Reducing The Number of Calibration Surfaces

Calibration charts are used in colour imaging to determine color correction transforms and for spectrally characterising imaging devices. Traditionally, quite complex charts have evolved as it was reasoned that the more reflectances in a chart the more the chart could represent all other reflectances. However, a chart with many reflectances is both expensive, difficult and tedious to use. The difficulty lies in assuming constant lighting conditions over the whole chart and the tedium appears when the chart must be measured using a spectrophotometer. To circumvent these problems researchers have sought methods to find smaller sets of reflectances which, in some sense, represent larger reflectance sets. In this paper we develop an iterative selection procedure where we select individual reflectances from a colour chart. The first is chosen so it best accounts for the majority of the spectral variance. The next best accounts for the variance that is left. In general the ith selected chart reflectance best accounts for the variance among reflectances (given that i i 1 reflectances are already selected). We show that this procedure is weakly optimal and as such compares with prior art which chooses reflectances using simple heuristics. The new method is also much faster than algorithms that are built on stronger optimality conditions. Experiments demonstrate that our new method represents a reasonable compromise between fast (and feasible) reflectance selection and the optimality of the chosen set.