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considered in the fitness function: the smoothness of the reflectance spectrum is not an issue, due to the characteristics of the linear mo<strong>del</strong> basis employed. Many different spectra can generate the same XYZ triplet. If we assume that the tristimulus values referred to different illuminants are also known, a more effective fitness function can be designed: f * * 2 * * 2 * * 2 [ L − L ) + ( a − a ) + ( b − b ) ] + δ ( R( λ)) + δ ( R( λ)) K k ( 1 input, Illk input, Illk input, Illk Illk 1 2 = ∑ = where K is the number of illuminants considered, and the other symbols are those used in equation (9). 5. Experiments and Results Different data sets of reflectance functions have been used for benchmarking: the Macbeth ColorChecker Chart, the whole Munsell Atlas 14, a set of 120 Dupont paint chips 15 and a set of 1000 silk color samples 16. The following experiments were performed. For each dataset, given R(λ) we computed the tristimulus values for three illuminants: D65, A, and F2. Then, for each type of basis set, we estimated the weights of equation (4) by means of a genetic algorithm using the fitness function described in (10). We conducted three experiments for each basis set and for each dataset: one considering only the D65 illuminant, a second considering the D65 and the A illuminants, and a third considering all three illuminants (D65, A and F2). The results for the different basis sets are described in Section 3. We computed four basis sets by applying Principal Component Analysis to the datasets used for benchmarking. We then estimated the reflectance spectra for each dataset, using the corresponding basis set. Table 1 reports the statistics of results obtained using the PCA basis set of each dataset considered. In Table 1, the results are reported as average error, maximum error and standard deviation of the distance in CIELAB space between the coordinates of the measured and the estimated spectra under the illuminants D65, A, and F2. The spectral mismatch is reported as the mean absolute error between reflectance spectra. For each dataset, the first row reports the results for the estimation, assuming the tristimulus values for the D65 illuminant are available. In this case, the colorimetric error ΔE D65 is low, while colorimetric errors for the A and F2 illuminants are larger, and indicate that the estimated spectra are metameric with respect to the original ones. The use of two or three illuminants, as reported in the second and third row of each dataset, reduces the difference between colorimetric errors. As a consequence, the spectral error is also reduced. Table 2 reports the statistics of results obtained using the fitness in equations (10), and the FG basis set. Table 3 shows the statistics of the results obtained employing the VG basis set. (10) 153
Tab. 1 – Statistics of results obtained using the PCA basis set of each of the dataset considered (MAE = mean absolute error, avg = mean value, M = maximum value, sdv = standard deviation) PCA ΔE D65 ΔE A ΔE F2 MAE avg M sdv avg M sdv avg M sdv avg M sdv Macbeth, D65 0.00 0.09 0.02 2.72 8.24 2.01 2.26 6.20 1.52 3.19 5.82 1.58 D65,A 0.19 0.60 0.14 0.20 0.51 0.14 0.75 1.79 0.54 2.15 5.11 1.10 D65,A,F2 0.18 0.66 0.14 0.26 0.94 0.20 0.32 1.02 0.27 1.66 5.50 1.03 Munsell, D65 0.00 0.08 0.01 1.67 9.73 1.50 1.32 8.69 1.18 1.81 8.57 1.30 D65,A 0.13 0.87 0.11 0.14 1.06 0.12 0.90 7.54 0.84 1.82 7.58 1.22 D65,A,F2 0.18 2.21 0.17 0.29 1.90 0.24 0.27 2.14 0.23 1.25 4.64 0.70 Dupont, D65 0.06 0.72 0.13 3.85 22.9 4.77 3.16 16.8 3.43 2.81 7.38 1.43 D65,A 0.35 1.55 0.36 0.40 2.62 0.48 2.28 17.9 2.98 1.98 6.10 1.13 D65,A,F2 0.47 2.68 0.58 0.77 7.55 1.07 0.79 6.35 1.09 1.48 5.69 0.79 Silk, D65 0.01 0.38 0.04 