Testing Tau: Which Tau is Actually Used?
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As Tresilian (1991) remarked, there are three definitions of Lee's tau that should be distinguished. First, there is the global tau, involving the separation of the image of a certain feature and the focus of expansion (Lee, 1980; Tresilian, 1991). Second, there is one local tau that can be defined, using a planar model, as the inverse of the relative rate of dilation of the optical size of the object (rI1; Lee, 1976; Tresilian, 1991). We will call this linear tau. In this case, the projection of any pair of points lying opposite to each other (such as p and q in Figure 1) can specify time-to-contact (te). Third, another local tau can be defined. Here the entire solid visual angle of a surface patch can specify te. We call this area tau; it is defined as 2a13, where a is simply the projected area of the surface patch (r2) and 3, its rate of change over time (2rl?' see Lee & Young, 1985; Tresilian, 1991).