The stimulus within each circled region in
Figure 1A is
S i T (
d, t) =
N i (
d, t) + T(
d, t) or
S i NT (
d, t) =
N i (
d, t) + NT(
d, t) (depending on whether it contained target or nontarget). T(
d, t) =
δ (
d −
d T) ·
s, where
d T is the target direction (e.g., downward) and
s is the number of signal dots (T(
d, t) is independent of time
t, because signal dots were present at every motion transition throughout stimulus presentation). Similarly for NT(
d, t), we convolved
S with a directionally selective receptive field defined by a two-dimensional Gaussian function
RF(
d, t) =
Gauss(
σ d,
σ t) with
σ d = 40 deg (broadly consistent with, e.g., Cook & Maunsell,
2004; Treue & Martínez Trujillo,
1999) and
σt = 1 frame duration = 30 ms (broadly consistent with Bair & Movshon,
2004) to obtain
oiT(
d, t) =
SiT *
RF, and similarly for
oiNT. We only used the two outputs at preferred and antipreferred directions
dT and
dNT for each convolution, i.e., pref
iT (
t) =
oiT(
dT,
t) and antipref
iT(
t) =
oiT(
dNT,
t). Similarly for pref
iNT and antipref
iNT. The final response to the circled stimulus region containing signal dots moving in the target direction was
riT = 〈pref
iT − antipref
iT〉
t (this is a scalar) and similarly for the response to the other region
riNT. Finally, on each trial
i, the model selected the region associated with the largest response between
riT and
riNT as being the target region (i.e., it responded correctly if
riT >
riNT, and incorrectly otherwise). Before being temporally averaged and combined into
r, filter outputs pref and antipref self-normalized their value as follows:
with Δ
t = 3 frames (90 ms) and
k = 2 (this expression for normalization is similar to that used by Schwartz & Simoncelli,
2001). These parameter values were selected following pilot simulations. We used the same self-normalization for antipreferred. We challenged the model with 25 K trials taken directly from the data used with psychophysical observers. The black symbols in
Figure 6 were obtained by simulating the response of a linear amplifier model (Murray, Bennett, & Sekuler,
2005) that uses the empirical classification image as a template. If
F(
d, t) is the empirical classification image, the response corresponding to
SiT (
d, t) on trial
i was simply obtained by template matching
riT =
F(
d, t) ·
SiT (
d, t), and similarly for
SiNT (
d, t) to obtain
riNT. The linear amplifier model chooses the stimulus region associated with largest
r as target (correct when
riT >
riNT).