Principal Component Analysis of Spectral Data: A Contribution to the Knowledge of the Materials Constituting Works of Ar
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vuj = ý-Juj
(1)
where V = DTD andj l=._,v. The vxv matrix the contribution of the different wavelengths to each Usually, as above said, only a few components the variance. Accordingly, a nxp score matrix C can
U is the so-called weight matrix, which makes Principal Component. (the first p) are sufficient to describe most of be defined as:
39 Mat. Res. Soc. Symp. Proc. Vol. 462 @1997 Materials Research Society
(2)
C=D.U
where now the vxp matrix U is obtained by retaining the first p columns in the weights matrix. The scores are only the coordinates of the n samples in the new coordinate system. EXPERIMENT Details of the FORS technique and IS instrumentation can be found in [4,5]. A test wood panel was prepared in the laboratory as follows. A gesso-glue preparatory layer was placed on the panel; then twelve strips, parallel to each other, were spread thereon, using the tempera technique. The binding medium was egg mixed with fig latex. Four pigments were selected (cinnabar, yellow ochre, malachite and chromium oxide) to cover a large range of dominant wavelengths and three strips were prepared for each pigment (pure pigment, 5% and 10% carbon black). The actual painting investigated was the "Predella della Trinit." a tempera painted panel of 32x204 cm by Luca Signorelli of the early XVIth century, currently on exhibit in the Leonardo Room at the Uffizi Gallery in Florence. The spectral behavior of the twelve strips on the laboratory panel was investigated using the FORS technique. The spectra of the pure pigments strips are reported in Figure 1; similar spectra were obtained from the strips containing carbon black, apart from a reduced reflectance. Later, image spectroscopy measurements were performed both on the same test panel and on the Predella, using an IS system set up at our laboratory, based on a Vidicon sensor in the visible and near infrared region (400-1800 nm), together with a set of narrow-band interferential filters. We obtained a set of 29 monochromatic images, from 420 to 1550 nm, which have been submitted to statistical PCA. The reflectance value of each pixel in a given image was considered as one of the n components of the D matrix, where v =29. RESULTS AND DISCUSSION In our approach, each pixel of a region of interest in the 754x572 pixel image sequence, was considered as an independent sample having 29 values of reflectance. Our aim to detect clusters of pixels showing similar spectral behavior is certainly a difficult one. We could, for example, plot the 2-D histogram of the pixels on the plane defined by two different wavelengths X1 and k,2 and look for the couple that best separates the different pigments.
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Figure 1 - Reflectance spectra of the four pure pigments used on the test panel 40
Such a method can be effective only when few pure pigments are present in the examined image or when a priori known spectra can help in selecting the best X, and X2. However, the clustering obtained is far less effective
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