91014, 24.36201, 40.40526, 18.97503, 32.86756, 72.80412,
39.20668, 48.53537},
{100.00000, 0.00000, 61.97257, 29.34183, 56.93753, 40.24329, 71.85536,
26.50693, 54.14554, 67.73280, 42.05900, 58.78266, 40.33892, 26.72007,
48.58504, 26.02320},
{27.29927, 61.97257, 0.00000, 53.66487, 28.72115, 44.76018, 33.08048,
56.92023, 14.00707, 21.06269, 17.36067, 19.62648, 24.37162, 61.72667,
35.29397, 37.10740},
{53.26580, 29.34183, 53.66487, 0.00000, 38.60884, 30.82463, 43.73660,
34.43323, 43.05106, 48.64282, 43.62700, 37.61613, 23.58306, 31.63124,
27.79863, 16.38323},
{33.36977, 56.93753, 28.72115, 38.60884, 0.00000, 63.67504, 13.95492,
69.94213, 40.00703, 47.52039, 30.66366, 24.06466, 25.52344, 73.27806,
13.99189, 35.70972},
{46.54540, 40.24329, 44.76018, 30.82463, 63.67504, 0.00000, 55.77398,
21.74555, 31.80033, 31.80176, 38.51345, 32.30988, 24.56106, 20.17950,
49.67790, 24.32458},
{27.91278, 71.85536, 33.08048, 43.73660, 13.95492, 55.77398, 0.00000,
80.90839, 43.71174, 48.31631, 39.23529, 24.73801, 31.07341, 74.86371,
17.74707, 43.54902},
{71.32101, 26.50693, 56.92023, 34.43323, 69.94213, 21.74555, 80.90839,
0.00000, 42.97277, 54.79072, 39.45047, 52.55362, 35.47933, 9.66140,
64.56892, 25.73341},
{30.91014, 54.14554, 14.00707, 43.05106, 40.00703, 31.80033, 43.71174,
42.97277, 0.00000, 12.50487, 17.45413, 19.77869, 20.96770, 47.52027,
42.70317, 32.11929},
{24.36201, 67.73280, 21.06269, 48.64282, 47.52039, 31.80176, 48.31631,
54.79072, 12.50487, 0.00000, 29.37105, 19.29903, 26.19519, 57.58782,
50.39976, 39.71692},
{40.40526, 42.05900, 17.36067, 43.62700, 30.66366, 38.51345, 39.23529,
39.45047, 17.45413, 29.37105, 0.00000, 25.82295, 19.35305, 45.64642,
32.88847, 22.69667},
{18.97503, 58.78266, 19.62648, 37.61613, 24.06466, 32.30988, 24.73801,
52.55362, 19.77869, 19.29903, 25.82295, 0.00000, 14.44913, 53.39135,
26.98485, 31.49222},
{32.86756, 40.33892, 24.37162, 23.58306, 25.52344, 24.56106, 31.07341,
35.47933, 20.96770, 26.19519, 19.35305, 14.44913, 0.00000, 36.41365,
23.94736, 15.38462},
{72.80412, 26.72007, 61.72667, 31.63124, 73.27806, 20.17950, 74.86371,
9.66140, 47.52027, 57.58782, 45.64642, 53.39135, 36.41365, 0.00000,
57.25129, 26.64841},
{39.20668, 48.58504, 35.29397, 27.79863, 13.99189, 49.67790, 17.74707,
64.56892, 42.70317, 50.39976, 32.88847, 26.98485, 23.94736, 57.25129,
0.00000, 29.63502},
{48.53537, 26.02320, 37.10740, 16.38323, 35.70972, 24.32458, 43.54902,
25.73341, 32.11929, 39.71692, 22.69667, 31.49222, 15.38462, 26.64841,
29.63502, 0.00000}
}; |
|
| | lft
Registered: Jul 2007
Posts: 369 |
Fascinating stuff.
I'm not quite sure I understand the intuition for these colour differences, though. For instance, going from black to white involves a difference of 100, but going from black to dark grey to white is only 19 + 59 = 78. So as a measure of distance, it doesn't satisfy the triangle inequality (which states that a detour can never give you a shorter path).
Could you elaborate on how one could use this table in practice? |
| | Digger
Registered: Mar 2005
Posts: 421 |
Reminds me of a small side project that can sort colors based on their luma distances: https://og2t.github.io/retro-palette-explorer/
Pick "Closest to $x" option from the Sort By dropdown. |
| | Ghostrider
Administrator
Posts: 43 |
Digger, interesting page and side-project! I especially like the idea of judging the mixed colours!
lft, I can tell you how I am using it. It is the simple matter of approximating one colour with another. As you know, various C64 graphics modes have some limitation on how many colours can be used within some limited area of the screen (like a char, for example). In my case, the original (input) image that I'm approximating already uses only the 16 VIC colours but with no limitations concerning "number of colours per area". So in choosing the best colours for my approximating output, I needed a way for the code to compare each original colour with a possible candidate. And as my studies led me to understand, RGB is not a very good basis for comparing colours, if we talk about how they look to the human eye. One could say that the table answers questions such as "If I wanted to approximate a red colour with that other colour which looks the closest to the human eye, which should it be?" (in this case the answer would be "orange", with a difference score to red of 14.00707, the lowest of any candidate). This, ofcoz, also allows one to select the second best or third best (and so on) candidate.
