Testing of Supra-Threshold Hue Differences in Hue Dependencies Colour- Difference Formulas Jiří Militký, Michal Vik Textile Faculty Technical University of Liberec, Czech Republic Abstract One of main problems of developing a new colour-difference formula is a hue dependency of visual colour difference matches. Our study show that hue differences variability depended on hue value of standards and must be implemented in colour-difference formula as a statistically significant factor. In this paper are first discussed problems of Cui-Hovis „General Form of Color Difference Formula Based on Color Discrimination Ellipsoid Parameters“ – mainly polynomial form of ∆Θ function, second is testing MV-1 colour difference formula adopted on different ∆Θ functions together with the other advanced CIELAB based equations using the combined data set and each individual data set. Key words: colour-difference perception, colour difference equation, linear regression Introduction Work in area colour differences has concentrated on collecting reliable data and developing equations that describe the perceived colour - difference results. Newer equations have been developed on base of the CIELAB (CIELCH) colour space with application weighting difference components such as DL*, DC* and DH*. Weighting functions S L , S C , S H are computed from regression analysis used linear (CIE1994) or hyperbolic model (CMC(l:c)). During the development of a new colour – difference formulas (CIE1994, C94CHR and MV-1(l:c) ) was considerable discussion about possible hue dependencies, as exemplified by the CMC and BFD equations. The CMC (l:c) colour – difference formula was a refinement of the JPC79 equation developed by Dr. McDonald. McDonald found that, for brown and purple-blue colours, CIELAB tolerances were over predicted. Therefore was implemented in CMC equation hue-angle dependent correction. The BFD colour – difference formula was based on the Luo-Rigg (BFD) dataset. Luo-Rigg found that green colours were also over predicted. Berns studies on RIT-Du Pont dataset showed that, this hue dependency is not necessary condition by development of a new colour – difference formula. In 1995 Cui and Hovis have published an article: „General Form of Color Difference Formula Based on Color Discrimination Ellipsoid Parameters“ [1]. This derivation of the colour-difference formula is not fully acceptable, because has three significant errors. First is in ignorance of cylindrical character of LCH space. Hue component of colour-difference is valid only for small ∆h values. Second and third incorrectness are in function ∆ θ. Cui-Hovis 9-th order polynomial regression of LRM data (Luo-Rigg data set [2] and Melgosa and all. translated [3]) strongly oscillated between this data points and has opposite orientation [4]. Strongly oscillation of Cui-Hovis 9-th order polynomial fitting follows from numerical problems of calculation linear regression on computer. These problems we can solve by some methods, which are described in this article. Modification of Cui Hovis function Cui and Hovis used for approximation of ∆Θ function the 9-degree of polynomial. Due to strong multicollinearity the incorrectness of parameter estimates obtained by using of classical least squares occurs. In this contribution the criterion of mean error of prediction combined with various strategies of biased estimation was used for improving the predictive ability of polynomial approximation. The approximating function ∆Θ = f(h) (1) is selected from class of polynomials Ordinal least squares A linear regression model is a model which is formed by a linear combination of explanatory variables x or their functions, y i = β 0 + β 1 x 1,i + β 2 x 2,i + ... + β m x m,i + ε i , (2) i = 1, ..., n, Linear model means generally linear according to model parameters. Special types of linear model are polynomials in the form y i = β 0 + β 1 x ,i + β 2 x 2 ,i + ... + β m x m ,i + ε i , (3) In this models are explanatory variables powers of one variable x only