

COLOR
SCIENCE
Our work in different issues of color science has been motivated by the development of Colorlab (a comprehensive color processing toolbox for Matlab). Specifically, the computational implementation of the standard tristimulus colorimetry and the advanced color appearance models as described in Faichild's excellent book [Color Appearance Models, Addison Wesley 98] has given us a deep understanding of color vision problems that allowed us to give alternative solutions in Color Constancy, Color Perception in Dichromats, Physiological Color Representation Spaces, or CRT calibration procedures. Color Constancy [Martínez96, Martínez97] The human visual system assigns constant chromatic attributes to objects in spite of the alterations in spectral distribution of the illuminant or the spatiochromatic arrangement of the visual field. This visual capacity is called colour constancy. An example of this is shown below: Artificial vision systems that operate by using the (linear) tristimulus colorimetry do not have this ability, so they give rise to significant chromatic errors when operating outdoors. As an example, figure (a) shows the change of the chromatic coordinates of a set of Munsell samples when changing the illuminant (from CIE C to CIE A). According to the retinex theory, in this work we have implemented different versions of algorithms for colour constancy [Martínez96, Martínez97]. We proposed new nonlinear colour descriptors for a stimulus, practically invariant to the spectral change of the illuminant. Not surprisingly, the proposed descriptors are based in normalization of the tristimulus values by the tristimulus values of the surroundings as in other color appearance models [Fairchild98] or in contrast divisive normalization models [Simoncelli01]. Finally, we check experimentally the statistical stability of these descriptors corresponding to standard colour samples against a range of standard illuminants as well as their validity rank. Figure (b) shows that the proposed descriptors are far more stable than chromatic coordinates under a variety of different illuminants.
Colorlab and the corresponding pair paradigm (see below the application to predict dichromatic perception) allows the interested reader to play with other (more standard) color appearance models to obtain color descriptions with color constancy. Simulating Dichromatic Perception: the corresponding pair procedure. [Capilla04] In the literature of color appearance [Fairchild98],
two scenes are referred as to be corresponding scenes if (despite their
physical differences, e.g. different illumination) they give rise to the
same color perception. Invertible color appearance models that incorporate
surround information can be easily used to compute corresponding scenes
by changing the values of the surround under the new illumination conditions.
U_{test} = m( T_{test},T_{surr }) When illumination conditions change, the tristimulus description of test and surround change, but the perceptual description, U, does not. This can be used to compute color descriptions with color constancy or to compute corresponding scenes by using: T_{test}' = m^{1}( m( T_{test }, T_{surr }) , T_{surr}' ) In our work on
dichromats perception simulation [Capilla04]
we adapt the above corresponding pair ideas to the case of observers with
different observation conditions: normals and dichromats, but experiencing
the same color perception.
S = m^{1}( m( T_{ }, p'_{ }) , p ) The analytical form highlights the requisites
that a color vision model must verify for this procedure to be used. To
show the capabilities of the method, we apply the algorithm to different
color vision models that verify such requisites. This algorithm avoids
the need to introduce empirical information alien to the color model used,
as was the case with previous methods. The relative simplicity of the procedure
and its generality makes the prediction of dichromatic color appearance
an additional test of the validity of color vision models. In the example
below, we show how different dichromats see the Picasso's Dora Maar:
In these review works [Capilla98, Capilla02], we analyse and compare several linear and nonlinear colour representation spaces at different physiological levels, show the relationships between spaces and discuss the mathematical properties they should exhibit. At the photoreceptor level we examine the cone excitation and cone contrast spaces. We discuss the secondstage spaces, usually known as ATDspaces, paying particular attention to Boynton's space and including a nonlinear space, the opponent modulation space. In addition, we approach thirdstage transformations, which might take place at the cortical level. Finally, we analyse a perceptual ATDtype space, discussing how it might be derived as a thirdstage transformation of an LGNbased ATDspace. In this book chapter [Malo02]
(in spanish!) we analyze the general problem of color reproduction. However,
we restrict ourselves to the solution in CRT monitors. Appropriate references
of the mathematical techniques required to solve the problem are given:
fitting techniques, solution of nonlinear equations and multidimensional
interpolation.