Apparently there's ongoing research in the area of humanly perceived colour-difference. The CIEDE2000 colour-difference formula was the best I could find, with an implementation available on:
http://www.ece.rochester.edu/~gsharma/ciede2000/
Wikipedia also has some info on the topic and the formula.
I believe that if one wanted to make the ultimate general "png to koala" converter (or something like that), as of 2016 this might be the "visually optimal" formula to use. Though I have no idea how many hours of number-crunching such a tool would need to do, using the formula to derive the best possible koala picture from a general png. :D |
| | Copyfault
Registered: Dec 2001
Posts: 466 |
Interesting and helpful indeed! Up to now I was fiddling with an avarage of RGB-distance and YUV-distance, but this approach seems to bring it down to one comparison formula.
Nontheless, lft is right in saying that this formula gives no proper distance function. Then again, who said that the colour spaces we deal with (i.e. a rather tiny discrete space as a subspace of another huge discrete space) are metric spaces ;)? |
| | Copyfault
Registered: Dec 2001
Posts: 466 |
Quoting Ghostrider
[...] In my case, the original (input) image that I'm approximating already uses only the 16 VIC colours but with no limitations concerning "number of colours per area".
[...]
Upon furhter thinking, I wonder how the first conversion of the original data to the 16 VIC-Cols were done. Did you do that by RGB comparison or was the CIELAB-difference-formula already applied in this early step?
This should make a difference as the RGB comparison is based on the euclidian norm whereas the CIELab-formula is _a little bit_ more complicated.
In case you have done the first conversion step with the CIELab-difference-formula: would you care to share it (be it C+/java/Kickass/ACME-macro or whatever "frontend")? Having read through the mentioned paper I decided to refrain from exchanging the existing standard comparsion (suddenly RGB comparison is not THAT bad after all ;)) |
| | Ghostrider
Administrator
Posts: 43 |
Copyfault, actually I haven't done the "early step" you mention. And you are right, the formula is _a little bit_ complicated, haha :D
I only used a slightly modified version of the Matlab sources to calculate the table I've shown.
But since the Matlab implementation of the formula is less than 2 pages of code, it shouldn't be too hard to translate it to C (or whatever) line by line.
One just has to also find an RGB-to-CIELAB conversion formula (I used Photoshop), since that's what the CIEDE2000-formula eats - but I guess such a formula should be quite possible to find. I haven't looked into this.
In case you didn't notice, the code is under the "Matlab function" link on the page I linked to. |
| | Copyfault
Registered: Dec 2001
Posts: 466 |
Ok, thanks for the fast reply! Hmm, maybe I should give it a try transferring the MATLAB-code to e.g. Kickass line-by-line... let's see.
On the German Wikipedia pages I found some information on how to convert from sRGB to CIEL*a*b*. This is done by
1. a linear transformation to convert sRGB to CIEXYZ-coordinates -plus-
2. a nonlinear transformation to convert the CIEXYZ-values into CIEL*a*b*-values
The way to go should be to define a "new" distance function for RGB-values by
d(RGB_1, RGB_2) := CIEDE2000 (T(RGB_1), T(RGB_2)),
where T denotes the transformation as described above.
Quite something to do! Thanks again for the pointers! |
| | Ghostrider
Administrator
Posts: 43 |
That was fast, finding that sRGB -> CIELAB formula. Thanks for the link!
Yeah, that seems like the right steps to take. And something I think we haven't seen in the C64 scene yet.
A KickAss-script implementation _would_ be really really cool! (I wonder how fast it would be). |
| | Oswald
Registered: Apr 2002
Posts: 5022 |
I dont understand half of that german wiki. so rgb to xyz then xyz to lab ? what if I got heiligkeit grun blaue etc, how do I calculate a distance if i have 2 sets of values of those for 2 colors ?
Die Faktoren 500 bzw. 200 sollen die resultierenden Werte für a* und b* in die gewohnten Größenordnungen bringen, die auch zum maximalen L* von 100 passen.
wat ? :) |
| | chatGPZ
Registered: Dec 2001
Posts: 11135 |
what exactly are you trying to do with this anyway? from when i experimented with this stuff, i remember that YUV would always give the better result... the LAB stuff didnt help for what i was doing :) |
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