Quantification of three-dimensional structures

Abstract

A mathematical model, based on additive subcomponents of grouping, subitizing and adding, was derived to account for quantification latencies of three-dimensional block arrangements. Subitizing is the process that people use to directly quantify a small number of objects without counting. It was found that most people consistently subitized up to four blocks. With more than four blocks, people resorted to grouping and adding, and the model was able to account for these data. The structural variables of compactness, symmetry, linearity, and planarity were shown to have small effects on quantification latencies relative to the large effect of number of blocks. Of these structural variables, compactness had the largest effect, and in terms of the model, it is suggested that visual structure had its effect on the perceptual grouping subcomponent.