Fig 1.
Shows twelve random examples from each of nine collections of spectral reflectances functions.
Plot labels indicate the theme and size of each collection. Reflectance functions are plotted in the colour they would appear under daylight (D65) illumination.
Fig 2.
Frequency amplitude spectra for individual collections (blue), averaged over collections (red), and modelled (green).
Fig 3.
Example images from the THINGS dataset.
Fig 4.
The mean RGB histogram of the THINGS dataset.
All views show iso-density surfaces of the histogram, coloured according to the corresponding RGB Value. The top row shows views of the iso-density surface that encloses 80% of the mass of the histogram, the bottom row enclosing 96%.
Fig 5.
Visualizes RGB histograms using swatches, which are random samples of colour from the density.
The top swatch is for the mean image histogram. The bottom row compares the top (T) and bottom (B) half-image histograms. The central swatch is for the intersection histogram (min(T,B)); the left and right swatches for the excesses (clip+(T−B) and clip+(B−T)). The swatch sizes reflect the density mass in the intersection and excess histograms, so the left and middle swatches combined are a swatch for the top-half histogram. The ratio of sizes is 0.08:0.92 so the intersection distance (ID) between the half histograms is 8%.
Fig 6.
The left and centre panels illustrate the colours arising from shading and specularity in the case of an object with homogeneous spectral reflectance.
At right is shown an example page from the Ostwald Atlas, which can be considered a chart of the colours that can arise in this way.
Fig 7.
An example Ostwald distribution.
Left: Ostwald triangle coordinates as functions of the latent domain; with an example bivariate normal distribution superimposed (green). Middle: the bivariate normal distribution transformed to the Ostwald triangle. Right: a swatch from the Ostwald triangle distribution.
Fig 8.
Each row shows a gallery of visualizations for an RGB histogram.
Reading left-to-right these are: a swatch; the 80%-mass-containing iso-density surface; the hue×saturation marginal (grey-level indicating log-density); the lightness marginal; the saturation marginal; the hue marginal; the Basic Colour Category marginal.
Table 1.
Distances between the mean image histogram and empirical histograms.
JSD = Jensen-Shannon Divergence; EMD = Earthmover’s Distance; ID = Intersection Distance. The ‘+5’ is a reminder of the number of parameters tuned to minimize the ID.
Fig 9.
The PCA model of spectral reflectance.
Top-left: the mean reflectance function. Top-middle: standard deviations of principal components. Top-right: first six principal components, colouring corresponds to the top-middle panel. Bottom-left: reflectances generated by the PCA model; a fraction (red and blue) have values outside the legitimate [0,1] range. Bottom-right: generated reflectances after clipping to [0,1].
Fig 10.
The latent variable (t) representation of reflectance (r).
Functions from wavelength to t (left) can be converted to functions from wavelength to r (right) using the sigmoid transfer function (middle, top), or back the other way using its inverse (middle, bottom).
Fig 11.
Comparison of empirical (left) and modelled (middle and right) reflectance functions. All functions are plotted in their colour under the uniform-illumination formation model. Left column: one function randomly chosen from each of the nine collections (same in top and bottom panels). Top row: unconstrained model reflectance functions. Bottom row: colour-matched model reflectance functions.
Fig 12.
Average fourier amplitude spectra for empirical and synthetic reflectance functions.
Fig 13.
Same layout as Fig 8 but comparing the RGB histogram from the images (top row) to the histograms from two existing models of the distribution of reflectance.
Table 2.
Realism scores comparing the empirical dataset approach with the two existing models of spectral reflectance.
For all metrics lower numbers indicate greater realism. The shaded columns contain the most important realism metrics. The left concerns individual reflectance functions, and the right the distribution of colours arising. The ‘+5’ note for Ostwald-shading reminds of the number of parameters tuned to minimize the ID scores.
Fig 14.
Shows computation of a sigmoid-sum reflectance.
In this example, the random number of sigmoid components (left) was 10. These are summed and normalized to zero-mean (middle, solid) then added to a random DC component (middle, dotted). The sum is then transformed to the reflectance domain (right).
Fig 15.
Synthetic reflectance functions (columns 2–4) colour-balanced with the same randomly chosen empirical reflectance functions as in Fig 11 (right).
Fig 16.
Average fourier amplitude spectra for empirical and synthetic reflectance functions.
Fig 17.
Table 3.
Realism scores for all models.
The shaded columns are the key metrics. Figures in parentheses indicate the number of parameters tuned to minimize ID scores. The best scores in each column are bolded. Final row of table reminds of the difference between top and bottom half-image histograms, given as context.
Fig 18.
In each column, one panel shows a random selection of reflectance functions (one per collection), the other panel shows colour-balanced sigmoid-sum reflectance functions.
Fig 19.
Compares the empirical and model image histograms (top) and shows the breakdown into intersection and excess histograms that give rise to the intersection distance of 20% (bottom). The failure of the model to capture the abundance of vegetation green is apparent in the empirical excess histogram (bottom-left). The models broader range of blues than required to capture sky-blue is apparent in its excess histogram (bottom-right).