The weighted principal component analysis technique is employed for reconstruction of reflectance spectra of surface colors from the related tristimulus values. A dynamic eigenvector subspace based on applying certain weights to reflectance data of Munsell color chips has been formed for each particular sample and the color difference value between the target, and Munsell dataset is chosen as a criterion for determination of weighting factors. Implementation of this method enables one to increase the influence of samples which are closer to target on extracted principal eigenvectors and subsequently diminish the effect of those samples which benefit from higher amount of color difference. The performance of the suggested method is evaluated in spectral reflectance reconstruction of three different collections of colored samples by the use of the first three Munsell bases. The resulting spectra show considerable improvements in terms of root mean square error between the actual and reconstructed reflectance curves as well as CIELAB color difference under illuminant A in comparison to those obtained from the standard PCA method.
Most of spectral estimation methods are based on improving the learning-based procedures which mainly modify the training sets used by the basic methods. In this article, a new method is developed for analyzing of superiority of these modified processes to the basic methods in terms of normality of datasets. Hence, two qualitative terms, named generality and similarity are introduced to interpret the recovery achievements of different databases and their roles as training and testing sets. Also, a simple technique based on dataset modification of pseudo-inverse method is introduced for the recovery of reflectance spectra of samples from their corresponding colorimetric data. The method modifies the training dataset according to the color specifications of test sample. In fact, different weighting matrices are employed as dynamic modifiers to improve the pseudo-inverse estimation as a simple recovery method. The employed datasets are examined in the self as well as cross test conditions and the results are spectrally and colorimetrically evaluated. The root mean square errors between the reconstructed and actual spectra along with the corresponding color difference values under different illuminants decrease by employing the suggested modification method in comparison to classical pseudo-inverse technique as well as the recently improved version named optimized adaptive Wiener method.
A new matching strategy based on the equalization of the first three principal component coordinates of sample and target in a 3D eigenvector space is stated. Two series of databases including 1269 specimens of Munsell Color Book and a virtual sample population of textile materials were selected. Their first three basis functions were extracted and considered as axes of eigenvector space. The principal component coordinates of two different collections of textile samples were determined in these spaces and considered as matching criteria. The performance of the proposed algorithm is evaluated by the color difference values under different light sources as well as the root mean square differences of reflectance curves. Results indicate some types of improvements in comparison with previous algorithms in terms of spectral as well as colorimetric accuracy.
This paper describes the representation of the total radiance factor of fluorescent whitening agents by up to three basis components. Applying the dimensionality reduction technique to the total radiance factor of 84 cotton samples treated with different fluorescent whitening agents, it was possible to reconstruct the spectral behavior of specimens by using a very small number of basis functions, accurately. In order to study the properties of the basis function, a three-dimensional Euclidean spectral space was implemented to represent the samples. The orientation of the samples that confirmed the whiteness index limitations of CIE1982 were along a line in this space, as expected from a set of white specimens. The perfect correlation was also found between the CIE1982 whiteness index, W, and the first derived principal component coordinates of the samples.
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