4 Spectral shape descriptors

This table is adapted from and lists all spectral descriptors that are computed by the summary function in pavo.

Color variable Names used Formula Reference
Brightness Total brightness, total reflectance, spectral intensity $B_1=B_T=\int_{\lambda_{min}}^{\lambda_{max}} R_i = \sum_{\lambda_{min}}^{\lambda_{max}} R_i$ ,,,,,,,
Mean brightness $B_2=\frac{\sum_{\lambda_{min}}^{\lambda_{max}} R_i}{n_w}=\frac{B_1}{n_w}$ ,
Intensity $B_3=R_{max}$ ,,
Saturation Chroma, reflectance ratio, spectral purity $S_1= \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{\sum_{\lambda_{min}}^{\lambda_{max}} R_i} = \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{B_1}$ ,,,,,
Spectral saturation $S_2 = \frac{R_{max}}{R_{min}}$
Chroma $S_3 = \frac{\sum_{\lambda_{R_{max}}-50}^{\lambda_{R_{max}}+50} R_i}{B_1}$
Spectral purity $S_4 = \lvert b\text{max}_{neg}\lvert$
Chroma $S_5=\sqrt{(B_r-B_g)^2+(B_y-B_b)^2}$
Constrast, amplitude $S_6 = R_{max} - R_{min}$ ,
Spectral saturation $S_7 = \frac{\left(\sum_{\lambda_{320}}^{\lambda_{R_{mid}}} R_i - \sum_{\lambda_{R_{mid}}}^{\lambda_{700}} R_i\right)}{B_1}$ ,
Chroma $S_8=\frac{R_{max}-R_{min}}{B_2}$ ,
Carotenoid chroma $S_9=\frac{R_{\lambda_{700}}-R_{\lambda_{450}}}{R_{\lambda_{700}}}$
Peaky chroma $S_{10}=\lvert b\text{max}_{neg} \lvert\frac{R_{max}-R_{min}}{B_2}$
Hue Hue, peak wavelength, spectral location $H_1=\lambda_{R_{max}}$ ,,,,,,,
Hue $H_2 = \lambda_{b\text{max}_{neg}}$ ,
Hue $H_3 = \lambda_{R_{mid}}$ ,,
Hue $H_4 = \arctan\left(\frac{B_y-B_b}{B_r-B_g}\right)$
Hue $H_5 = \lambda_{b\text{max}_{pos}}$
• $$R_i$$: percentage (or proportional) reflectance at the $$i$$th wavelength
• $$\lambda_{max}$$, $$\lambda_{min}$$: upper and lower (respectively) limits of wavelengths
• $$n_w$$: number of wavelength intervals used to calculate $$B_T$$
• $$R_{max}$$, $$R_{min}$$: maximum and minimum percent reflectances, respectively
• $$\lambda_{R_{max}}$$: wavelength at maximum reflectance
• $$b\text{max}_{neg}$$, $$b\text{max}_{pos}$$: maximum negative and positive slopes of reflectance curve in a region of interest
• $$B_r$$, $$B_y$$, $$B_g$$, $$B_b$$: total brightness in red ($$r=625-700\,nm$$), yellow ($$y=550-625\,nm$$), green ($$g=475-550\,nm$$) and blue ($$b=400-475\,nm$$) segments of the spectrum
• $$\lambda_{R_{mid}}$$: wavelength at the reflectance midpoint between $$R_{max}$$ and $$R_{min}$$ (i.e., $$\frac{R_{max}+R_{min}}{2}$$)