Fig 1.
Colorimetric characterisation of the selected target colour pairs.
a. Linear RGB representation of the X-rite ColorChecker SG highlighting the seven colour pairs selected for the experiment. The samples comprising each colour pair are identified by the same roman numeral. b. Reflectance spectra for the 14 individual colour samples making up each one of the colour pairs and their chromaticity difference values (ΔC). Chromaticity difference values were calculated from chromaticity coordinates (Table 2) using formulae and diagrams by MacAdam [48] and assuming a mercury discharge lamp illumination. Individual colour samples are identified by their unique coordinates in the chart (panel a). c. Colour samples in the 1931 CIE chromaticity diagram: (+) pair I, (×) pair II, (*) pair III, (◻) pair IV, (○) pair V, (△) pair VI and (⋄) pair VII. Colour key of each pair is a crude representation of the linear RGB combination for each pair in panel a.
Table 1.
Details of the composition, source and number of colour samples included as part of the calibration set and target colour sample pairs.
Fig 2.
Spectral power distribution (irradiance) and chromaticity of the mercury discharge lamp used as light source for the experiment.
Chromaticity coordinates corresponding to the light emitted by lamp (insert) were calculated from tristimulus values obtained after solving Eq (2) using the CIE 1931 colour matching functions [20]. Spectral irradiance from the light source was measured with an ILT 900 spectroradiometer (International Light Technologies, USA), calibrated for irradiance measurements. Blue solid line in the insert represents the CIE daylight locus for correlated colour temperatures between 4000 to 25000 K [80].
Fig 3.
Convex hull in linear RGB space corresponding to the 1395 samples available in our calibration set, and 95% quartile ellipsoids from the 10 pixels sampled from each colour sample.
Colour samples constituting a pair are coded using the same colour and code as in Fig 1: pair I pale orange, pair III blue, pair IV purple, pair V green, pair VI red and pair VII pink. Pair II are not ellipsoids but lines as these samples only present variation along the green axis. The red line represents the theoretical RGB responses for a range of spectrally uniform, achromatic samples (ρR = ρG = ρB) varying in brightness, and the asterisk markers represent measured linear camera responses (ρ) for the 31 achromatic samples available in the Munsell Book of Colour. The magenta sphere indicates the center of the hull corresponding to a theoretical, spectrally flat, achromatic sample reflecting 50% of incident radiation.
Fig 4.
Mean number of metamers recovered from a given ρR, ρG, ρB triplet camera response as a function of distance from the mid point of the RGB linear space.
In panel a. each point corresponds to the mean number of metamers recovered for each ρ triplet and the error bars represent standard deviation from the mean. Solid line represents the best fit of an exponential model of the form y = y0 exp−(bx) (Eq 5) fitted by means of a least absolute deviation (LAD) regression [107]. b. Metamer set (477,341 metamers) for ρR = 0.508, ρG = 0.327, ρB = 0.246 located at 0.307 linear RGB units from the center (red circle in a.) corresponding to a pixel sample from colour target H8 in Fig 1. c. Metamer set (483 metamers) for ρR = 0.337,ρG = 0.025,ρB = 0.097 located at 0.644 linear RGB units from the center (green circle in a.) corresponding to a pixel sample from colour target M2 in Fig 1.
Fig 5.
Mean reflectance (panel a.) and radiance (panel b.) spectra recovered from 10 pixel samples of an hyperspectral image cube containing each one of the colour targets in Fig 1.
Reflectance spectra in first column of panel a. correspond to the radiance spectra in panel b. after calibrating the radiance responses against a spectrally flat, achromatic surface included in the hyperspectral image cube. Second column in panel a. depicts the result of performing a robust local regression (loess) with a 0.1 span parameter to smooth the peaks observed at about 435 and 545 nm.
Fig 6.
Density scatter plot expressed as hexagonal bins [108] summarising the frequency of chromaticity values obtained from the metamer sets reconstructed from 10 camera response triplets corresponding to each of the 14 colour samples in Fig 1.
The number of metamers resulting in the same chromaticity values is represented by grey shades as indicated under the label ‘counts’ for each colour sample. The red arrow on each panel indicates the chromaticity coordinates obtained from the measured reflectance spectrum (panels b and c in Fig 1), and presented in Table 2.
Table 2.
Colorimetric properties of samples as chromaticity areas: Chromaticity coordinates corresponding to reflectance spectra measured for each sample constituting the colour pair samples used for the experiment (third column) and chromaticity areas for the spectra reconstructed with an RGB (fourth column) and a hyperspectral camera (fifth column).
Fig 7.
Chromaticity areas (CAs) corresponding to the convex hull of chromaticity coordinates calculated from the metamer sets reconstructed from 10 ρRGB responses of the different colour samples in Fig 1 recorded with an RGB camera.
A. Panels correspond to each one of the seven different colour pairs used in our experiment; colour difference values (ΔC) between the pair members are included on each panel. Shaded areas correspond the the CA’s for each colour sample in a sample pair and their intersection represents the confusion region (ARC) expected for a given sample pair. Chromaticity coordinates calculated from measured reflectance spectra are indicated by the (*) and (●) markers. Ellipses represent MacAdam’s [48] (blue) and Newhall [50] (green) colour-difference thresholds calculated for the chromaticity coordinates obtained from measured spectral data. Both ellipses are drawn at their actual scale. B. Regions in the 1931 CIE Chromaticity Diagram covered by the x and y axis of the panels in A. Variations in area size are due to differences in scale required for plotting the two colours making up each sample pair.
Fig 8.
Chromaticity areas (CAs) corresponding to the convex hull of chromaticity coordinates calculated from the radiance and smoothed reflectance spectra reconstructed from 10 pixel responses in the hyperspectral image cube containing the hyperspectral camera responses for the different colour samples in Fig 1, and assuming a mercury discharge lamp as light source (Fig 2).
A. Panels correspond to each one of the seven different colour pairs used in our experiment; colour difference values (ΔC) between the pair members are included on each panel. Patterned areas correspond to CA’s calculated from reconstructed radiance spectra, whilst solid shaded areas to CAs calculated from smoothed reflectance spectra for the two colours of each sample pair. Note that confusion regions were not obtained from CAs reconstructed from the hyperspectral camera responses. Chromaticity coordinates calculated from measured reflectance spectra are indicated by the (*) and (●) markers. Ellipses represent MacAdam’s [48] (blue) and Newhall [50] (green) colour-difference thresholds calculated for the chromaticity coordinates obtained from measured spectral data. Both ellipses are drawn at their actual scale. B. Regions in the 1931 CIE Chromaticity Diagram covered by the x and y axis of the panels in A. Variations in area size are due to differences in scale required for plotting the two colours making up each sample pair.
Fig 9.
Effect of colour difference (ΔC) in the size of the confusion region for the chromaticity areas corresponding to the metamer sets recovered from the seven colour pairs in Fig 1.
The confusion region for each sample pair is defined as the ratio of intersected area to the sum of the individual chromaticity areas of the two colour samples constituting a pair. Chromaticity areas correspond to those displayed in Fig 6. Solid line represents the best fit of an exponential model of the form y = y0 exp−(bx) (Eq 6) resulting from a logistic regression using a logit link function.
Fig 10.
Hyperspectral image scans generated outdoors under a) partially cloudy and b) windy conditions using sunlight as the only illumination.
a) Passing clouds blocked the sun during image recording resulting in various underexposed image regions. Similarly, darkened portions of (b) are a result of overhead leaf cover shading direct sunlight at the end of the scan as the wind increased their movement. Integration time for both scans was set to 50.00 ms.