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)
“It is thus tolerance that is the source of peace, and intolerance that is the source of disorder and squabbling.”
—Pierre Bayle (1647–1706)