Adaptive non-negative bases for reconstruction of spectral data from colorimetric information |
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Authors: | Seyed Hossein Amirshahi Seyed Ali Amirhahi |
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Institution: | 1. Department of Textile Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, 15914, Iran 2. CIMET Erasmus Mundus Consortium, University Jean Monnet, Bat. B, 18 rue Professeur Lauras, 42000, Saint-Etienne, France
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Abstract: | The positive basis functions of the reflectance spectra of Munsell color chips are extracted by using the classical nonnegative
matrix factorization method. Different numbers of basis, i.e., 3 to 5, are determined and used as projection spaces. The spectral
reflectances of samples are defined in the desired compact spectral spaces and the performances of the spaces are evaluated
through the cost of the “lost data” by computing of the root mean square error between the actual and the reconstructed spectra
as well as the corresponding color difference values under different viewing conditions. The method is also compared with
the most welcomed technique, i.e., principal component analyzing, and its priority is shown to some extent in the three dimensional
space. To show the importance of the spectral behaviors of samples in the dataset on the extracted basis and consequently
the error of the spectral reconstruction trial, the adaptive non-negative matrix factorization method is introduced and examined
in the reconstruction of spectral data from the colorimetric tristimulus values. The suggested method weights the samples
in the database proportional to the colorimetric differences between the specimens in the dataset and the sample whose spectral
has been aimed, prior to the extraction of all positive bases. The root mean square errors between the actual and the reconstructed
spectra as well as the metamerism indices under A and F11 illuminants are calculated and the results show considerable improvement
over the classic non-negative matrix factorization method as well as the principal component analyzing technique. |
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