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Unifying Time to Contact Estimation and Collision Avoidance across Species
Figure 1
The modified Tau function (“m-Tau”).
(a) The figure shows two m-Tau functions which are distinguished by 
(with values 
and 
, see legend). The horizontal bars denote their respective maxima for the default stimulus values (
, 
, 
, 
). The maxima shift to the left (circles) upon doubling the object radius 
to 
(“size effect”). They shift in the opposite direction (triangles) upon doubling both the approach velocity 
and the initial distance 
(“velocity effect”), such that 
remains unchanged (
). The thin dotted lines (not identified in the legend) show the m-Tau functions with correspondingly doubled values. For the m-Tau function with 
, the two factors 
and 
are furthermore plotted, see equation (1). The shift directions of the maxima are identical with the corresponding shifts observed with the 
-function, see Text S1. (b) Here it is shown how the maxima of seven m-Tau functions shift when the object diameter is halved or doubled with respect to its default value 
. Each point indicates 
(time of maximum) along with its corresponding amplitude 
. Circular symbols represent the default case with 
. All maxima lie on a line. With a smaller object diameter all maxima shift to the right (towards 
), and an increase in object size causes a shift of all maxima to the left (away from 
). All shifts proceed along the same straight line. Notice that some artifacts occur for the two leftmost points, because all maxima were computed numerically. The velocity effect is illustrated in Text S1.
doi: https://doi.org/10.1371/journal.pcbi.1002625.g001