Nonlinear principal component analysis (NLPCA) was used for compression and reconstruction of the total radiance factors (TRFs) of fluorescent samples. The spectral dataset included a total of 358 fluorescent reflectance spectra in the visible range of the spectrum. Spectral data compression was followed by extracting the parameterized nonlinear manifolds using the NLPCA technique. To compare the performance of NLPCA-based compression with the linear method, the orthonormal feature vectors of the dataset were also extracted by the linear PCA. The spectral performance of NLPCA and PCA-based compression approaches was assessed by the root mean square error and the goodness-fitting coefficient between the real and the reconstructed spectra. The percentages of feasible spectra by each method, i.e., those with nonnegative TRFs, were also reported as other criteria for the evaluation of methods. Furthermore, the colorimetric performance of methods were appraised by the measuring the CIELAB 1976 color difference values between the actual and reconstructed spectra under illuminants D65 and A and the 1964 standard observer. The NLPCA-based compression method performed significantly better than the standard PCA-based technique particularly in the lower dimensional spaces of the spectral radiance factors of fluorescent colors.
The handmade Persian carpet is famous worldwide not only for its elegant design and artistic structure, but also for its brilliant color harmony and incomparable raw materials. Various natural dyes accompanied by different mordants are used on various woolen yarns to obtain a wide range of unrepeatable shades for carpet. In this article, as a first step, the diversity of the undyed woolen yarns used in Persian carpets was statistically investigated by implementation of the Principle Component Analysis. Then the second derivative of Kubelka-Munk function of samples dyed with madder was considered to reach a pattern for identifying madder. The results show that, although the spectral reflectance of different selected woolen yarns has at least 3 dimensions, all derivative curves are qualitatively very similar with the same minimum and maximum peaks at 510 and 605 nm, respectively. The findings are confirmed when various types of madder were used in the dyeing process. As a result, it is shown that the nondestructive derivative spectrophotometry is able to identify madder on alum mordanted woolen yarns used in Persian carpets and to eliminate the effect of substrate. It is a useful technique for preservation, conservation, and dissemination of the Persian carpet. K E Y W O R D S derivative spectrophotometry, Kubelka-Munk function, madder, Persian carpet, woolen yarn 238 | V C 2017 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/col Color Res Appl. 2018;43:238-246.
In this work, the extraction of significant features of Persian carpet patterns was studied. Four aesthetic related features were extracted for a collection of Persian carpet images. To this purpose, a set of 134 color images of three different categories of traditional Persian designs, named "Afshan," "Lachak Toranj," and "Torkaman" were collected. At first, the PHOG (Pyramid of Histogram of Orientation Gradients) measure was derived for all patterns to calculate complexity, anisotropy, self-similarity, and Birkhoff-like features. Based on the results, anisotropy and Birkhoff-like features significantly categorize three carpet designs. According to the results, the combination of anisotropy and Birkhofflike features increases the accuracy of classification of samples to 97%.
The reflectance factors of the polyamide rods which were dyed with different concentrations of three commercial yellow, red, and blue disperse dyes are recovered from their RGB data obtained from scanning of the cross sections of rods with the desktop scanner. The RGB data are converted to device independent XYZ tristimulus values by simple polynomial regression technique. Then, the principal component analysis (abbreviated by PCA) technique is employed for the recovery of reflectance spectra from the tristimulus values by using three different datasets, i.e. using the reflectance factors of Munsell chips, MacBeth ColorChecker SG, and a dynamic dataset prepared from the reflectance factors of dyed rods samples. The first three eigenvectors of each dataset are extracted and employed in the reconstruction process of spectral reflectance from XYZ colorimetric data. Finally, the well known Kubelka-Munk function is implemented for estimation of concentration of dye from the recovered spectral reflectance. The root mean square (RMS) errors between the reconstructed and the actual reflectance data over the visible spectrum are calculated. According to results, the RMS errors for the reflectance recovery are within the acceptable range. Error of estimation of dye concentration in the rods varies for different hues as well as concentrations and changes with applied dataset.
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