Criticism of Application of Simplex Optimization Method for Reconstruction of Reflectance Spectra from Colorimetric Data

In this article, criticisms of DuPont’s suggestion for employing of simplex method in spectral reconstruction is presented. The advantages and disadvantages of the Nelder-mead simplex method as an optimization tool in solving the underdetermined problem of reflectance reconstruction from the corresponding tristimulus values are discussed. To this aim, the performances of different objective functions, starting point, and normalization filters have been investigated on the reflectance spectra of Munsell dataset, and the optimal model has been reported. For evaluation of results, root mean squared error (RMSE), goodness fit coefficient (GFC), and CIE LAB color difference values between the actual and synthetic spectra have been reported. Results are compared to the most popular reconstruction method, i.e., principal component analysis methodology. It is observed that the most optimal condition is achieved by using the objective function, including the color difference values under three light sources and two metamerism indices, while the mean of the reflectance spectra of Munsell dataset is introduced as an initial point. Finally, the reasonable reflectance spectra have been attained by passing the results from suitable median filter. In general, it is observed that in the similar condition, using of simplex as an optimization method provides results that are less precise than those obtained by the principal component analysis methodology.

کلیدواژه ها:

Simplex ، Nelder-mead ، Reflectance reconstruction ، Median filter ، Gaussian filter ، Optimization method