Area Dominates Edge in Pointillistic Colour

Abstract

In Pointillism and Divisionism, artists moved from tonal to chromatic palettes, as Impressionism did before them, and relied on what is often called optical mixture instead of stirring paints together. The so-called optical mixture is actually not an optical mixture, but a mental blend, because the texture of the paint marks is used as a means to stress the picture plane. The touches are intended to remain separately visible. These techniques require novel methods of colour description that have to depart from standard colorimetric conventions. We investigate the distinctiveness of transitions between regions as defined through such artistic techniques. We find that the pointillist edges are not primarily defined by luminance contrast but are achieved in almost purely chromatic ways. A very simple rule suffices to predict transition distinctiveness for pairs of cardinal colours (yellow, green, cyan, blue, magenta, and red); it is simply distance along the colour circle or in the RGB cube. Distinctiveness of partition depends mainly on the colours of the regions, not the sharpness of the transition.

Keywords: Pointillism; colour; edges; macchie; textures; transitions.

Figure 1.

Paul Signac (1863–1935), Auxerre, La Rivière (1902–1903). Oil on canvas, height: 55.5 × 46.5 cm, private collection (image in the public domain). At left, a reproduction in colour; at centre and right, two attempts at monochromatic rendering. At the centre, the straight luminance image; at right, an interpretation using the “max rule” (see later); neither is particularly successful in capturing the spirit of the chromatic version. Alternative translations from hues to tones can do much better (see later) but necessarily involve idiosyncratic interpretation.

Figure 2.

At top, two uniform areas of stripes abut in a nonexistent edge. At centre, two uniform, but mutually different areas are connected by way of a smooth transition; there is hardly a notion of an edge. The areas are perceived as similar. At bottom, two identical uniform areas are divided by a local edge. The areas are perceived as different.

Figure 3.

Example of the hard-edge stimulus. On top, the achromatic reference; at bottom, a polychromatic case. The structure of the colour gamuts and the relevance of the global layout are discussed later.

Figure 4.

Example of the soft-edge stimulus. On top, the achromatic reference; at bottom, a polychromatic case. The structure of the colour gamuts and the relevance of the global layout are discussed later.

Figure 5.

Schematic examples of hard achromatic edges. Notice that the left and right regions are both nonuniform; yet, the contrast of the overall pattern is well defined.

Figure 6.

Monochromatic colour samples in the CWK (Ostwald) triangle (see Appendix A). Notice that the distribution is skewed so as to favour saturated colours over tints and shades of the hue.

Figure 7.

Polychromatic hue samples from a triangular distribution (see Appendix A). In this example, the average hue is yellow, and outliers range from red to green. The painter would speak of analogous or related colours. (Probability density on a linear scale, hue index defined in Appendix A.)

Figure 8.

The instruction sheet used in the experiment.

Figure 9.

A schematic overview of the stimuli used in each condition. (Impressions of the actual screen images were presented in Figures 3 and 4.) The columns show monochromatic colour gamuts at left and polychromatic colour gamuts at right. The rows show hard edges at top and soft edges at bottom. In all these cases, we test all pairs of cardinal hues, thus YG, YC, YB, YM, YR, GC, GB, GM, GR, CB, CM, CR, BM, BR, and MR. The reader might find it useful to keep this schematic overview in mind. In referring to any case, we will specify the colour pair (like YR, say), the nature of the transition (“hard” or “soft”), and the nature of the colour gamut (“monochromatic” or “polychromatic”). In all cases, the response will be the Michelson contrast of the matching (qua “distinctiveness of the bipartition”) achromatic image.

Figure 10.

Paired histograms of the responses over all observers and colour pairs, differentiated with respect to the stimulus categories. Notice that the dichotomy monochromatic–polychromatic yields a large difference and that of soft–hard edge quality rather less so. (All counts marked on the same scale for convenient comparison.)

Figure 11.

Distinctiveness responses are plotted against the median of the distinctiveness response over observers. Original data plotted at left; observers are distinguished by colour. The lines are fits for each observer. At right, the same data normalised with respect to idiosyncratic offset and slope of the individual observers. (SE–MG stands for “soft-edge, monochromatic gamut”)

Figure 12.

As Figure 11; here, HE–MG stands for “hard-edge, monochromatic gamut.”

Figure 13.

As Figure 11; here, SE–PG stands for “soft-edge, polychromatic gamut.”

Figure 14.

As Figure 11; here, HE–PG stands for “hard-edge, polychromatic gamut.”

Figure 15.

