samples with a low saturation. This helps to stabilise the neutral axis, and prevents an overall colour cast most noticeable in the neutral colours. It provides an eective measure to counter this eect visible in Fig. 8.7of Sect.8.2.3.
8.6 Conclusions on Adaptive Colour Transformations
In this chapter colour changes induced due to changes of light conditions were analysed. Compensating for them is a matter of nding a suitable transformation, that ideally reveals the canonical representation of the colours encountered. Of course this is impossible, and we can only achieve a more or less well suited approximation of this ideal. Already an ideal white point adaptation on an sRGB encoded image introduces an estimated error of roughly∆Eab∗ = 2[17]. We are dealing in this case with non-ideal colour shifts, which we are
trying to compensate for. Lots of computations on colour spaces are involved, so our overall error can be expected to lie beyond this threshold, no matter how accurate the determined transformation is.
For many of the colours sampled, we have been able to achieve quite good results already, just by using an ane transformation. This ane transformation was determined by means of using a 3-dimensional vector eld regression computation. This transformation requires a minimum of four source/destination pairs of colours to match the current to the refer- ence colours. An over-determination results in a more accurate determination of the ane transformation, while in the presence of measurement noise or other inaccuracies. Higher order polynomial transformation may lead to further improvements of the transformation quality, but they also demand a much higher number of input parameters. This happens at the expense of a decreased over-determination of the problem to solve. For cases with many accurately determinable colour pairings, this approach however could lead to an improved quality.
We were able to improve the range of tolerance for dierent machine vision applications regarding colour detection robustness. The robustness is still dependent both on the degree of similarity of the illuminant type (a dierent spectral power distribution), as well as the magnitude of change in illumination intensity. Further limitations are given by the dynamic range of the capturing device (camera). The usable range could be extended in all cases over the non-corrected imaging cases. Even in cases beyond adequate correction for certain colours, some results could still be made usable.
This study showed, that results tended to be best when the ane transformation was determined and applied directly on an L∗a∗b∗ based colour space. A prior application of a white point adaptation (using a Bradford transformation) proved to be rather hindering than supporting. This was revealed by a visual evaluation, even though the quantitative analysis did not expose this eect.
Overall, an ane transformation on top of an ICC based colour compensation (as deter- mined for the reference) proved to be a good compromise towards a practical adaptation of colour appearance. A high over-determination of the regression problem, as well as accurate data and not too extreme illumination shifts (of quality as well as intensity), can be handled quite well by the methods discussed.
In future enhancements, some improvements to the long term correction of static per- spectives can be expected by using alternative scene segmentations. The current strict segmentation by a regular, orthogonal grid into rectangles often yields local colour aver- ages close to the neutral axis. More distinct object segmentation approaches would provide more saturated data samples. This would promise to improve the accuracy of the ane transformation, as the samples used for the regression computation appear less clustered.
Chapter 9
ICC Prole Adaptation
In Chap.7we have discussed creating an ICC prole from characterisation data. In Chap.8 we have discussed a way of correcting for colour shifts, that have occurred in the duration of a measuring sequence after the initial characterisation. In this chapter, the focus will be on a way to update an initially generated ICC prole, so that it incorporates the determined colour correction determined in Chap.8. This way, the colour adaptation can be completely decoupled from a simple and fast colour correction, that only has to rely on an ICC prole. For further explanation see Fig. 6.1 in Chap.6, outlining a workow including a worker process dealing with the ICC colour correction, and a decoupled adaptation process that deals with the creation of adapted ICC proles suitable for the current time. The goal is to fuse the whole applicable colour transformation chain into a single ICC prole, so the worker process only deals with a single, comprehensive ICC prole transformation.
In the following, Sect. 9.1 will rst introduce what needs to be adapted within the structure of ICC proles. Sect. 9.2 outlines the transformations to be undertaken in this process to update the information embedded in the prole. The implementation of these steps are described in Sect. 9.3. Finally, Sect. 9.4 sums up results gathered with adapted ICC proles.
9.1 Correcting ICC Proles
To modify an ICC prole, we will rst have to go back to have a look into the anatomy of an ICC prole. For an input prole (correcting the colour input for example for a camera), the active ingredient of an ICC colour transformation is the AToBx tag. For a Colour Look-Up Table (CLUT) based prole as we are dealing with here the AToBx tags may only contain these three used transformation steps (see Fig. 7.1): A pre-linearisation using the A tables, a CLUT table, and a post-linearisation using the B tables. All non- participating transformation steps either because they are not allowed, or because they are not used are set to identity transformations and can be ignored (see Sect.7.1.1).
We are assuming that all these three allowed transformations (the two sets of linearisation tables and the CLUT) are used. If not, their identity transformation will result in a neutral outcome and can therefore be ignored in the following discussion of this chapter, as it will not inuence the outcome in the processing.
In order to fuse our specic colour adaptation into the input process chain, we need to manipulate the content of one or more of these three transformations in the AToBx tag for an input prole. To enable the full adaptation possible through an ane transformation derived in Chap. 8, the CLUT has to be adapted. The linearisation tables are sometimes not used, and will be left as they are, but they do need to be considered in the process of updating the AToBx tag's content.
In the case where the linearisation tables are used, theoretically re-balancing of the totality of the three transformations towards optimising the overall behaviour of the prole could be considered. However, an optimisation attempt could, if not done properly, introduce further rounding errors into the total transformation. A signicant change in the quality of the updated ICC prole cannot be expected for the small changes in the quality and quantity of the illuminant. For larger changes, the error introduced through measurement and the adaptation process (from Chap.8) is expected to be dominant, so that re-balancing the transformations is not an eective means of improving the quality.