On the non-rigid perception of looming

Purpose: Our goal was to understand the computations underlying the perception of three-dimensional shape. Previously we reported that some nonrigid and affine motion is not easily distinguishable from rigid rotational motion; i.e., people perceive affine motion to be as rigid as rotational motion. In this work we report that rigid motion which included translation in depth (backward/forward motion) resulted in poor judgments of rigidity. Methods. Subjects judged the coherence or rigidity of 4, 5, or 12 moving points rendered by different colors. The motion of the points was rigid, affine, or rotation perturbed by a different independent amount at each point. On a proportion of trials, the rotation motion was combined with translation in depth (looming). Conclusions: Our experiments showed surprising results, that are not in agreement with traditional models of rigid $3D$ structure from motion. On one hand, the expected categorical perception of rigidity was not apparent in the data; rigid motion was judged only slightly more rigid than affine motion. On the other hand, the most significant result of this experiment is that for the rotating stimuli used in our experiments the addition of looming significantly impaired the ability of subject to judge rigidity. Further extensions of the experimental work supported the notion that rigid translation in depth is often interpreted a deformation or non-rigid scaling. None of several simple models of $3D$ structure accounted individually for the data.