1.92 8.34 1.52 1.85 8.70 1.27 2.01 8.80 1.54 D65,A 0.23 1.13 0.18 0.24 1.54 0.19 1.28 7.72 1.17 1.66 7.96 1.21 D65,A,F2 0.28 1.29 0.21 0.46 3.17 0.37 0.47 2.49 0.36 1.55 7.77 1.14 Tab. 2 – Statistics of results obtained using the Fixed Gaussian basis set (MAE = mean absolute error, avg = mean value, M = maximum value, sdv = standard deviation) Fixed ΔE D65 ΔE A ΔE F2 MAE Gaussian avg M sdv avg M sdv avg M sdv avg M sdv Macbeth, D65 0.13 0.45 0.11 3.87 9.13 2.60 3.19 5.67 1.51 5.68 10.2 2.94 D65,A 0.45 1.03 0.23 0.43 1.06 0.22 1.92 4.25 0.96 3.66 9.04 1.95 D65,A,F2 0.45 1.11 0.24 0.53 2.25 0.44 0.69 1.76 0.42 3.09 7.45 1.72 Munsell, D65 0.12 0.81 0.10 4.44 14.3 2.90 3.47 10.0 1.82 6.43 18.3 3.57 D65,A 0.38 1.62 0.21 0.36 1.33 0.19 1.67 6.21 0.98 3.35 11.7 1.98 D65,A,F2 0.41 1.67 0.26 0.46 1.87 0.27 0.58 2.17 0.32 2.59 8.36 1.54 Dupont, D65 0.19 2.56 0.33 3.16 11.3 2.15 2.36 9.58 1.48 5.28 16.2 3.45 D65,A 0.49 2.68 0.40 0.47 2.05 0.40 1.51 3.79 0.80 3.41 11.9 2.26 D65,A,F2 0.53 2.57 0.43 0.64 2.28 0.46 0.73 2.60 0.50 2.96 7.31 1.89 Silk, D65 0.16 1.43 0.16 3.71 14.3 2.52 3.08 9.88 1.66 5.17 15.8 2.84 D65,A 0.43 2.40 0.27 0.42 2.46 0.26 1.68 6.58 0.99 3.79 10.8 1.99 D65,A,F2 0.51 3.57 0.35 0.55 2.37 0.32 0.66 2.88 0.36 3.42 10.6 1.76 Tab. 3 – Statistics of results obtained using the Variable Gaussian basis set (MAE = mean absolute error, avg = mean value, M = maximum value, sdv = standard deviation) Variable ΔE D65 ΔE A ΔE F2 MAE Gaussian avg M sdv avg M sdv avg M sdv avg M sdv Macbeth, D65 0.00 0.01 0.00 1.93 7.50 2.03 1.71 7.38 2.04 2.95 9.01 2.40 D65,A 0.24 0.75 0.23 0.23 0.62 0.21 1.43 4.09 1.37 2.67 9.84 2.42 D65,A,F2 0.43 1.49 0.43 0.45 1.76 0.52 0.56 1.51 0.47 2.35 6.26 1.71 Munsell, D65 0.00 0.25 0.01 2.26 11.2 1.89 1.77 10.4 1.52 3.10 15.2 2.05 D65,A 0.18 1.02 0.16 0.18 1.44 0.18 0.94 10.9 0.87 2.08 10.6 1.54 D65,A,F2 0.26 2.79 0.27 0.30 2.34 0.28 0.38 2.88 0.32 1.85 9.61 1.33 Dupont, D65 0.04 1.07 0.12 3.20 18.5 3.17 2.16 9.83 1.96 3.87 11.7 2.36 D65,A 0.32 2.70 0.43 0.37 3.95 0.61 1.25 4.24 1.05 2.98 12.4 2.26 D65,A,F2 0.41 3.92 0.50 0.50 5.03 0.69 0.53 2.45 0.50 3.02 10.6 2.35 Silk, D65 0.01 0.73 0.05 3.08 11.5 2.15 2.43 12.4 1.90 5.14 17.5 2.84 D65,A 0.28 2.50 0.28 0.30 4.22 0.38 1.52 12.0 1.44 3.68 12.5 2.23 D65,A,F2 0.42 4.72 0.48 0.47 5.55 0.52 0.62 5.00 0.63 3.16 10.4 1.94 The Variable basis set performs better here than the Fixed set of Gaussian functions, as can be observed by comparing Tables 2 and 3. 154
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SOCIETÀ ITALIANA DI OTTICA E FOTON
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Proposta di una stazione a camera d
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icostruire il fattore di riflession
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costruttive. In ambito applicativo
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quindi fondamento nel salvaguardare
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e, raggiungibile e controllabile co
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Tale ricerca di solidità è atta a
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Scanner ottico iperspettrale per la
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- R( λi ) è il fattore di rifless
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spaziale della scena mentre le colo
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consentendo la ripresa di immagini
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Fig. 5 - Immagine dell’interfacci
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Fig. 6 - Fattore di riflessione spe
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perpendicolare e parallela alla dir
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3. J. Y. Hardeberg, F. Schmitt, H.
