3 Spectral shape descriptors
This table is adapted from Montgomerie (2006) 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 | \[B_1=B_T=\int_{\lambda_{min}}^{\lambda_{max}} R_i = \sum_{\lambda_{min}}^{\lambda_{max}} R_i\] | Andersson (1999),Andersson et al. (2002),Örnborg et al. (2002),Andersson et al. (1998),Smiseth et al. (2001),Saks et al. (2003),Pryke et al. (2001),Shawkey et al. (2003) |
| Mean brightness | \[B_2=\frac{\sum_{\lambda_{min}}^{\lambda_{max}} R_i}{n_w}=\frac{B_1}{n_w}\] | Delhey et al. (2003),Siefferman and Hill (2005) | |
| Intensity | \[B_3=R_{max}\] | Andersson (1999),Keyser and Hill (2000),Keyser and Hill (1999) | |
| Saturation | Chroma, reflectance ratio, spectral purity | \[S_1= \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{\sum_{\lambda_{min}}^{\lambda_{max}} R_i} = \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{B_1}\] | Örnborg et al. (2002),Andersson et al. (1998),Smiseth et al. (2001),Siefferman and Hill (2005),Peters et al. (2004),Shawkey et al. (2003) |
| Spectral saturation | \[S_2 = \frac{R_{max}}{R_{min}}\] | Andersson (1999) | |
| Chroma | \[S_3 = \frac{\sum_{\lambda_{R_{max}}-50}^{\lambda_{R_{max}}+50} R_i}{B_1}\] | Shawkey et al. (2003) | |
| Spectral purity | \[S_4 = \lvert b\text{max}_{neg}\lvert\] | Andersson (1999) | |
| Chroma | \[S_5=\sqrt{(B_r-B_g)^2+(B_y-B_b)^2}\] | Saks et al. (2003) | |
| Constrast, amplitude | \[S_6 = R_{max} - R_{min}\] | Keyser and Hill (2000),Keyser and Hill (1999) | |
| Spectral saturation | \[S_7 = \frac{\left(\sum_{\lambda_{320}}^{\lambda_{R_{mid}}} R_i - \sum_{\lambda_{R_{mid}}}^{\lambda_{700}} R_i\right)}{B_1}\] | Andersson et al. (2002),Pryke et al. (2001) | |
| Chroma | \[S_8=\frac{R_{max}-R_{min}}{B_2}\] | Andersson et al. (2002),Smiseth et al. (2001) | |
| Carotenoid chroma | \[S_9=\frac{R_{\lambda_{700}}-R_{\lambda_{450}}}{R_{\lambda_{700}}}\] | Peters et al. (2004) | |
| Peaky chroma | \[S_{10}=\lvert b\text{max}_{neg} \lvert\frac{R_{max}-R_{min}}{B_2}\] | Örnborg et al. (2002) | |
| Hue | Hue, peak wavelength, spectral location | \[H_1=\lambda_{R_{max}}\] | Andersson (1999),Örnborg et al. (2002),Andersson et al. (1998),Delhey et al. (2003),Smiseth et al. (2001),Keyser and Hill (2000),Siefferman and Hill (2005),Shawkey et al. (2003) |
| Hue | \[H_2 = \lambda_{b\text{max}_{neg}}\] | Andersson et al. (1998),Smiseth et al. (2001) | |
| Hue | \[H_3 = \lambda_{R_{mid}}\] | Andersson et al. (2002),Smiseth et al. (2001),Pryke et al. (2001) | |
| Hue | \[H_4 = \arctan\left(\frac{B_y-B_b}{B_r-B_g}\right)\] | Saks et al. (2003) | |
| Hue | \[H_5 = \lambda_{b\text{max}_{pos}}\] | Keyser and Hill (1999) |
- \(R_i\): 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., \(\frac{R_{max}+R_{min}}{2}\))