One of the main functions of vision is to represent object shape. Most theories of shape perception focus exclusively on geometrical computations (e.g., curvatures, symmetries, axis structure). Here, however, we find that shape representations are also profoundly influenced by an object’s causal origins: the processes in its past that formed it. Observers placed dots on objects to report their perceived symmetry axes. When objects appeared ‘complete’—created entirely by a single generative process—responses closely approximated the object’s geometrical axes. However, when objects appeared ‘bitten’—as if parts had been removed by a distinct causal process—the responses deviated significantly from the geometrical axes, as if the bitten regions were suppressed from the computation of symmetry. This suppression of bitten regions was also found when observers were not asked about symmetry axes but about the perceived front and back of objects. The findings suggest that visual shape representations are more sophisticated than previously appreciated. Objects are not only parsed according to what features they have, but also to how or why they have those features.

In everyday life, we can often identify when an object has been subjected to some kind of transformation that alters its shape. For example, we can usually tell whether a can has been crushed, or a cookie has been bitten. Conversely, our ability to recognize objects is often robust across such shape transformations: we can still identify the can even though it has been dented. This ability to determine and discount the causal history of objects suggests the visual system may partially decompose the observed shape of an object into original (untransformed) elements plus the transformations that were applied to it. We sought to shed light on this possibility, using 'bending' as an example transformation. In one experiment subjects matched the degree of bending applied to random 3D shapes. We find that subjects could match the degree of bend, although there was a tendency to overestimate bends, especially for the least bent objects. In two other experiments, observers had to identify individual objects across different degrees of bending. Subjects performed significantly above chance although not as well as when the objects differed by rigid rotations without any bends (cf. traditional mental rotation experiments). Together our findings suggest that subjects can to some extent extract information about transformations applied to shapes, while ignoring other differences. At the same time subjects show a certain degree of invariance across shape transformations. This suggests scission of a shape's representation into its causes - a base shape and transformations applied to it.

Objects in our environment are subject to manifold transformations, either of the physical objects themselves or of the object images on the retina. Despite drastic effects on the objects' physical appearances, we are often able to identify stable objects across transformations and have strong subjective impressions of the transformations themselves. This suggests the brain is equipped with sophisticated mechanisms for inferring both object constancy, and objects' causal history. We employed a dot-matching task to study in geometrical detail the effects of rigid transformations on representations of shape and space. We presented an untransformed 'base shape' on the left side of the screen and its transformed counterpart on the right (rotated, scaled, or both). On each trial, a dot was superimposed at a given location on the contour (Experiment 1) or within and around the shape (Experiment 2). The participant's task was to place a dot at the corresponding location on the right side of the screen. By analyzing correspondence between responses and physical transformations, we tested for object constancy, causal history, and transformation of space. We find that shape representations are remarkably robust against rotation and scaling. Performance is modulated by the type and amount of transformation, as well as by contour saliency. We also find that the representation of space within and around a shape is transformed in line with the shape transformation, as if shape features establish an object-centered reference frame. These findings suggest robust mechanisms for the inference of shape, space and correspondence across transformations.

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.

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