Unsupervised filtering of color spectra

Abstract

We describe a class of unsupervised systems that extract features from databases of reflectance spectra that sample color space in a way that reflects the properties of human color perception. The systems find the internal weight coefficients by optimizing an energy function. We describe several energy functions based on second- and fourth-order statistical moments of the computed output values. We also investigate the effects of imposing boundary conditions on the filter coefficients and the performance of the resulting systems for the databases with the reflectance spectra. The experiments show that the weight matrix for one of the systems is very similar to the eigenvector system, whereas the second type of system tries to rotate the eigenvector system in such a way that the resulting filters partition the spectrum into different bands. We also show how the system can be forced to use weight vectors with positive coefficients. Systems consisting of positive weight vectors are then approximated with Gaussi n quadrature methods. In the experimental part of the paper we investigate the properties of three databases consisting of reflectance spectra. We compare the statistical structure of the different databases and investigate how these systems can be used to explore the structure of the space of reflectance spectra.