Measuring Abstraction Levels of Sculptural Objects

Abstract Freestanding sculpture can be scored for abstraction using order scales such as the three-rank ‘realistic,’ ‘mixed,’ and ‘abstract.’ Subjective but invaluable, the ranks support ordering but not arithmetic. Numeric limitations can be addressed via information-theoretic metrics that measure collective uncertainty about a sculpture; to this end 60 participants view 25 images of sculpture via an internet questionnaire. They (i) score each depicted object and (ii) type a caption stating what impression the object evokes. Captions for the image are simplified to their English simple subject, sorted into classification categories and counted. A metric converts an image’s categories and counts into viewers’ uncertainty. The investigation examines four-rank and five-rank scales plus metrics CC (category count), H (entropy) and EC ≡ 2H (equalized category count). Medians of scores or uncertainties reduce variability as appropriate. Comparisons of scores vs uncertainties show the two generally correlate well. Results also highlight inherent design tradeoffs. Scale/metric pairings affect both ranks (which should be statistically distinct) and rank/uncertainty correlations. Two good combinations are [four-rank; median CC] and [five-rank; median EC]. Metric CC is easy to compute and correlates slightly better than EC, although the latter supports five evenly separated ranks. Shifting focus to image scatterplots, the pair [four-rank median score; CC] yields a very strong correlation. Once uncertainties are linked to ranks to ‘calibrate’ them, one gets a quantitative sense of the rank order scale. The augmented framework offers the speed and ease of scoring along with valid numeric estimates of uncertainty unavailable from ranks alone.