RESUMO
In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both methods utilize a spherical sampling approach, but they calculate mismatch volumes in two different ways. The first method uses a linear programming optimization, while the second is a computational geometry approach based on half-space intersection. We show that under certain conditions the theoretically maximal metamer mismatch volume is significantly larger than the one approximated using a prior art method.
RESUMO
An algorithm to calculate the best global mapping from color to grayscale is presented. We assert that the best mapping minimizes the difference between the multi-channel local tensor and the tensor of the resultant mono-chromatic image. To minimize the objective function, we represent the grayscale image as a weighted sum of the RGB channels, three channels and their second-order polynomial and three channels and their root polynomial. The optimization searches for the best weights to combine the linear, polynomial, and root polynomial functions. Our results show that the optimal weights can half the root mean square difference between the color gradients and those achieved by the conventional luminance transformation. Further improvement is achieved by adding the squared and root squared channels to the solution. The improvements are also visually evident.
