Evaluating logarithmic kernel for spectral reflectance estimation-effects on model parametrization, training set size, and number of sensor spectral channels.

In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone and HKS color charts. Especially, we focus on the estimation model evaluations in case the selection of model parameters is optimized using a cross-validation technique. In experiments, it was found that the Gaussian and logarithmic kernel outperformed the linear kernel in almost all evaluation cases (training set size, response channel number) for both sets. Furthermore, the spectral and color estimation accuracies of the Gaussian and logarithmic kernel were found to be similar in several evaluation cases for real and simulated responses. However, results suggest that for a relatively small training set size, the accuracy of the logarithmic kernel can be markedly lower when compared to the Gaussian kernel. Further it was found from our data that the parameter of the logarithmic kernel could be fixed, which simplified the use of this kernel when compared with the Gaussian kernel.