CIELab of the Macbeth standard calculated from the Hyperspectral Cube  

CIELab or CIE L*a*b * is a color space specified by CIE (International Commission on Illumination). There are  three coordinates in this color space. L represents the lightness of the color where L = 0 is black and L = 100 is diffuse white, a represents the position between red/magenta and green, and b represents position between yellow and blue. Different metrics are used to measure the distance between colors to give a numerical representation of perceived difference in color. The easiest distance to implement is the Euclidean distance in the Lab vector space. Distance values smaller  than 1 are considered to be not perceptible by humans and color differences perceptible through close observation have higher values dependent on the observer ability and experience.

In our application we have extracted  the average reflectance spectra from the HyperCube of the MacBeth standard illuminated with a xeno lamp and normalized with respect to a normalized white tile. XYZ and Lab are then calculated with the algorithm described in CIE publication CIE 15:2004 [1]. In Fig 1 we present the table with the calculated Lab value of our Macbeth ColorChecker for the lamp D50 with 2° compared with the reference values available on internet, for example in the site of X-rite [2].

In the last but one column we report the values of DEoo where green are the values smaller than 4, orange the values between 4 and 8 and red the values bigger than 8. We can see that in the column some colors have important distances values, we believe that this is due to the non uniformity in intensity of the xeno light source.  We report also the Euclidean distance in the subspace a,b that is reported in the last column of the table 1.

[1] CIE 15:2014

[2] http://xritephoto.com/ph_product_overview.aspx?ID=1192&Action=Support&SupportID=5884&catid=28

Table 1, The table contains the reference Lab value for each color square for the lamp D50 at 2° from [2] and the Lab values calculated from the spectra of the HyperCube with the CIE algorithm. DEoo is the Euclidean distance in Lab space, dab is the Euclidean distance in the subspace a-b.   The three colors represent the magnitude of the distance, green the closest.

In the following Figure we present on the RGB of our Macbeth standard rendered with the D50 lamp. On the right the table with the values and the colors associated to the value of  DEoo.