The Correspondence Principle

Theory
#1

Guideline: The same data should produce the same visualization (D->V).
Source: G. Kindlmann and C. Scheidegger. “An Algebraic Process for Visualization Design”. http://vis.cs.ucdavis.edu/vis2014papers/TVCG/papers/2181_20tvcg12-kindlmann-2346325.pdf

I agree with this guideline in an illusive manner. But I am not sure what “same visualization” really means. If one replaces a bar chart with a pie chart, one high-res display with a low-res one, one view of a 3D scene with another view, one iso-value with another, and so on, do they lead to a different or the same visualization? If the function D->V is absolutely fixed, different people may see different visualizations due to the difference of their visual systems or environments (e.g., color blindness, and lighting in the room).

#2

I think the clearest statement of the rule is that in the introduction of the paper:

The Principle of Visual-Data Correspondence (or just Correspondence) says that significant changes in the data should meaningfully correspond with noticeable changes in the visual impression and vice versa. If an important change in data is not clearly manifested in the visualization, it has jumbled the data. If a clear and obvious transformation of the visualization corresponds with an unimportant change in the data, the visualization is misleading.

The rule is concerned with how the visualization changes when the input data is transformed.

The paper contains examples of how a visualization would be expected to respond to a transformation of the data:

  • negating a scalar field before visualizing it should be equivalent to visualizing it and then negating the colours: a diverging colormap has this property, so satisfies the Correspondance Principle; a Hue+Luminance colourmap does not, so violates the principle.

  • scaling a tensor field before visualizing it with glyphs should be equivalent to visualizing it and then scaling the corresponding glyphs: an ellipsoidal tensor glyph has this property, so satisfies the Correspondance Principle; a Superquadratic Rensor Glyph does not, so violates the principle.

In contrast, replacing a bar chart with a pie chart or changing the resolution of the visualization is not a transformation of the data, so I am not sure how your examples are relevant to the rule.