The current color-difference formulas were developed based on 2D samples and there is no standard guidance for the color-difference evaluation of 3D objects. The aim of this study was to test and optimize the CIELAB and CIEDE2000 color-difference formulas by using 42 pairs of 3D-printed spherical samples in Experiment I and 40 sample pairs in Experiment II. Fifteen human observers with normal color vision were invited to attend the visual experiments under simulated D65 illumination and assess the color differences of the 82 pairs of 3D spherical samples using the gray-scale method. The performances of the CIELAB and CIEDE2000 formulas were quantified by the STRESS index and F-test with respect to the collected visual results and three different optimization methods were performed on the original color-difference formulas by using the data from the 42 sample pairs in Experiment I. It was found that the optimum parametric factors for CIELAB were $k_L$ = 1.4 and $k_C$ = 1.9, whereas for CIEDE2000, $k_L$ = 1.5. The visual data of the 40 sample pairs in Experiment II were used to test the performance of the optimized formulas and the STRESS values obtained for CIELAB/CIEDE2000 were 32.8/32.9 for the original formulas and 25.3/25.4 for the optimized formulas. The F-test results indicated that a significant improvement was achieved using the proposed optimization of the parametric factors applied to both color-difference formulas for 3D-printed spherical samples.

An improved spectral reflectance estimation method was developed to transform captured RGB images to spectral reflectance. The novelty of our method is an iteratively reweighted regulated model that combines polynomial expansion signals, which was developed for spectral reflectance estimation, and a cross-polarized imaging system, which is used to eliminate glare and specular highlights. Two RGB images are captured under two illumination conditions. The method was tested using ColorChecker charts. The results demonstrate that the proposed method could make a significant improvement of the accuracy in both spectral and colorimetric: it can achieve 23.8% improved accuracy in mean CIEDE2000 color difference, while it achieves 24.6% improved accuracy in RMS error compared with classic regularized least squares (RLS) method. The proposed method is sufficiently accurate in predicting the spectral properties and their performance within an acceptable range, i.e., typical customer tolerance of less than 3 DE units in the graphic arts industry.