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`Color Science  Uniform Color Spaces (Chapter 4)1- Uniform Chromaticity Diagrams, 3- CIE Uniform Color Spaces 5- Comparing CIELAB and CIELUV Color Spaces, 7- Color Difference Equations Based on CIELAB 2- Uniform Lightness Scales (ULS), 4- Correlates Perceived Attributes 6- Converting of Color Difference,and Measurement and Calculation of Colorimetric Values (Chapter 5)1- Direct Measurement of Tristimulus values 3- General Conditions for Measurement 5- Colorimetric Values in CIELAB and CIELUV Uniform Color Spaces 2- Spectral Colorimetry4- Calculation of Colorimetric Values1 Color Science  The Most Important Drawback of CIEXYZ:  &quot;The system is not uniform!&quot; Equal distances in xy diagram do not mean equal perception for observers.  Non uniform chromaticity diagram  Colors at the two ends are perceptually same 2 Color Science  Non Uniform Chromaticity Diagram Wright experiment(pairs have same perceived difference)  Just noticeable difference   Just noticeable difference  in the wavelength of monochromatic light 3 Color Science  MacAdam's ellipses(10 times magnification)  MacAdam's ellipses show: MacAdam ellipses are far from being uniform  Small difference of chromaticity coordinates is perceptible for bluepurple colors, while a difference in chromaticity coordinates of about 10 times that is hardly perceived for the green colors Ideally the MacAdam ellipses should all be circles of same radius in the chromaticity diagram 4  Color Science  Totally the non uniformity of xy chromaticity diagram means: Such space can not be directly employed for presentation the color differences between the samplesTo change ellipses to circles Stretching the CIEXYZ system  Squeezing the CIEXYZ System  Hence Different mathematical conversions have been introduced to change CIExy to more uniform systems. Such systems are called Uniform Color System, i.e. UCS 5 Color Science  CIE 1960 UCS Diagram u= 4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 6y 6Y   v= = (- 2x + 12 y + 3) (X + 15Y + 3Z)(A linear transformation), while Y is kept And the shapes of ellipses(Chromaticity diagram)  It seems that the ellipses become a bit closer to circles! 6 Color Science  CIE 1976 UCS Diagram u = 4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 9y 9Y   = v = (- 2x + 12 y + 3) (X + 15Y + 3Z)(A linear transformation), again Y is kept And the shapes of ellipses(Chromaticity diagram) Still better but not good enough 7 Color Science  Uniform Lightness Scales (ULS) Lightness is relative brightness, so Brightness Lightness = Brightness ( White)  Lightness approximately could be expressed by &quot;Y&quot;  And non pleasant fact:  Y does not also have a uniform scale with respect to lightness Munsell Value and Y  The figure shows the non uniformity of Y 8 Color Science  Conversion of Y and VA fifth-order polynomial can estimate Y from Munsell value, V: Y = 1.2219V - 0.23111V 2 + 0.23951V3 - 0.021009V 4 + 0.0008404V59 Color Science  Weber's Law I = constant   IThe equation is hold when a small change &quot; I &quot; in the intensity &quot; I &quot; of a stimulus is just noticeable  Weber law could be improved to: I S = k   IWhereS is the change in sensation and k is another constant Weber-Fechner Law I   IBy integrating from S = k I  S = k log  I   0    where I 0 is the minimum detectable stimulus value10Color Science  Weber-Fechner Law in luminance  11 Color Science  CIE Uniform Color Spaces Uniformity in the chromaticity diagram, i.e. uv and u'v' systems, Uniformity in the lightness, Now, look for the    Uniformity in 3 dimensional color space12 Color Science  There Are Several Types of UCS They could be divided to   Linear and non linear transformation of CIEXYZ system The Genealogy of such transformation 13 Color Science  The Most Welcomed UCSs are: CIE 1976 L*a*b* color space (abbreviated by CIELAB), and CIE 1976 L*u*v* color space (abbreviated by CIELUV)    Both are non linear transformation of CIEXYZ color space. (Neither them nor others satisfy perfect uniform chromaticity diagram)14 Color Science  CIE 1976 L*a*b* color space Its three-dimensional orthogonal coordinates are:  Y L* = 116 Y  n* 1   3- 163  X a = 500   X n    Y b = 200   Yn *       1 Y - Y  n  Z - Z  n       13    1313   (Abbreviated by CIELAB)     841  X =  108  X   n     841  Y =  108  Y   n     841  Z =  108  Z   n    16 +  116   16 +  116   16 +  116 Dark colors in CIEL*a*b* color spaceWhen:X Y Z  0.008856 ,  0.008856 and  0.008856 (dark samples), then  Xn Yn Zn X f X  n        Y  L* = 116 f   Y  - 16   n   X   Y - f a * = 