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esolution multispectral images, and
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function R. In mathematical terms,
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in standard and professional photog
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The acquisition output vectors are
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and then ‘stitched together’ to
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36 Template matching Fig. 6 - A sem
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References 1. Fairchild M.D., Rosen
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40 Sistema stereoscopico di visione
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macroscopiche sullo stato di conser
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44 Fig. 1 - Il sistema SVA Due di e
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Si pone un piano di calibrazione, f
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a 20 000 K. I valori corrispondenti
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50 Tabella 1 Colore LSVA xSVA ySVA
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52 Spectral-based printer modeling
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2. Printer Model The model of the p
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covered is computed as the differen
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The spectra were measured with a Gr
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60 Spettrofotometro a scansione per
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icostruire il profilo tridimensiona
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dalla fibra è a sezione circolare.
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con maniglie e ruote per semplifica
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In fig. 5 sono riportati i risultat
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70 380nm….430nm….470nm…510nm
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inciderebbero sulla forma del fatto
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Infine in Fig. 9 sono riportati i r
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2. D. Anglos, C. Balas, C. Fotakis,
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78 Fig. 1 - Filtri interferenziali
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E’ chiaro tuttavia che uno strume
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scientifici e di restauro è affian
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Per quanto riguarda la precisione d
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immagini componenti principali (aut
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6. A. Casini, F. Lotti, M. Picollo,
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� necessità di una movimentazion
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92 Trasmittanza % 90 80 70 60 50 40
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lungo l’asse di scansione. Con lo
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I valori di Riflettanza (R T % e R
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Minolta. Una matrice di corrisponde
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Tab. 3 - Confronto in termini di Δ
Page 107 and 108: Bibliografia 1. Fermi F., Antonioli
Page 109 and 110: 2. Quali diagnostiche per l’Arte
Page 111 and 112: 106 Fig. 3 - Rappresentazione delle
Page 113 and 114: e tre i riquadri, anche in quelli c
Page 115 and 116: Fig. 8 - PCA delle misure rilevate
Page 117 and 118: Colorimetria multispettrale per la
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Page 121 and 122: 116 Immagini aeree o da satellite M
Page 123 and 124: Non solo sono identificate per ogni
Page 125 and 126: vigneto, e non si sofferma certamen
Page 127 and 128: 1. Introduzione 122 Spettrometria d
Page 129 and 130: Negli anni successivi, mentre veniv
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Page 133 and 134: Nei colori a basso contrasto, l’o
Page 135 and 136: 130 Proposta di una stazione a came
Page 137 and 138: Fig. 2 − Singola immagine cattura
Page 139 and 140: 134 400 500 600 700 nm lunghezza d
Page 141 and 142: 6. dal confronto di misure di coppi
Page 143 and 144: Bibliografia 1. P.C. Hung, “Color
Page 145 and 146: movimento. Se infatti il filtro ste
Page 147 and 148: 142 a b Fig. 2 - Trasmittanza di un
Page 149 and 150: Fig. 5 - Trasmittanza teorica di un
Page 151 and 152: dimensione della memoria di bordo p
Page 153 and 154: 148 Estimating Surface Reflectance
Page 155 and 156: 150 ~ ∑ j= = N w R( λ ) ( λ) (3
Page 157: R( λ) = E ⎡ 2 ⎤ ⎡ 2 ⎛ λ
Page 161 and 162: 13. D.E. Goldberg, Genetic Algorith
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Page 173 and 174: 3. Joao Carlos de Andrade, Jiulio C
Page 175 and 176: 2. Generalità Richiamiamo brevemen
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Page 185 and 186: 9. Conclusioni Abbiamo cercato di a
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