Romain Vuillemot bio photo

Romain Vuillemot

Assistant Professor
École Centrale de Lyon
LIRIS Laboratory

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Using Concrete Scales: A Framework for Visual Depiction of Complex Measures

Fanny Chevalier, Romain Vuillemot, Guia Gali

Conference: InfoVis 2013
Proceedings: IEEE Transactions on Visualization and Computer Graphics (InfoVis '13)
Paper: /publis/infovis13-concrete-scales.pdf

From financial statistics to nutritional values, we are frequently exposed to quantitative information expressed in measures of either extreme magnitudes or unfamiliar units, or both. A common practice used to comprehend such complex measures is to relate, re-express, and compare them through visual depictions using magnitudes and units that are easier to grasp. Through this practice, we create a new graphic composition that we refer to as a concrete scale. To the best of our knowledge, there are no design guidelines that exist for concrete scales despite their common use in communication, educational, and decision-making settings. We attempt to fill this void by introducing a novel framework that would serve as a practical guide for their analysis and design. Informed by a thorough analysis of graphic compositions involving complex measures and an extensive literature review of scale cognition mechanisms, our framework outlines the design space of various measure relations---specifically relations involving the re-expression of complex measures to more familiar concepts---and their visual representations as graphic compositions.

Visual Language

One of the main contribution of the paper is to introduce a visual language as a mechanisms to support a systematic break down of visual material related to scale explanation. While the language can get complex, the main graphic decomposition mechanisms are as below:

Measure Relations


A comparison is a relation between objects that results in equality, inferiority, or superiority. There usually are types of comparisons: exact and approximate. Exact relations concern cases where magnitudes of objects can be accurately compared along a property (e.g., a $100 bill is 10 times superior than a $10 bill in terms of monetary value). Approximate is when the magnitudes are vaguely defined d (e.g, the height of an average person).


A containment is when objects are placed within a container, both objects become linked by a containment relation. Containers are common in concrete scales especially because they allow several objects into a single entity,which can facilitate comparison.


A unitization is an improvised—yet subjective—systematization of units where observers can break down scales, using a preferred new unit, into more specific and relatable chunks.

Below is an illustration of super-massive black hole (complex measure) measured in suns (simple unit).

Analogy: Simultaneous Pairwise Comparison

An analogy conveys the size of relationships by comparing the size difference between a pair of objects, the target, and another pair of more familiar objects: the base.


A zoom is the progressive adjustment and containment when the magnitude is too large to both see details on a relative scale while having an overview of the absolute scale. When the tools are dynamic, the zoom effect is executed through animation.


A lock strategy is the progressive adjustment and containment. The general idea builds on locking the possible relation of an object to a specific type as a constraint.

Small Multiples: Build a Collection

The small multiples are the small elementary objects juxtaposed together to aid in establishing a concrete scale through the use of a singular measure relation.


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