500 f  Y    n   Xn   b * = 200   Y f Y  n  -    Z f Z  n While  Y f Y  n  Z f Z  n WhereXYZ: The tristimulus values of object XnYnZn: The tristimulus values of source,  Hence, system is normalized to the employed light source 15 Color Science  CIELAB (CIEL*a*b*) View  Two important features of CIELAB system Color opponencies,  . Simple color adaptation16 Color Science  CIE 1976 L*u*v* color space Its three-dimensional orthogonal coordinates are:  Y  3 L = 116  Y  - 16   n u * = 13L* (u  - u n )*1v = 13L (v - vn )* * While,u =4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 9y 9Y   = v = (- 2x + 12 y + 3) (X + 15Y + 3Z)(Abbreviated by CIELUV) 17 Color Science  CIELAB Color System Is Usually Used for Surface color while CIELUV Color System Is More Practical in Colored lights, such as TVs, monitors, illuminations 18 Color Science  Color Difference Formula (CIELAB) The most generally accepted color difference formula (also the base for several new color difference formulas) E* ab= (L *) + (a *) + (b *)2 2{2 1/ 2} L* = L* - L*2 1where, * a * = a 1 - a * 2b =** b1- b* 2 Color Difference Formula (CIELUV) E* uv= (L *) + (u *) + (v *)2 2{2 1/ 2} where L* = L* - L*2 1* u * = u1 - u * 2v =** v1- v* 2 19 Color Science  CIE 1976 LightnessY L* = 116  Y   n1/ 3- 16 for non dark samplesY  841  X    903.3  L* = 116   Y  for dark samples    108  X n   n20 Color Science  CIELAB Metric Chroma, C* Metric distance from origin in a*b* chromaticity diagram:  C = a* ab{(* 2) + (b ) }* 212 CIELAB Hue Angle, ho   b*  h ab = tan -1  *  a   21 Color Science  In Three Dimensional Space  22 Color Science  CIELAB Metric Hue, H* H = 2 C* ab(* ab ,1C* ab , 2)12 h  sin  ab     2 * If E ab would be available:H = E* ab{(* 2 ab) - (L ) - (C ) }  * 2 * 2 ab 1 2Its sign is positive if hoab is positive and negative if hoab is negative 23 Color Science  Color Difference Formulas CIELAB color difference formula can be written asE = L*{(* 2) + (C ) + (H ) }* 2 * 212, too. * * However, the values of L , C and H* are not equal for normalobservers. They could be weighted, by different weights:  L*  2  C*  2  H *  2   *    +  + E =          l   c   h    1 2 24 Color Science  Small Color Difference Formulae Based on CIELAABDifferent weights have been applied to improve the CIELAB color difference formula. The general form of such formulas is:  L* 2  C* 2  H* 2  ab ab E =  k S  +k S  +k S         L L   C C   H C    1/ 2 This type of formula could be applied when two sample have small color difference value. 25 Color Science  CIE94 Color Difference Formula The values of constants in this formula are: SL = 1  SC = 1 + 0.045C* , and, abSH = 1 + 0.015C* ab Where the values ofKL , KCandKHdepend to the nature of samples as wellas the types of evaluation, i.e. perceptibility or acceptability criteria.26 Color Science  Uniformity of CIELAB and CIELUV Color Spaces Both are absolutely better than CIEXYZ color space. The uniformity of them were approved by plotting the MacAdam ellipses in a*b* as well as u*v* chromaticity diagrams. Uniformity of ellipses in a*b* diagram  Uniformity of ellipses in u*v* diagram  27  Color Science  Uniformity of Munsell Chips in a*b* Diagram  Munsell samples of value 5Uniformity of Munsell Chips in u*v* Diagram  Munsell samples of value 528 Color Science  Measurement and Calculation of Colorimetric ValuesDefinition of color measurement,Measurement is possible:Directly by Colorimeters, Indirectly by Spectrophotometers and SpectroradiometersTo measure:Tristimulus values, chromaticity coordinates, ...29 Color Science  Direct Measurement of Tristimulus ValuesLuther condition?Luther condition can be provided by: 1- Template method 2- Optical filter methodIndirect MeasurementSpectral colorimetry30 Color Science  Template MethodUsing 3 different templates placing in spectrum31 Color Science  Optical Filter MethodDuplication of color matching functions Serial arrangement Parallel Arrangement32 Color Science  Spectral ColorimetrySpectrophotometers for indirect measurement33 Color Science  Radiance Factor, Reflectance Factor and Reflectance34 Color Science  Geometrical Conditions for Measurement35 Color Science  Standard CIE Geometrical Condition for Measurement of Reflecting Objects36 Color Science  Standard CIE Geometrical Condition for Measurement of Transmitting Objects37 Color Science  Calculation of Colorimetric ValuesXYZ Tristimulus values Dominant wavelength and excitation purity CIELAB and CIELUV tristimulus values Metric chroma (C*), hue angle (ho) and Metric Hue (H*) Color difference value38 `

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