Set theoretic estimation in color scanner characterization

A set theoretic approach for the spectral characterization of a color scanner is described. These devices usually employ three channels to obtain a device dependent RGB (red, green, blue) image. To display/print an image, the device dependent RGB values must be correctly transformed to the color space of the target device. To determine accurate and efficient transformations for a number of devices, knowledge of the spectral sensitivity of the scanner is essential. Direct measurement of the sensitivity requires a set of expensive narrow band reflectances and is often infeasible. Methods that estimate the spectral sensitivity based on measurements with typical reflectance samples are therefore of interest. Due to the low dimensionality of the space of object reflectance spectra, this is a highly ill-conditioned problem. As a result, conventional estimation techniques that fail to take a priori knowledge into account perform rather poorly on this problem. A set theoretic approach that incorporates available a priori knowledge into the estimation framework yields better results. Results are presented for a simulated scanner characterization problem and for an actual characterization to demonstrate the increased accuracy compared with conventional methods. © 1996 SPIE and IS&T.