Representation of natural reflectance spectra by auto-associative neural network

The representation of spectral reflectance data by linear systems has been extensively studied [1-3] and it has been shown that colour information can be accurately represented by relatively few, although certainly more than three, parameters. In contrast Usui, Nakauchi and Nakano [4] have suggested that a non-linear system such as an auto-associative neural network can allow surface spectral reflectance data to be encoded by, and subsequently recovered from, just three parameters. We have repeated the analysis by Usui et al. using a set of 1269 Munsell reflectance spectra and have considered the representation of colour signals resulting from the spectral energy distributions of the Munsell surfaces viewed under D65 illumination. A five-layer wine-glass-shaped auto-associative neural network was used to encode and subsequently decode both reflectance spectra and colour signals. The middle layer of the neural network contained between 2 and 6 units so that the network was constrained to find efficient representations. Colour difference errors of reconstruction reduced with increasing number of hidden units as expected on the basis of theoretical considerations.
Errors were smaller for networks trained with reflectance data rather than with colour signals derived from D65 illumination. Colour signals for surfaces viewed under D65 illumination are less constrained than the spectral reflectances of surfaces themselves. Spectral properties of light sources must be taken into account in computations of sampling rates required for recovery of colour signals and the subsequent recovery of surface reflectance spectra.