Improving the Hawkyard method for generating reflectance functions

Reconstruction of reflectance data by modification of Berns' Gaussian method

“…The Hawkyard's method was recently formulated by Wang and his coworkers 10 by rearranging of formulae into matrixes and vectors and keeping the main structure of the system. It was claimed that the computation time of revised method is faster and the confirmation of the convergence of system toward the suitable reflectance val-ues is more predictable.…”

“…1,[4][5][6][7][8][9][10] In this section, the most customary methods i.e., principal component analysis (PCA) technique, Hawkyard's iterative as well as typical Berns' methods are briefly reviewed. Finally, the new methods for the recovery of reflectance curves which have been derived from Berns' method are presented.…”

“…Many mathematical techniques such as simplex method, genetic algorithm, simulated annealing, application of subtractive and additive primaries, neural networks, and principal component analysis technique have been introduced for extracting reflectance data from the relevant color coordinates. 1,[4][5][6][7][8][9][10] In this article, the Berns classical method for reconstruction of reflectance data, 6 which benefits from exceptional simplicity has been modified by using different types of primaries. Firstly, the Gaussian red primary has been changed to sigmoidal one for better simulation of the reflectance curve of natural objects in the red parts of visual spectrum.…”

Effect of classification by competitive neural network on reconstruction of reflectance spectra using principal component analysis

“…However, this representation is affected by several parameters such as the illuminant, observer and metameric issues and imaging sensors . Therefore, the most informative and complete way to characterize a color is to give its reflectance spectrum, which is defined as the ratio of the reflected radiant flux to the incident flux under a specific condition …”

“…The transformation from spectral reflectance to colorimetric coordinates is many‐to‐one and therefore colorimetric data for objects cannot be unambiguously transformed back to spectral reflectance . Thus, different methods such as simulated annealing, simplex method, neural networks, application of subtractive and additive Gaussian primaries, linear methods, the Hawkyard method, the improved Hawkyard method, genetic algorithms, matrix R method, Principal Component Analysis (PCA), nonnegative matrix factorization, Independent Component Analysis, the lookup‐table method, and local linear interpolation method have been developed to extraction the reflectance spectrum from their corresponding colorimetric data …”