Tolerance
Tolerancing concerns the question "What is a set of colors that are imperceptibly/acceptably close to a given reference?" If the distance measure is perceptually uniform, then the answer is simply "the set of points whose distance to the reference is less than the just-noticeable-difference (JND) threshold." This requires a perceptually uniform metric in order for the threshold to be constant throughout the gamut (range of colors). Otherwise, the threshold will be a function of the reference color—useless as an objective, practical guide.
In the CIE 1931 color space, for example, the tolerance contours are defined by the MacAdam ellipse, which holds L* (lightness) fixed. As can be observed on the diagram on the right, the ellipses denoting the tolerance contours vary in size. It is partly due to this non-uniformity that lead to the creation of CIELUV and CIELAB.
More generally, if the lightness is allowed to vary, then we find the tolerance set to be ellipsoidal. Increasing the weighting factor in the aforementioned distance expressions has the effect of increasing the size of the ellipsoid along the respective axis.
Read more about this topic: Color Difference
Famous quotes containing the word tolerance:
“In full view of his television audience, he preached a new religion—or a new form of Christianity—based on faith in financial miracles and in a Heaven here on earth with a water slide and luxury hotels. It was a religion of celebrity and showmanship and fun, which made a mockery of all puritanical standards and all canons of good taste. Its standard was excess, and its doctrines were tolerance and freedom from accountability.”
—New Yorker (April 23, 1990)
“For all the injustices in our past and our present, we have to believe that in the free exchange of ideas, justice will prevail over injustice, tolerance over intolerance and progress over reaction.”
—Hillary Rodham Clinton (b. 1947)
“Persecution was at least a sign of personal interest. Tolerance is composed of nine parts of apathy to one of brotherly love.”
—Frank Moore Colby (1865–1925)