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:
“Children who begin life with an eagerness to please, need to know that not pleasing is also all right now and then. They learn tolerance for others’ faults through our tolerance of their own.”
—Cathy Rindner Tempelsman (20th century)
“Our first line of defense in raising children with values is modeling good behavior ourselves. This is critical. How will our kids learn tolerance for others if our hearts are filled with hate? Learn compassion if we are indifferent? Perceive academics as important if soccer practice is a higher priority than homework?”
—Fred G. Gosman (20th century)
“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)