Shape from Dots: A Window into Abstraction Processes in Visual Perception Provisionally Accepted

Nicholas Baker^1* Philip J. Kellman²

• ¹Loyola University Chicago, United States
• ²University of California, Los Angeles, United States

A remarkable phenomenon in perception is that the visual system spontaneously organizes sets of discrete elements into abstract shape representations. We studied perceptual performance with dot displays to discover what spatial relationships support shape perception. In Experiment 1, we tested conditions that lead dot arrays to be perceived as smooth contours vs. having vertices. We found that the perception of a smooth contour vs. a vertex was influenced by spatial relations between dots beyond the three points that define the angle of the point in question. However, there appeared to be a hard boundary around 90 degrees such that any angle 90 degrees or less was perceived as a vertex regardless of the spatial relations of ancillary dots. We hypothesized that dot arrays whose triplets were perceived as smooth curves would be more readily perceived as a unitary object because they can be encoded more economically. In Experiment 2, we generated dot arrays with and without such “vertex triplets” and compared participants’ phenomenological reports of a unified shape with smooth curves vs. shapes with angular corners. Observers gave higher shape ratings for dot arrays from curvilinear shapes. In Experiment 3, we tested shape encoding using a mental rotation task. Participants judged whether two dot arrays were the same or different at five angular differences. Subjects responded reliably faster for displays without vertex triplets, suggesting economical encoding of smooth displays. We followed this up in Experiment 4 using a visual search task. Shapes with and without vertex triplets were embedded in arrays with 25 distractor dots. Participants were asked to detect which display in a 2IFC paradigm contained a shape against a distractor with random dots. Performance was better when the dots were sampled from a smooth shape than when they were sampled from a shape with vertex triplets. These results suggest that the visual system processes dot arrangements as coherent shapes automatically using precise smoothness constraints. This ability may be a consequence of processes that extract curvature in defining object shape and is consistent with recent theory and evidence suggesting that 2D contour representations are composed of constant curvature primitives.