Perceptual Limits on Low-Dimensional Models of Munsell Reflectance Spectra

Abstract

Abstract. Some experimental and theoretical approaches to surface-colour perception depend on approximating surface reflectance spectra by low-dimensional models. In the psychophysical experiment reported here, observers had to discriminate between patterns of Munsell surfaces and their spectral approximations under either the same or different illuminants. The approximations were produced by principal component analysis, by independent component analysis, and by artificial neural networks trained with a supervised-learning rule. In all experimental conditions, observers required, on average, at least 5 basis functions for discrimination performance to be at chance, thus placing a lower limit on the dimensionality of models of Munsell reflectance spectra.

Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes

“…It seems that PCA is not itself special, in that experiments like those reported here but with Mondrian arrays of Munsell surfaces 17 have shown that there is little difference in the minimum number of components whether determined by PCA, by independent component analysis, or by artificial neural networks, although other methods of obtaining basis functions, such as nonnegative matrix factorization, 29 may give different results. More important, as Vrhel et al 5 have emphasized, PCA does not minimize the color difference ⌬E ab * .…”

“…14 Curiously, all these estimates of the minimum number of basis functions needed to represent reflection spectra were obtained by theoretical methods. Apart from studies by Oxtoby and co-workers with Munsell surfaces, [15][16][17] the question of how many basis functions are actually required seems not to have been addressed empirically.…”

Perception, Color, and Realism

“…6, such normative issues are just the sort of thing that philosophers are encouraged to take up. David Foster and his colleagues have challenged traditional approaches to evaluating the adequacy of low-dimensional models of surface reflectance; see Nascimento et al (2005) and Oxtoby and Foster (2005), which in what follows will be referred to together as ' 'Foster et al'' They contend that too much emphasis has been placed on theoretical considerations when determining how few dimensions a linear model needs to satisfactorily approximate reflectance spectra. For example, variance accounted for (VAF) has ''overwhelmingly'' been the measure of choice for evaluating linear models (Maloney 2003, p. 289), with the usual criterion of adequate approximation being to account for [99% of the total variance.…”

Reflectance spectra of Munsell standard chips and their appearance

“…10,11 Since then, quite a few related articles have appeared in this journal and in others. [13][14][15][16] The second is multiple regressions of r j (k) to underlying physiological processes. [17][18][19] Some new results in these two lines will be described below.…”