Date of Award

Fall 2011

Degree Type


Degree Name

Master of Science (MSc)




Hong-jin Sun


Patrick J. Bennett



Committee Member

Daphne M. Maurer


As an object approaches an observer’s eye, tau, defined as the inverse relative expansion rate of the object’s image on the retina (Lee, 1976) approximates time-to-collision (TTC). Many studies have suggested that human observers use TTC information, but evidence for the use of tau remains inconclusive. Here we present two studies that investigated the use of tau in object-motion and observer-motion situations. In Study I, we dissociated several monocular variables that potentially contributed to TTC perception, and found that participants were most sensitive to TTC information when performing a relative TTC estimation task; and less sensitive to non-time variables such as distance-to-collision, speed and object size. Additionally, when we manipulated sources of information to specify conflicting time-of-arrivals, TTC specified by tau was weighted more than TTC derived from distance and speed. Thus, we concluded that even in the presence of monocular depth information, observers strongly utilize tau when estimating TTC.

In Study II, observers estimated TTC of a looming target in the presence or absence of background expansion. Results demonstrated that participants overestimated TTC in situations where the surroundings of the target’s contours expanded at a reduced rate. Moreover, simulated self-motion was unnecessary to induce this bias, as results were comparable in situations where this relative expansion was limited to the target’s immediate surroundings. Therefore, we also concluded that a relative tau variable, based on the relative rate of expansion, is utilized whenever expansion beyond the object’s immediate boundaries is less than the target’s absolute rate of expansion.

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