Thursday, February 23, 2012

Local optimization

I received a question about the paper Assessing color reproduction tolerances in commercial print workflow mentioned in a recent post. The interlocutor asks why I bother creating custom color scales, instead of just using the Farnsworth's 100 Munsell hues: the implementation would be much simpler.

I believe this question is a nice example of the difference between a color engineer and a color scientist. Let me explain:

To an engineer the reproduction of color images is a matter of finding a good transfer function and implementing it efficiently. The scientist's assignment is much more difficult: color is not a physical entity but an illusion occurring in our visual system. Thus, the reproduction of color images entails the creation of models that can predict illusions.

The implementation is also made difficult by the limitations of colorants—requiring gamut mapping—and the representation of real numbers as floating point numbers. Even when a device can address millions of colors, they are not all perceptually distinct. And not all colors can be represented, because the set of floating point numbers is discrete and the arithmetic is neither commutative nor associative, for example, if a, b, c, d are floating point numbers and d := a+b, then a+b+c≠c+b+a (because of normalization) and a+b+c≠d+c (because registers are wider than memory).

In the real world of cost optimization, the gamut limitations in size and discretization entail that the best color reproduction is achieved through local optimization of those colors that are important, rather than attempting a futile global optimization.

It may be a little stretched, but using the FM-100 set is like having a camera with a tiny sensor and short focal length lens where everything is sharp but a little soft, versus using a big sensor camera with the lens at full aperture and focussing only on the important regions of interest.

Maybe it is useful to note that this completely different approach by color scientists versus color engineers goes much deeper that just applying Occam's razor pluralitas non est ponenda sine neccesitate. The limited color scales are not simplifications but stronger refinements. Preferred color reproduction has a similar foundation.