Robust Color Extrapolation with Median Matrices

Abstract

Color extrapolation is the estimation of color coordinates or transforms for values that lie beyond the sampled colors or training data. For example given a chart of measured color values and a digital image of that chart it is useful to be able to extrapolate values that are beyond the color samples provided by the chart. One option is to use linear multivariate regression based on a sampling of nearby points. This will result in a matrix transform which can be used for extrapolation. This abstract proposes the derivation of a median matrix based on a sampling of nearby points. That is given random triplets of points a closed form inverse of the first order polynomials is used to directly compute matrix elements. The final matrix is determined by the median of the individual elements. The median matrix extrapolation is shown to be more accurate than conventional multivariate regression, more robust to noise, does not require linear algebra, and can potentially be applied to streaming data.