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Ronald Rensink; An Entropy Theory of Correlation Perception. Journal of Vision 2016;16(12):811. doi: https://doi.org/10.1167/16.12.811.
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© ARVO (1962-2015); The Authors (2016-present)
The perception of correlation in scatterplots with gaussian distributions can be described by two simple laws: a linear one for discrimination and a logarithmic one for perceived correlation magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To determine what these might be, just noticeable differences (JNDs) and perceived magnitudes were measured for 20 observers, for each of four conditions. The first tested scatterplots of 100 points with a bivariate gaussian distribution of equal variance in both dimensions; values of Pearson correlation r ranged from 0.0 to 0.9. JND was proportional to u = 1-br, with bias b such that 0 less than b less than 1; perceived magnitude was proportional to log(u). The two functions were related via the common bias b for both JND and perceived magnitude. Three other conditions were also examined: a scatterplot with 25 points, a horizontal compression of the scatterplot, and a scatterplot with a uniform distribution of dots. For all conditions, the same laws were found to hold. The generality and nature of these laws—together with the finding that the same laws exist when features other than spatial position are used to map information to visual structure (Rensink, VSS 2015)suggests that the underlying perceptual structure is not a geometric one such as the shape of the scatterplot dot cloud, but a probability distribution inferred from the dots, with perceived correlation proportional to its information entropy. This entropy theory not only explains the shape of the curves for discrimination and perceived magnitude, but also why they are related via their common bias b. More generally, these results also show that the graphical representations commonly used to display information form an interesting class of stimuli, one that can help us uncover important new insights into the nature of our visual intelligence.
Meeting abstract presented at VSS 2016
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