Is there a better non-parametric alternative to von Kries scaling?

The effect on cone excitations of a change in illuminant on a scene may be predicted by von Kries scaling, but these predictions are not perfectly accurate. Here, a non-parametric method was used instead, but which preserved the principle of independence of activity in cone or cone-opponent mechanisms. Performance was evaluated over samples taken from 50 hyperspectral images of vegetated and non-vegetated natural scenes under large changes in daylight illuminant. Taking due account of differences in degrees of freedom, the non-parametric model gave significantly better predictions than von Kries scaling of cone or cone-opponent activity. Introduction Von Kries scaling refers generally to the idea that the spectral effects of the prevailing light on the sensitivity of each class of cone receptor of the eye depend only on activity in that cone class [1, 2]. Although originally conceived for the adaptation of the eye to stimulus lights, many models of colour constancy, including Land’s Retinex models [3, 4], have assumed that von Kries scaling applies also to cone activity in response to lights reflected from surfaces. Thus, if l, m, and s are the excitations of long-, medium-, and short-wavelength-sensitive cones for light reflected from a surface under one illuminant and l′, m′, and s′ are the corresponding excitations for another illuminant, then von Kries scaling models their relationship by a simple multiplication; that is, l′ = kL l, m′ = kM m, (1) s′ = kS s, where the coefficients kL,kM,kS are constants, which are dependent only on activity in the corresponding cone class, and which may be estimated from the data by ordinary least squares or from the ratio of excitations of a spectrally neutral surface. [The error terms representing random variation, which would normally be included on the right-hand side of (1), have been omitted for clarity.] It is emphasized that the statement (1) is not about chromatic adaptation (e.g. [5, 6, 7]) but about how activity in a given cone class—or sensor type—varies with the spectrum of the illumination on a scene [8, 9]. In principle, the latter provides a recipe for the former. Because interactions between different cone classes are not involved in (1), this form of von Kries scaling is referred to as a diagonal-matrix transformation [10]. When tested in computer simulations, von Kries scaling has indeed been found to give a good description of the effects of daylight illuminant change on natural scenes [11], and also with other surfaces and illuminants [12]. The predictions are not, however, perfectly accurate. Figure 1 (left panel) shows an example of the excitations of medium-wavelength-sensitive cones for light reflected from 100 surfaces drawn randomly from a natural vegetated scene under a daylight of correlated colour temperature 4000 K plotted against the corresponding excitations for light reflected from the same surfaces under a daylight of correlated colour temperature 25000 K. Similar distributions were obtained for shortand long-wavelength-sensitive cones. The straight line is a linear regression passing through zero. Although the fit is good, there are regions where there appears to be a local bias with the data mainly on one side of the curve, as the expanded section in the right panel of Fig. 1 makes clear. Figure 2 shows the scene from which these excitations were calculated. 0 10 20 30 40 0 10 20 30 40