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How does the visual system combine motion signals from disconnected locations? To address this question, we examined stimuli having individually ambiguous motion signals. We constructed demonstrations consisting of simple polygons moving behind a set of small windows. Motion measurements made through small windows, or apertures, are inherently ambiguous because the component of motion parallel to an edge’s orientation cannot be measured. Many researchers have proposed that observers reduce ambiguities by choosing image interpretations consistent with rigid objects. This hypothesis suggests that observers of our demonstrations will combine ambiguous motion signals across apertures so that their image interpretations are consistent with rigid polygons. Surprisingly, observers interpret our demonstrations nonrigidly.

We have investigated the perceived rigidity of rotating ellipses in a variety of conditions, following Wallach et al. (1956), who observed that rigidity is seen only when the eccentricity or aspect ratio is large. We measured the degree of rigidity as a function of aspect ratio, and found that a number of factors besides aspect ratio can have a profound effect on the percept. For example, a single rotating ellipse is often perceived to be more rigid than a family of concentric ellipses of the same aspect ratio. In a similar finding, we have observed that an asymmetric Gaussian blob with elliptical contours is seen to be more rigid than a single ellipse, suggesting that low-frequency content may be important for rigidity.

Assumptions of local rigidity and smoothness have been used to explain how the visual system reconstructs a representation of physical objects and their motion from spatially sampled images. Using moving stimuli of limited complexity, viewed through several spatially separated apertures, we investigated the effectiveness of various constraints on the reconstruction process. These constraints are essential when the image within each aperture does not permit a unique determination of local optical flow. Our results indicate that, when the image contains sufficient information, translation motion is perceived vertically and can be effectively integrated over large spatial separations. For example, a translating hidden corner viewed through two rectangular apertures is perceived as a single rigid object. In contrast, pure rotation of smooth contours is perceived with strong biases. In addition, observers are generally not able to integrate pure, uniform rotational motion information from different, nonoverlapping apertures. We found that these results are affected by the complexity of the object motion. Objects are more likely to be perceived correctly when the motion is more complex, e.g., has nonuniform velocity or consists of a combination of translation and rotation. We propose a simple statistical framework for describing these results.