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.