Concavities, negative parts, and the perception that shapes are complete

When we perceive the shape of an object, we can often make many other inferences about the object, derived from its shape. For example, when we look at a bitten apple, we perceive not only the local curvatures across the surface, but also that the shape of the bitten region was caused by forcefully removing a piece from the original shape (excision), leading to a salient concavity or negative part in the object. However, excision is not the only possible cause of concavities or negative parts in objects-for example, we do not perceive the spaces between the fingers of a hand to have been excised. Thus, in order to infer excision, it is not sufficient to identify concavities in a shape; some additional geometrical conditions must also be satisfied. Here, we studied the geometrical conditions under which subjects perceived objects as been bitten, as opposed to complete shapes. We created 2-D shapes by intersecting pairs of irregular hexagons and discarding the regions of overlap. Subjects rated the extent to which the resulting shapes appeared to be bitten or whole on a 10-point scale. We find that subjects were significantly above chance at identifying whether shapes were bitten or whole. Despite large intersubject differences in overall performance, subjects were surprisingly consistent in their judgments of shapes that had been bitten. We measured the extent to which various geometrical features predict subjects' judgments and find that the impression that an object is bitten is strongly correlated with the relative depth of the negative part. Finally, we discuss the relationship between excision and other perceptual organization processes such modal and amodal completion, and the inference of other attributes of objects, such as the material properties.