tag:blogger.com,1999:blog-1840985738235902482.post284181384842364134..comments2017-09-22T17:13:09.281-05:00Comments on John the Math Guy: How many colors are there - the definitive answerJohn Seymourhttps://plus.google.com/107565394741171719003noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1840985738235902482.post-86576159159844864652014-07-02T22:19:36.273-05:002014-07-02T22:19:36.273-05:00The graduated cotton bud test is far more accurate...The graduated cotton bud test is far more accurate. Lighter hues are more easily discernable than bright saturated colours.<br /><br />The test involves placing cotton buds in the correct order of an ascending chromatic scale. The average unimpaired subject, can usually differentiate several million shares and hues of colour with this very practical test. The lighter the hue the easier it gets! <br /><br />Ask any automobile spray painter, and they will tell you that 'White' is the most difficult colour to match. If it's a door panel with a minute scratch, the entire door has to be repainted the closest match, and the spray painter just hopes the customer does not complain! (I serve as Company Secretary with an Industrial Coatings Company, we were consultants for The Brooklyn Bridge, and held the Concorde Supersonic Coatings Contract)Alastair Carnegiehttps://www.blogger.com/profile/14681204887978650419noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-12492282712526642932013-09-15T20:07:26.846-05:002013-09-15T20:07:26.846-05:00Yeah, it would be good to sample at a finer resolu...Yeah, it would be good to sample at a finer resolution. It would be tractable to go down to (say) 1 DE sampling in terms of memory, but the big issue is computer time, not storage. If I were to increase the resolution by a factor of five in all dimensions, then it would take 125 times as long to get counts in the boxes. As it is, this was about ten hours on my computer (running non-compiled Mathematica code) to generate the half a billions spectra.<br /><br />Even with that many spectra, there is a little bit of fringe near the edge. Look to the left of the top in the diagram above. There is a green pixel next to a hole just to the right. Is this hole reality, or i it the fact that I didn't generate quite the right spectra to fill that box?<br /><br />You mentioned the cube root thing... this was another tactic to speed up the convergence - that is, to speed up the rate that boxes get checked off.<br /><br />As for the piecewise linear thing... that was another attempt to speed things up. This one I can justify for my particular use, since I live in a world of measuring the color of light reflected from solid objects. Generally speaking these spectra are "smooth".<br /><br />The fact that there were two previous papers (doing this is different ways) that came up with very similar numbers leads me to believe that my assumptions are not that far off. John the Math Guyhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-35215958191408843082013-09-15T12:07:08.449-05:002013-09-15T12:07:08.449-05:00I do not follow your reasoning for using cube root...I do not follow your reasoning for using cube root sampled, piecewise linear reflectance curves for the optimization. Since you are using Monte Carlo and we know that worst case estimate for the number of points s L*=100, a*=160, b*=180 which should mean tht there are 2,880,000 points in CIELAB separated by 1 step along any one axis. If we halve the step size to 0.5 CIELAB units then the maximum number of points is 23,040,000. That is still a tractable number.Unknownhttps://www.blogger.com/profile/03791815228024493846noreply@blogger.com