3.5. Evaluation of camera performance

As mentioned earlier, humans might be able to discriminate colours which are indiscriminable for colour camera and vice versa. Those colours which are indiscriminable under one condition but discriminable under another are called metameric colours. Metamerism can be used to evaluate the camera’s ability to handle small colour difference measurements (Paper I).

For human vision, the metamerism of samples can be evaluated using metamerism indices or colour difference formulae. CIE 1976 Lab colour difference is widely used in industry (Pierce & Marcus 1994) and implemented as a Euclidean distance between CIE Lab parameters of two samples:

Equation 8.

where ΔE_ab = the CIE 1976 Lab colour difference,

L = lightness,

a = a coordinate indicating location of colour in a greenness-redness axis, and

b = b coordinate indicating location of colour in a blueness-yellowness axis.

For evaluating metamerism, the following general metamerism indices are often used: Bridgeman’s index BMAN (Bridgeman & Hudson 1969 according to Choudhury & Chatterjee 1996),

Equation 9.

and that of Nimeroff et al. (N+Y) (Nimeroff & Yurow 1965):

Equation 10.

where x(λ ), y(λ ) and z(λ ) = the CIE colour-matching functions for the CIE 1964 Supplementary Standard Colorimetric Observer, and

ρ(λ ) = spectral reflectance of the sample.

It is interesting to note that these two metamerism indices do not include illumination information in the evaluation. For colour cameras, the Minkowski’s distance formula can be used to evaluate the colour difference ΔE_RGB in the camera’s RGB colour space (Novak & Shafer 1992):

Equation 11.

where n = power.

Typical values of n are 1 (the sum of absolute difference in values in each band or city block distance), 2 (Euclidean distance) and ∞ (chessboard distance). However, this formula induces a bias against bright colours but it is used because it is the best available.

For the simulated experiments, the sample spectra were obtained from a NCS colour block (NCS 1989) (Natural Colour System block with 1526 samples and measured by a Minolta CM-2002 spectrophotometer), the illuminants were A, D65, and F11, the camera selected was a Temet TVI camera (TVI 1995) with 2 options (8 and 12 bit). For human vision modelling, the CIE 1964 Supplementary Standard Colorimetric observer was used.

In the first experiments, the predictions for human vision are evaluated. Table 3 displays the number of samples within a certain distance range calculated from metrics presented in Eqs. 8-10. In total, there are 2327150 (1526x1525) possible sample pairs. A colour pair is defined as similar if its value for the general metameric index is in the range of 0-5, or for the CIE Lab difference formula in the range of 0-3. In many colourant industries, a sample pair with a CIE Lab difference in the range 0-1.5 is classified to be metameric (Choudhury & Chatterjee 1996 and Choudhury & Chatterjee 1992) and in the range 1.5-3 similar colours. As can be seen from Table 3, different evaluation methods produce different predictions on the amount of sample pairs for the difference range. This leads us to an obvious conclusion that there is disagreement between these methods on asserting metamerism on sample pairs. CIE Lab formula predicts that the amount varies with prevailing illumination over the samples. For the further study, the effects of metamerism due to illumination are investigated and therefore only the CIE Lab formula is utilized.

The results in Table 4 prove that the predicted number of metameric samples is different under different illumination conditions even for human vision. Perfect colour constancy is therefore impossible even for human vision. This implies that for colour cameras, when comparing colour distribution taken under different conditions, precision is limited and robustness is needed.

The different discrimination capabilities of human and colour cameras are demonstrated in the second simulated experiments. The results are shown in Tables 5-7: some colour pairs which are predicted to be metameric or similar for human vision are not necessarily that for the TVI camera. In the Table 5, the sample pairs are arranged into subsets according to their calculated human colour space ΔE_ab values for the prevailing illuminant. For these subsets of sample pairs, their minimum (marked as min in the table), maximum (max) and average (avg) colour differences in the camera space are calculated for each illuminant case. The number of metameric pairs for the camera is shown in the rows called pairs. The subsets in the Tables 6 and 7 are constructed by using their colour difference in the camera space (ΔE_RGB). The minimum (min) and average (avg) difference values of these subsets are computed in the human colour space. The amount of sample pairs in each column is shown in the rows marked as a number. At least for ideal, noiseless colour cameras the increase in the bit number will improve discrimination capabilities: the 12-bit option produced an increased discrimination capability for those colours which are strongly metameric for human vision.