Non-additivity of parts in the apparent size expansion effect

Abstract

The human visual system overestimates the length of structured contours relative to adjacent empty intervals of the same physical size (Fig. 1) [1]. The effect appears in whole geometric contours and in isolated parts of them alike [2]. Complete rectangles and pentagons, isolated apices and pedestals, and pairs of parallel horizontal or vertical lines all looked longer than they were, with consistently positive mean errors in psychophysical experiments. Overestimation magnitude followed contour geometry rather than physical size alone: an isolated segment could expand as much as, less than, or more than the shape it came from. The sum of the part effects therefore does not predict the whole-object effect, nor can the parts be predicted from the whole. The summed expansion of the isolated apex and pedestal far exceeded that of the corresponding whole pentagon: 25.1 vs. 15.8 arc min (Fig. 2a), 30.0 vs. 13.8 arc min (Fig. 2b), and 30.0 vs. 7.7 arc min (Fig. 2c). Such a pattern is incompatible with a model that assembles perceived size by summing the apparent sizes of parts measured independently. Instead, it suggests that segments within a whole object are integrated into a single representation whose expansion depends on the relational structure of the complete configuration — a holistic rather than structural coding of shape [3, 4]. The comparison between line pairs and rectangles points the same way. Adding two vertical segments to a pair of horizontal lines forms a rectangle, thereby lengthening the contour and closing it. At every length, the rectangle expanded less than the line pair: 7.5 vs. 14.2 arc min, 15.5 vs. 17.4 arc min, and 20.4 vs. 22.9 arc min. The reduction fits the proposal that corner junctions introduce a contraction component that partly offsets expansion. Here too, the summed expansion of the horizontal and vertical line pairs exceeded that of the rectangle: 18.9 vs. 7.5 arc min, 22.9 vs. 15.5 arc min, and 25.5 vs. 20.4 arc min. These findings support a configuration-dependent account of apparent-length expansion and argue against simple additivity of parts.