Mental object rotation based on two-dimensional visual representations.

The discovery of mental rotation was one of the most significant landmarks in experimental psychology, leading to the ongoing assumption that to visually compare objects from different three-dimensional viewpoints, we use explicit internal simulations of object rotations, to 'mentally adjust' one object until it matches the other1. These rotations are thought to be performed on three-dimensional representations of the object, by literal analogy to physical rotations. In particular, it is thought that an imagined object is continuously adjusted at a constant three-dimensional angular rotation rate from its initial orientation to the final orientation through all intervening viewpoints2. While qualitative theories have tried to account for this phenomenon3, to date there has been no explicit, image-computable model of the underlying processes. As a result, there is no quantitative account of why some object viewpoints appear more similar to one another than others when the three-dimensional angular difference between them is the same4,5. We reasoned that the specific pattern of non-uniformities in the perception of viewpoints can reveal the visual computations underlying mental rotation. We therefore compared human viewpoint perception with a model based on the kind of two-dimensional 'optical flow' computations that are thought to underlie motion perception in biological vision6, finding that the model reproduces the specific errors that participants make. This suggests that mental rotation involves simulating the two-dimensional retinal image change that would occur when rotating objects. When we compare objects, we do not do so in a distal three-dimensional representation as previously assumed, but by measuring how much the proximal stimulus would change if we watched the object rotate, capturing perspectival appearance changes7.