Fall 2021
Elementary Perceptual Tasks

Cleveland and McGill propose a series of Elementary Perceptual Tasks of which many overlap with Bertin’s proposed Visual Variables, and some with Bertin’s Visual Implantations. This Alluvial Diagram shows the equivalency in each categorical classification of these visual tasks:

7 out of 10 Elementary Perceptual tasks have an arguable Visual Variable equivalent.

Position with non-aligned scale and Length do not have and Visual Variable equivalents. However, it is arguable to value Position with non-aligned scale as the Implantation of Point, since Bertin only defines it as a “location on the plane” without referring to the number of possible scales on that plane. Volume is unheard-of in Bertin’s Semiology of Graphics as his work mostly focused on 2 Dimensional scientific visualizations.

Mackinlay refers to the ordering of elementary perceptual proposed by Cleveland and McGill. With some additional elements, he ranked them in terms of accuracy for the ordinal and nominal perceptions.

*Density is the equivalent of Cleveland and McGill’s Shading.

- The additional tasks are:

Texture, Connection, Containment and Shape. However, Cleveland and McGill’s definition of Curvature could be part Mackinlay’s definition of Shape.

- Quantitative, Ordinal and Nominal perceptions are accomplished most accurately with Position.

- Following Position; Group 1 (Length, Angle, Slope, Area and Volume, in that order) are the best ranked for Quantitative perceptions; however, they end up with the low rankings for Ordinal tasks, with Shape being lowest ranking element for both Quantitative and Ordinal tasks.

- Group 2 (Density, Color Saturation, Color Hue, Texture, Connection, Containment in that order) are ranking low for Quantitative perceptions but rank high (after Position) for Ordinal.

- Nominal perceptions ranking of Group 1 and 2 is similar than that of Ordinal perceptions: With Position still the most accurate. However, in high-ranking Group 1, Density and Color Saturation are the least efficient. This time Shape gives more accuracy than the lower ranking Group 2 with Volume being the least accurate task for Nominal perceptions.

Steven’s power law of theoretical psychophysics seems to be a good model to describe bias in quantitative visual perception, it is expressed with:
p as the perceived magnitude .
a as the actual magnitude.
p is related to a by p = k.a(e^(α)), “only if α = 1 is the perceived scale the same as the actual physical scale” which means that there is no bias in the perceptual task.

Baird (1970) reports “that the values of α tend to be reasonably close to 1 for length judgements, smaller than 1 for area judgements, and even smaller for volume judgements. This means that length judgements tend to be unbiased, whereas there tends to be distortion in area judgements and even more in volume judgements” (Cleveland and McGill).

Jock Mackinlay explains that design issues are codified as Expressiveness and Effectiveness “criteria for graphical languages”.

Expressiveness criteria define how well a graphical language can express the desired information: “a set of facts is expressible in a language if it contains a sentence that:

1 encodes all the facts in the set and
2 encodes only the facts in the set”.

Effectiveness criteria define how effectively a graphical language in a given situation uses the capabilities of the output medium and the human visual system.

Sources:

Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods - William S. Cleveland and Robert McGill - 1984

Automating the Design of Graphical Presentations of Relational Information - Jock Mackinlay - 1986