The following abstract is taken from the dissertation submitted by Vien in partial fulfilment for the MSc in Colour Imaging (2000) at University of Derby.
ABSTRACT
The reflectance spectra for a set of natural surfaces collected in Derby have been shown to be highly constrained. Statistical analyses have been conducted to analyse the smoothness of the spectra to confirm that the natural surface reflectance spectra are band-limited functions with frequency limit of approximately 0.017 cycles/nm. These data are having good agreement with those in the Keele region (Westland et al., 2000) and at Trieste University, hence implicate the general properties of the physical world.
The band limits of nine common illuminants have been estimated and found to be 0.007 to 0.0499 cycles/nm depending on the smoothness of the illuminant power distributions. Band limits for colour signals have been estimated under these illuminants; they are found to be approximately the additive band limits of reflectance spectra and illuminant (Maloney, 1986). These constraints may allow the effect of natural and artificial light sources on the representation of colour signals by imaging systems to be resolved. The statistical analyses contribute to the fundamental properties and constraints of natural surfaces and hence support the notion of regularities in the natural world.
Although the natural surfaces have been shown to be smooth functions as a function of wavelength, they are not sufficiently constrained to allow the computational recovery of reflectance spectra by an imaging system (human or machine) with just three sensors. The practical issue upon the efficient storage of reflection data is suggested based on the experimental data having reconstruction errors less than 0.8 CIELAB colour difference unit using six principal components. The applications of using three to six principal components for reconstruction of sample spectra is then extended to the notion of efficient recovery of reflectance data by multispectral and hyperspectral imaging systems that sample colour signals.
In practice, imaging systems that sample colour signals using typically three sensors would only obtain a smoothed version of colour signals. Statistical results concerning both smoothed colour signals and smoothed illuminant power distributions show that the recovery of reflectance data provide CIELAB colour difference under each nine common illuminants are approximately 0.6 unit. Moreover, smoother illuminant power distributions are found to achieve smaller reconstruction errors and this property should be carefully considered when it is necessary to recover the highest accuracy of surface spectral reflectance. Disregarding to the empirical approach of efficient recovery of reflectance data, the notion of spectral modulation transfer function (sMTF) which considers the modulation of a imaging system across the spectral frequency spectrum would possibly be a better solution to recover real colour signal and thus original surface reflectance. However, regarding to some uncertainties upon the approach to achieve sMTF, further analyses of colour statistics are required.
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Dissertation Abstract
Natural Surface Images