Theoretical Design Formulas For The Objective Evaluation Of Color Depth

Color depth is the comprehensive expression of three attributes of color,it play important roles in the evaluation of color fastness,dying properties,and so on.Subjective evaluation of color depth is prone to be affective by people,environment,etc..As to objective evaluation,there are 13 formulas for color depth calculation,but these formulas have their own applicable conditions and scopes,and some are even misused.Therefore,An intensive investigation on these formulas is needed,which can be of help for their applicability and accuracy of calculation.In this study,13 color depth formulas are inspected by SINO COLOR BOOK(SCB)which owns 18195 chips at 24 color depth grades.All the samples are measured by applying an X-Rite Color i7 Spectrophotometer,and all their depth values were calculated and statistically analyzed by programming Matlab?.Result show that: among the 13 formulas,the formulas of Sato,Godlove,Rabe-Koch,Berns and Yang are better than the others.Among them,Yang formula is designed by our research group,it not only has a wide applicable range and a simple calculation process,but also has the best differentiation degree.However,Yang formula' linearity to color depth is not ideal.Therefore,this thesis aims to revise Yang's formula and achieve better formulas for color depth.In order to overcome the shortcomings of Yang formula,two new color depth formulas,Y1 and Y2,are revised by the mathematical method basing on SCB'depth values calculated by Yang formula.Then,According to colorimetric theories,six color depth formulas named Y3 to Y8 were designed,which based on the tristimulus of neutral grey chips in Munsell Color Book,Natural Color System(NCS)and SCB.Through inspection and analysis,Y4 and Y7 show better calculation effects,hence,were named as Yang2 and Yang3 respectively.Then,the new theoretically designed formulas of Yang2 and Yang3 are compared with other five better color depth formulas,results show that: Yang 2 shares the second linearity to SCB-D with R=0.9983 and the second differentiation degree with average CV=4.74%;Yang 3 presents the highest linearity with R=0.9997 and the thirdCV 5.24%.Comparing to Yang's lowest linearity(R=0.9757)and smallest CV value(average 3.49%),Yang2 and Yang3 can be regarded as successful revisions.Also,three Yang formulas are more better for different hue and chroma of SCB.Therefore,according to the equations and calculation effects of Yang formula,Yang2 formula and Yang3 formula,these three formulas are merged into Yangn formula,n=1,2 or 3.Users can choose n' number freely according to the characteristics of the samples.