To display the isosensitivity contours in the space–time distance plot, we use Equations 5–8 of Kelly (
1979), with which he fit the spatiotemporal thresholds for the detection of drifting sinusoidal gratings. Following Nakayama (
1985, p. 637), we computed the spatial and temporal
distances between successive discrete stimuli that correspond to Kelly's spatial and temporal frequencies. Nakayama assumed that motion is detected by pairs of spatial-frequency filters (“quadrature pairs”; Adelson & Bergen,
1985; Gabor,
1946), in agreement with physiological (Marcelja,
1980; Pollen & Ronner,
1981) and computational (Sakitt & Barlow,
1982) evidence. The two parts of such a detector are tuned to the same spatial frequency
f_{s}, but their spatial phases differ by
π/2, a quarter of the spatial period of the optimal stimulus (see also van Santen & Sperling,
1984). When such a detector is stimulated by a luminance grating with spatial frequency
f_{s}, a spatial shift by
S = 1 / (4
f_{s}) will activate the detector optimally. Similarly, the optimal temporal interval
T of a detector is equal to the quarter period of its optimal temporal modulation:
T = 1 / (4
f_{T}). By this argument, there exists a simple correspondence between the frequency tuning of motion detectors and the spatial and temporal distance between successive stimuli that activate the detectors optimally. Using the above expressions for
S and
T, we mapped Kelly's spatiotemporal threshold surface (his Figure 15) to the logarithmic space–time distance plot in
Figure 1A. In the distance plot, the maximal sensitivity set is convex toward the origin. When plotted in the coordinates of spatial and temporal frequencies, as in Kelly's Figure 15, the maximal sensitivity set is concave toward the origin.