Colour correctability of a colour‐matching recipe

Different measures of sensitivity of the recipe colour to random and proportional dye concentration error. Part 1: Definitions, mutual relations and estimates of maximal colour errors

“…All the numerical estimates of colour sensitivity and colour correctability, developed previously [3,4], remain valid also in case of the above generalised defi nitions. Let us recall that these estimates can be computed from the matrix J CMC B appearing in match prediction calculations.…”

“…how to assess/quantify the ability to make small corrections of recipe colour, is as follows. The correctability of the recipe colour [4] is defi ned according to the magnitude [(∆c 1 ) 2 + (∆c 2 ) 2 +(∆c 3 ) 2 ] 1/2 of concentration change ∆c = (∆c 1 , ∆c 2 , ∆c 3 ) needed to produce the requested small colour change ∆v = [∆L*/(lS L ), ∆C*/(cS C ), ∆H*/S H ] = (∆L* S , ∆C* S , ∆H* S ) (see Figure 1).…”

“…The values of the first seven of the presented sensitivities and correctabilities are calculated using formulae and numerical estimates that were briefly reviewed in the previous section. For detailed explanation and development of these formulae see the earlier papers by Sluban and Nobbs [3,4]. The overall correctability is calculated by the approximation formula Eqn 12.…”

“…The colour sensitivity of a colour-matching recipe to random concentration errors [3] was introduced to enable a quantitative prediction and comparison of the stability-related properties of various possible recipes for the colour of a given standard. The colour correctability [4] of a colour-matching recipe was also quantified to enable the prediction and comparison of ability to make small corrections of the colour of various possible recipes. In the papers by Sluban and Nobbs [3,4], the numerical estimates of colour sensitivity and colour correctability were developed, which can be computed from a special matrix JB involved in match prediction calculations.…”

“…The colour correctability [4] of a colour-matching recipe was also quantified to enable the prediction and comparison of ability to make small corrections of the colour of various possible recipes. In the papers by Sluban and Nobbs [3,4], the numerical estimates of colour sensitivity and colour correctability were developed, which can be computed from a special matrix JB involved in match prediction calculations. Looking back at the theoretical models for the sensitivity and correctability of a recipe, some links and similarities between both of them can be observed and, consequently, the treatment of both quantities will be generalised and unifi ed in this paper.…”