Testing Tau

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 ( https://www.w3.org/1998/Math/MathML"> r / r • https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315799506/e3000455-006b-47f3-8dc3-986527b32979/content/inline-math_38_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ; 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 (t_c). Third, another local tau can be defined. Here the entire solid visual angle of a surface patch can specify t_c. We call this area tau; it is defined as https://www.w3.org/1998/Math/MathML"> 2 a / a • https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315799506/e3000455-006b-47f3-8dc3-986527b32979/content/inline-math_39_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , where a is simply the projected area of the surface patch (r ²) and https://www.w3.org/1998/Math/MathML"> a • https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315799506/e3000455-006b-47f3-8dc3-986527b32979/content/inline-math_40_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , its rate of change over time ( https://www.w3.org/1998/Math/MathML"> 2 r / r • https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315799506/e3000455-006b-47f3-8dc3-986527b32979/content/inline-math_41_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , see Lee & Young, 1985; Tresilian, 1991). Figure 1 Schematic representation of the experimental situation for the no-slit (A) and the vertical slit condition (B). R is the physical object size; r is the projected size of the object and k is the slit size https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315799506/e3000455-006b-47f3-8dc3-986527b32979/content/fig76_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>