Fig 1.
Illustrates the sRGB (left) and CIELAB (right) colour spaces. Left: the achromatic axis (vertical) and the full colour locus (non-planar hexagon) are marked by tubes. A selection of hue triangles span from the achromatic axis to the full colour locus. The curved full colour surface, bordered by the full colour locus, can just been seen. Right: the extent of the sRGB cube is shown in CIELAB space. The colours for which naming data was collected (section 2) are shown by spheres. The thin black horizontal ring marks a path which is analysed in section 5 Fig 8.
Fig 2.
a) Plots the distribution of naming responses (vertical) for different locations (horizontal) in a hypothetical 1-D colour manifold. Red points mark points in the colour manifold which can be followed across the panels. b) A replot of the previous panel, with location within the triangle indicating the distribution of naming responses. c) A replot of the previous panel, with location on the sphere indicating the distribution. d) Same horizontal scale as a, the vertical scale indicates the categorical distance (determined by the change in naming responses) for a small change in colour at that location in the colour manifold. e) A warp of a so that horizontal distances in the figure equal categorical distances.
Fig 3.
Same layout as Fig 2 but with a more complex pattern of naming responses.
Panels b and c are omitted as too high-dimensional for visualization.
Fig 4.
Histogram of global response rates for different colour names showing an exponential form.
Note the non-linear horizontal axis.
Fig 5.
Breakdown of responses by name, ordered by their global frequency.
Sectors are coloured by the mean colour of the chip generating the response. A subset of sectors are labelled by name, and a subset of those also show the number of responses in brackets.
Fig 6.
Visualizes, in CIELAB space, the individually-fitted response rate functions for the 82 most frequent names, which together account for 75% of all responses.
Each response function has a unimodal form decaying from a peak response rate in the centre. The ellipsoids mark where the response rate has reduced to half the peak value. The figure does not visualize the peak response rate itself. The CIELAB distance from the magenta corner (left) to the green corner (right) is 225.0 units.
Fig 7.
Each column shows the data and model for a different name n (shown in the top row).
2nd row: samples from the distribution of chips causing naming response n. 3rd row: the CIELAB locations of the chips causing response n are shown as black spheres, with volume proportional to the response fraction for that chip; other chips are shown as smaller grey spheres; the one sd limit of the fitted covariance is also shown. 4th row: like the 2nd row but according to the fitted model rather than direct from the data. 5th row: generalization of the 4th row from the 600 chips used as experimental stimulus to the full colour gamut.
Fig 8.
Left: Visualizations for a path along the achromatic axis. Right: for a circular path around the achromatic axis (see Fig 1 right). Top: Response distributions, piecewise linearly interpolated along sRGB paths, tied to observed response distributions at chip locations marked by grey vertical lines. Bottom: modelled response distributions along the same paths. In all panels the tick marks along the horizontal axis have spacing Δ = 0.1 (sRGB units), the smoothness length scale used in section 6. Vertical sections show proportions of naming responses (each colour corresponds to a different name) as in Figs 2 and 3.
Table 1.
Comparison of models.
Fig 9.
Tensor field of the categorical metric, visualized across sRGB space using a 3D version of Tissot’s indicatrix [72].
Each ellipsoid is a sphere from the perspective of the categorical metric, all spheres being of the same radius. That radius, chosen with an eye to visibility of the final figure, is in this case 1.6% of a grain. Where the ellipsoids are wide, categorical distance increases slowly with sRGB distance. So, for example, the large ellipsoid at the blue corner is indicating that there is very little difference between the naming response to colour 〈0.00,0.00,1.00〉sRGB and to colour 〈0.05,0.05,1.00〉sRGB. On the other hand, where the ellipsoids are narrow, categorical distance increases more rapidly with sRGB distance. Hence, the small ellipsoid midway along the cube edge from cyan to white is indicating that the naming responses to 〈0.50,1.00,1.00〉sRGB and 〈0.55,1.00,1.00〉sRGB are noticeably different.
Fig 10.
Top-left: distortions quantified as the standard deviation of the log2 of the ratio of distances. Histograms: local distortions between CIE2000 and the categorical metric. Colours indicate the location of the colour difference (which is always small). The double arrow at the bottom of the figure applies to all four histograms.
Fig 11.
The categorical metric restricted to the mid-lightness section of the sRGB cube.
See Fig 9 for interpretation of the ellipses. The corresponding sphere radius in this case is 5.3% of a grain.
Fig 12.
The categorical metric restricted to constant hue sections of the sRGB cube, with the achromatic axis running down the centre of each section.
See Fig 9 for interpretation of the ellipses. The corresponding sphere radius in this case is 4.0% of a grain.
Fig 13.
Each thick ring is an isometric embedding of the full colour locus (see Fig 1) according to the metric shown above the panel.
The hexagons and spokes show the correspondence to the vertices and edges of the RGB cube along which the locus runs, and emphasize the differences between the embeddings. The arc in the right panel shows a one grain extent (see section 7.4).
Fig 14.
The full colour surface (left) is constructed by interpolation from the full colour locus (Fig 1). In sRGB it has a highly negatively curved form. Right: three views of a close to isometric embedding of the full colour surface onto a sphere.
Fig 15.
The red hue triangle from the sRGB cube (left). Embedded onto the surface of a sphere (middle and right) with only minor distortion.
Fig 16.
A Voronoi partition [78, 79] of the full colour surface (see Fig 14).
The locations of the fifteen region centres (large spheres) were optimised to maximize nearest neighbour distances. All distances were measured within the approximately isometric embedding hence approximate geodesic categorical distances. Internal regions have area one areal-grain, boundary regions half an areal-grain. Region centres are coloured according to their locations, the colour of smaller spheres is randomly chosen from their containing region. The size of the regions is such that all colours within a region are categorically similar to the region centre, and all region centres are categorically distinct.