Bridging instrumental and visual perception with improved color difference equations: A multi-center study

Objectives: This multicenter study aimed to evaluate visual-instrumental agreement of six color measurement devices and optimize three color difference equations using a dataset of visual color differences (∆V) from expert observers.

Methods: A total of 154 expert observers from 16 sites across 5 countries participated, providing visual scaling on 26 sample pairs of artificial teeth using magnitude estimation. Three color difference equations (ΔE*_ab, ∆E₀₀, and CAM16-UCS) were tested. Optimization of all three equations was performed using device-specific weights, and the standardized residual sum of squares (STRESS) index was used to evaluate visual-instrumental agreement.

Results: The ΔE*_ab formula exhibited STRESS values from 18 to 40, with visual-instrumental agreement between 60 % and 82 %. The ∆E₀₀ formula showed STRESS values from 26 to 32, representing visual-instrumental agreement of 68 % to 74 %. CAM16-UCS demonstrated STRESS values from 32 - 39, with visual-instrumental agreement between 61-68 %. Following optimization, STRESS values decreased for all three formulas, with ΔE^' demonstrating average visual-instrumental agreement of 79 % and ∆E₀₀ of 78 %. CAM16-UCS showed average visual-instrumental agreement of 76 % post optimization.

Significance: Optimization of color difference equations notably improved visual-instrumental agreement, overshadowing device performance. The optimzed ΔE^' formula demonstrated the best overall performance combining computational simplicty with outstanding visual-instrumental agreement.