tag:blogger.com,1999:blog-1840985738235902482.post1453335287757647516..comments2017-08-16T10:14:41.460-05:00Comments on John the Math Guy: Is 1.0 delta E a "just noticeable difference"?John Seymourhttps://plus.google.com/107565394741171719003noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1840985738235902482.post-36268065810928394172017-08-02T16:32:35.862-05:002017-08-02T16:32:35.862-05:00Was it the TAGA paper from Tony Johnson, perhaps? ...Was it the TAGA paper from Tony Johnson, perhaps? I don't have a reference handy, either.<br /><br />I agree with you, as usual, Steve. CIELAB is icky all by itself, because 1) it is based on nonlinear functions applied to the XYZ functions which do not exist in nature, and 2) it applies a piecewise function, which again, does not exist in nature.John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-86309720139953181542017-08-02T16:20:36.281-05:002017-08-02T16:20:36.281-05:00The 2000 formula is only the second ugliest?
Ther...The 2000 formula is only the second ugliest?<br /><br />There is at least one study (sorry, I do not have the citation handy) that shows that the 2000 formula did not perform better than the 1994 color difference formula. An oblique application of Occam's razor would favor the 1994 formula, a relatively straightforward extension of the 1976 a*, b* formula.<br /><br />Personally, I believe if one must go to lengths as Herculean as those employed in the 2000 formula, there is a fundamental flaw in the foundation, and your time might be more productively spent elsewhere.<br /><br />IPT and related spaces are only slightly more complicated than CIELAB, and are far more uniform. They avoid the oversimplification made in CIELAB that the x-bar, y-bar, and z-bar color matching functions are cone fundamentals, and use a more realistic set of cone fundamentals. IPT-like spaces should be investigated further as a replacement for CIELAB.<br /><br />Apostasy, heresy, iconoclasm, or just plain practicality? I would like to think the latter, but many disagree with me.Steve Viggianohttp://acolyte-color.comnoreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-80563234376287517452017-07-30T09:22:16.449-05:002017-07-30T09:22:16.449-05:00I got an email from the venerable Danny Rich. It s...I got an email from the venerable Danny Rich. It seems that Google blogger doesn't like him, since it doesn't let him post a comment. If anyone else is having problems posting comments please post a comment here so that I can look into it.<br /><br />Danny has provided us with a bit more detail about JND:<br /><br />"I find a couple of premises in this blog that are not supported in the literature and lead to a questionable conclusion. The first is that visual color space (not some mathematical approximation to it) is visually uniform across all hues, lightness and chromas (using your Munsell notations). Thus trying to equate any form of DeltaE to a visual jnd is a bit like trying to catch the wind. The second is that someone, somehow invented MacAdam ellipses and then he just adopted them for his research. Reading his papers and his presentations to the OSA one observes, that despite the complicate schematic, his experiment was relatively simple. There was a reference color field and a test color field. They began as being equal and the test field was varied along a single direction in chromaticity (no differences in the brightness). When his observe (Mr. Nutting) could detect a visual difference the experiment stopped, the setting of the test color recorded and the experiment was repeated, moving in a different direction in chromaticity. This process was repeated a number of times and the distance to jnd determined from the standard deviations of the trials. So the final experimental data was the 20 or so color centers with a lot of little "sticks" pointing outward. Today we might cast a convex hull around those points but in the 1940s such arithmetic was not easy to do. Since the lengths of the sticks were not equal in all directions, a circle would not be a good fit and the next simple geometric figure was an ellipse. So ellipses were cast around his data points. A later paper by Brown, Jackson (also of Kodak) and Howe (an intern at Kodak from NC State) demonstrated that the ellipse was simply the 2D standard deviations of the bivariate Normal statistical distribution. Brown went on to derive the same mathematical analysis for combined lightness and chromaticity differences as the 3D ellipsoid, again simply represented by the trivariate Normal distribution. The reason that the shape should be elliptical or ellipsoidal lies in the relationship between the coordinates. (x,y) or (Y,x,y) are not independent but are correlated so that the covariance is not zero. A good discussion of this can be found in the section on Color Metrics in the textbook Color Science by Wyszecki and Stiles. The arguments apply to the work on differences in CIELAB space. L*, a*, b* all contain the Y tristimulus value and as a result are correlated. Since L*,a*,b* are not independent they will not form a Euclidean space and the standard deviations of visual judgments will always form an ellipsoid. So if we have to assign a cause for MacAdam's jnd's being elliptical perhaps it should be R. A. Fisher "John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.com