Depth from stereo-motion: Estimating the Intrinsic Constraint Line

Retinal velocities and horizontal disparities produced by the projection of a rigidly rotating object are linearly related. This relation identifies a one-dimensional subspace in the disparity-velocity space. A recent model proposed by Domini and Caudek (2004) predicts that the visual system derives 3D structure from stereo-motion signals by means of a two-stage process: a) in the first stage it estimates the direction of this subspace (defined as Intrinsic Constraint (IC) line) by performing a principal component analysis, and b) in the second stage it derives 3D properties from the IC line. Purpose of this work was to test the first hypothesized stage. In two experiments the observers binocularly viewed a rotating 3D cloud of dots and judged when a probe dot at the center of the structure appeared to be aligned in depth with two nearby target dots having both the same velocity and disparity (i.e. same simulated depth). In six conditions (four in the first experiment and three in the second experiment) we independently perturbed the disparity and velocity signals of the surrounding dots so to produce a noisy relationship among these signals (i.e. a noisy IC line). We reasoned that if the visual system recovers the IC line before estimating depth, then these perturbations should also influence the observers' task, even though it only concerns matching the velocity and disparity of the unperturbed probe and target dots. In fact, we found that different levels of noise (experiment 1) influenced the accuracy with which the observers' task was performed. Moreover, we also found that the noise distribution - and not only the noise level - in the velocity-disparity space influenced the observers' accuracy (experiment 2). These findings are compatible with a model that performs a Principle Component Analysis in the disparity-velocity space and recovers depth from the resulting lower-dimensional space.