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CATS                                89

             6.2.2  CMCCAT97

             The CMCCAT97 CAT (Luo and Hunt, 1998b) is a modified version of the
             Bradford (BFD) CAT (Lam, 1985) and is used in the CIECAM97s CAM. It is
             essentially based on the form of Equation (6.2) where M CAT  ¼ M BFD , and
                             0.8951   0.2664   0.1614
                          2                           3
                            0.7502    1.7135    0.0367 .
                          4                           5
                  M BFD ¼
                             0.0389   0.0685    1.0296
             However, in CMCCAT97 the transformation to RGB space is performed upon
             the tristimulus values normalized by the Y value of the sample. Thus,
                  R ¼ 0.8951X/Y þ 0.2664Y/Y   0.1614Z/Y,
                  G ¼ 0.7502X/Y þ 1.7135Y/Y þ 0.0367Z/Y,                         ð6:6Þ
                  B ¼ 0:0389X/Y   0:0685Y/Y þ 1:0296Z/Y,

             where X, Y and Z are the tristimulus values of the sample under the test
             illuminant.
               Note that this stage is equivalent to multiplying the 361 column matrix of
             normalized tristimulus values by the 363 matrix M BFD . The XYZ values of the
             adopted test and reference illuminants must also be subject to the generic form of
             Equations (6.6) to yield R WT , G WT , B WT , and R WR , G WR , B WR , respectively. To
             avoid confusion, the equations for these transforms are given in full by
             Equations (6.7) and (6.8),

                  R WT ¼ 0:8951X WT =Y WT þ 0:2664Y WT =Y WT   0:1614Z WT =Y WT ,
                  G WT ¼ 0:7502X WT =Y WT þ 1:7135Y WT =Y WT þ 0:0367Z WT =Y WT ,  ð6:7Þ
                  B WT ¼ 0:0389X WT =Y WT   0:0685Y WT =Y WT þ 1:0296Z WT =Y WT ,
             and

                  R WR ¼ 0:8951X WR =Y WR þ 0:2664Y WR =Y WR   0:1614Z WR =Y WR ,
                  G WR ¼ 0:7502X WR =Y WR þ 1:7135Y WR =Y WR þ 0:0367Z WR =Y WR ,  ð6:8Þ
                  B WR ¼ 0:0389X WR =Y WR   0:0685Y WR =Y WR þ 1:0296Z WR =Y WR ,
             where X WT , Y WT , Z WT  and X WR , Y WR , Z WR  are the tristimulus values of the
             adopted test and reference illuminants, respectively.
               CMCCAT97 incorporates the degree of adaptation D and this is computed
             using Equation (6.9),
                                    1=4   2
                  D ¼ F   F=½1 þ 2ðL A  Þþ L =300Š,                              ð6:9Þ
                                          A
             where F ¼ 1 for surfaces seen under typical viewing conditions, F ¼ 0.9 for
                                                                                 2
             surfaces seen under dim or dark conditions and L is the luminance (cd/m )of
                                                          A
             the adapting test field. The degree of adaptation D is then used with the ratios of
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