Premium
Construction of discrimination ellipsoids for surface colors by the method of constant stimuli
Author(s) -
Indow Tarow,
Morrison Melvin L.
Publication year - 1991
Publication title -
color research and application
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.393
H-Index - 62
eISSN - 1520-6378
pISSN - 0361-2317
DOI - 10.1002/col.5080160109
Subject(s) - ellipsoid , mathematics , sigmoid function , mathematical analysis , geometry , artificial intelligence , physics , computer science , astronomy , artificial neural network
Abstract First, methods to define the region of colors indistinguishable from a standard color are reviewed, both for aperture and surface colors. Then, an algorithm to define discrimination ellipsoids for surface colors in ( x,y,l ) space is described, where 1 is a function of Y. The data are a set of P i , the proportion that a comparison stimulus s i is judged discriminable from a standard stimulus S o (the method of constant stimuli). An ellipsoid is defined around S o such that, if the distance between S o and s i is evaluated by the radius of the ellipsoid in that direction, then that distance is related to P i in the form of a sigmoid curve (the cumulative normal distribution). The third axis of the ellipsoid is defined to be parallel with the Y axis and hence there are four free parameters. These parameters are estimated using the principles of either chi‐square minimum or maximum likelihood estimation. The algorithm was applied to the data obtained from, respectively, R.M. Rich, D.C. Rich, and Witt and Döring. Results by the present method were compared with their results, which were obtained using different procedures. The method was also applied to the data of Bartleson to test the possibility that the domain of colors called “brown” is ellipsoidal in form; the result was negative. A theoretical discussion on the naure of the sigmoid curve is included.