Some examples of chromatic transition structure. In each case, there is the chromatic transition shown in the bipartite disk at top; below it is an analysis in terms of the RGB colour channels. The RGB colour channels are the rows; the two columns represent the left and right regions of the transition. There are three groups of examples; at left, there is a transition in one, at centre in two, and at right in all three of the RGB colour channels. The first group illustrates the influence of the colour of the veil; the second group illustrates the effect of the absence or presence of a veil, whereas the third group illustrated the effect of the (relative) polarity of transitions in the individual RGB colour channels.

Figure 16.

Array plots of the observations. The response range has been mapped on the full grey scale, where black represents zero and white represents the maximum response. Notice that the diagonal entries (self–self comparisons) are trivially zero.

Figure 17.

Overview of the results for pairs of the analogous colours for the case of the soft-edge, monochromatic stimuli. The bars show quartile values of the distinctiveness settings for all observers. Below are schematic representations of the nature of the transition (YR, YG, MR, GC, CB, and BM) in bipartite disks, and below that an analysis in terms of the individual RGB channels is given.

Figure 18.

Results for the complementary colour pairs for the case of the soft-edge, monochromatic stimuli. The bars show quartile values of the distinctiveness settings for all observers. Below are schematic representations of the nature of the transition (YB, GM, and CR) in bipartite disks, and below that an analysis in terms of the individual RGB channels is given.

Figure 19.

At top-left, an attempt at an overview of some data for the case of monochromatic, soft-edge stimuli (results for the other cases are quite similar). The hexagon represents the colour circle from the perspective of a fiducial cardinal colour, here yellow. The connections to each of the other cardinal colours are drawn in a thickness proportional to the distinctiveness of the corresponding bipartition. To present all data for a case, one needs to draw five more of this type of plots, but the case of a yellow fiducial is quite instructive by itself. The three other hexagons show various model predictions: raw RGB cube distance (top-right), CIE luminance (bottom-left), and CIEDE2000 distance (bottom-right). (Notice that the average thickness has been normalised to the same value in all cases.)

Figure 20.

The array plots for the three models. Again, these have been normalised to use the full grey scale, from black (representing zero) to white (representing the maximum value). Compare Figure 16, representing the data. Notice again that the diagonal entries are trivially black and merely serve as a convenient landmark in comparing the patterns.

Figure 21.

The median data for the hard-edge, monochromatic gamut case (black bars) compared with the predictions of the RGB cube colour distances (red bars), CIE luminance contrast (cyan bars), and CIE colour distance (yellow bars). We show the results for the analogous pairs in the top box, the results for the transitions with two transitions in the individual RGB channels in the centre box, and the results for the complementary pairs in the bottom box. To make a fair comparison possible, we normalised with respect to the median over each of the families analogous, incongruous, and complementary colour pairs.

Figure 22.

The hard-edge, polychromatic transition at top has zero distinctiveness in the prediction of all three models. Yet, we find it easy enough to see the distinction between the left- and right-hand areas, although the edge appears rather soft. In the example at bottom (likewise a polychromatic transition of zero distinctiveness in the prediction of all three models), one sees a sharp transition. Apparently, “zero distinctiveness” transitions come in different varieties and are a worthy target for detailed investigation.

Figure 23.

Correlations of the predictions of the three models with the observer settings.

Figure 24.

Some mutually very different, but equally valid grey-level interpretations of the Signac painting (Figure 1).

Figure 25.

Paul Signac (1890), The Beacons at Saint-Briac, Opus 210, 65 × 81 cm, oil on canvas (public domain). At left, a hard on top and a soft edge below; both cutouts from the image at right. Notice the treatment of the hard edge; here, Signac modulated the edge in Craik–O'Brien–Cornsweet style.

Figure B1.

At left, the cases of a transition in a single RGB colour channel with veil in either one of the two remaining RGB colour channels. At right, the case of simultaneous edges in two RGB colour channels, with or without a veil in the third one.

Figure B2.

The case of simultaneous edges in all three RGB colour channels, in which case there will be no overlay. Here, the difference is in the polarity of the edges.

Figure C1.

Normalised data for the hard monochromatic condition as quartiles over observers as bar plots for the various colour pairs. The transition structures are illustrated in Figures B1 and B2. The bars show quartile values of the distinctiveness settings for all observers.

Figure C2.

Normalised data for the hard polychromatic condition as quartiles over observers as bar plots for the various colour pairs. The transition structures are illustrated in Figures B1 and B2. The bars show quartile values of the distinctiveness settings for all observers.

Figure C3.

Normalised data for the soft monochromatic condition as quartiles over observers as bar plots for the various colour pairs. The transition structures are illustrated in Figures B1 and B2. The bars show quartile values of the distinctiveness settings for all observers.

Figure C4.

Normalised data for the soft polychromatic condition as quartiles over observers as bar plots for the various colour pairs. The transition structures are illustrated in Figures B1 and B2. The bars show quartile values of the distinctiveness settings for all observers.