The time derivative (tau) of the inverse of the relative rate of optical expansion (tau) may have critical values with potential implications for controlling activity. The present research addresses the particular hypothesis that tau < -0.5 specifies "unsafe" collision courses and tau > or = -0.5 specifies "safe" collision courses. Optical expansion patterns were simulated on a computer with -1.0 < or = tau < 0 and judged as suggesting a "hard" or "soft" collision. tau < -0.5 led to significantly different decisions from tau > or = -0.5, but the critical value of -0.5 was not perceived reliably as soft, a deviation possibly due to discretely approximating continuous functions. Additional experiments evaluated terminal rates of change and display duration and examined the effects of biasing the presented displays toward the soft or the hard end of the tau continuum. The results were consistent with the tau hypothesis.

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Five experiments addressed the perception of curvilinear heading under various conditions of optical flow. Perception of heading was unaffected by optical noise (Experiment 1) and was successful and equally accurate for flows generated by circular and elliptical paths of locomotion (Experiment 2). In Experiment 3, random perturbations of vector magnitudes in general curvilinear fields did not reduce the accuracy of perceived heading. When vector directions were randomly perturbed in Experiments 4 and 5, curvilinear heading perception was impaired. Discussion focuses on the inappropriateness of the vector normal hypothesis to the general curvilinear case, the importance of the pattern of relative vector directions, and the practical and theoretical significance of investigating different forms of noncanonical optical flow.

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