Neurophysiological and psychophysical evidence indicates that neuronal surround modulation at cross-orientation (orthogonal to the preferred orientation of the classical receptive field) plays a key role in intermediate-level visual tasks, such as textural segregation and perceptual pop-out. What is missing is a psychophysical description of cross surround modulation at the spatial filter level in low-level vision. Moreover, neurophysiological evidence for how cross surround modulation is expressed at the neuronal level has been inconsistent. Here we report evidence for psychophysical facilitation of contrast detection by cross surround stimuli (orthogonal to the target orientation) that may provide insights into both the neurophysiology and psychophysics of cross surround modulation. We found that cross surround facilitation is a surround-contrast dependent effect mainly evident at low surround contrasts, and is narrowly tuned to spatial frequency and broadly tuned to orientation. To understand whether cross surround facilitation results from low-level processing of signal-to-noise enhancement or is due to uncertainty reduction at a higher-level decision stage, we (1) studied cross surround facilitation with an equivalent noise protocol, (2) estimated the changes in the slope of the psychometric function and the uncertainty parameter, M, and (3) measured cross surround effects at the dipper of the TvC function. The converging evidence suggests that cross surround facilitation of contrast detection is mainly a result of low-level signal-to-noise enhancement, and is little affected by uncertainty change.

^{2}mean luminance, and 3.8° × 3.0° usable screen size at the viewing distance of 5.64 meters. The luminance of the monitor was made linear by a 15-bit look-up table.

_{i}

^{2}+ N

_{e}

^{2})

^{1/2}, where Th is the contrast threshold, N

_{e}is external noise in noise threshold units, and k and N

_{i}are free parameters. Noise threshold is 0.12 for Y.C. and 0.09 for the other two observers. For the TvN functions measured with no surround (simple detection), k is the high noise slope on linear axes and k

^{2}is inversely proportional to efficiency (large k

^{2}indicates poorer efficiency), and N

_{i}is the equivalent internal noise (in noise threshold units). Data fitting indicates that the cross surround reduced both N

_{i}and k (Figure 4b, Table 1). The reduction of k represents a downward shift (facilitation) of the entire TvN curve, and the reduction of N

_{i}accounts for the remaining facilitation at zero and low external noise. For observers S.T. and Y.C., the cross surround/no surround ratio of N

_{i}(R

_{Ni}) is 0.80 ± 0.13 and 0.64 ± 0.07, and the cross surround/no surround ratio of k is 0.72 ± 0.05 and 0.74 ± 0.06, respectively. Because S.T.’s R

_{Ni}reduction is relatively small, most of this observer’s facilitation comes from the change of k, while R

_{Ni}and k have similar contribution to Y.C.’s facilitation.

cross surround | iso surround | ||||
---|---|---|---|---|---|

N_{i} | k | N_{i} | k | ||

ST | AJ | ||||

w/o sur | 1.38 ± 0.13 | 0.022 ± 0.001 | w/o sur | 1.16 ± 0.10 | 0.026 ± 0.001 |

w/ sur | 1.11 ± 0.14 | 0.016 ± 0.001 | w/ sur | 0.62 ± 0.04 | 0.026 ± 0.000 |

YC | YC | ||||

w/o sur | 1.81 ± 0.15 | 0.020 ± 0.001 | w/o sur | 1.73 ± 0.36 | 0.018 ± 0.003 |

w/ sur | 1.16 ± 0.09 | 0.015 ± 0.001 | w/ sur | 0.96 ± 0.22 | 0.018 ± 0.002 |

_{i}but no change of k (Table 1). The iso surrounds here provide not only the same temporal and spatial cues of the target (when, where, and what spatial frequency) as do the cross surrounds (Figure 4a), but also additional orientation and phase cues (it is also easier to compare spatial frequencies of collinear gratings). However, these target cues appear not useful to, or not used by, the visual system to reduce stimulus uncertainty and form a better stimulus template. It is unlikely that a threshold reduction at high noise due to these target cues is offset by iso surround suppression, because the butterfly-shaped iso surrounds at the current contrast (0.10) produce strong facilitation at low noise. On the basis of these iso surround data, we suspect that cross surrounds would have no effect on stimulus uncertainty. Therefore, facilitation at high noise and associated k reduction are mainly contributed by lower-level visual mechanisms, either multiplicative noise reduction or signal enhancement or their combination.

*th*) at the 75% correct level and the slope of the psychometric functions (

*β*). Here

*c*in the equation is the target contrast. A nonlinear least square method (the Matlab lsqnonlin function) was used for optimization. Because of the large run-to-run differences of

*β*within the same observer, we constrained

*β*to be the same across runs, with threshold being variable from run to run. The left half of Table 2 gives each observer’s mean thresholds (weighted mean across individual blocks) and

*β*. Figure 5b shows each observer’s mean percent correct data converted from d’ and the simulated psychometric functions based on each observer’s mean threshold and

*β*under surround and no surround conditions. Table 2 shows cross surround facilitation (reduced contrast threshold) in both observers. For observer J.E.,

*β*is unchanged by the cross surround (1.53 ± 0.19 vs. 1.58 ± 0.18), implying no uncertainty change. However, for observer M.L., β is reduced but the change is not significant (1.83 ± 0.20 vs. 1.53 ± 0.16 with a change of 0.30 ± 0.26). The slope data therefore do not provide strong support for uncertainty reduction in cross surround facilitation.

Weibull fit | M fit | ||||
---|---|---|---|---|---|

threshold | beta | gain | M | ||

JE | baseline | 2.33 ± 0.11 | 1.53 ± 0.19 | 0.50 ± 0.03 | 2.0 ± 1.2 |

cross | 1.75 ± 0.08 | 1.58 ± 0.18 | 0.65 ± 0.04 | 1.9 ± 1.1 | |

ML | baseline | 2.37 ± 0.10 | 1.83 ± 0.20 | 0.64 ± 0.04 | 6.0 ± 3.6 |

cross | 1.84 ± 0.07 | 1.53 ± 0.16 | 0.65 ± 0.03 | 1.9 ± 1.0 |

*c*is the target contrast,

*f(x)*is the Gaussian probability density function,

*F(x)*is the cumulative Gaussian,

*k*is the sensitivity or gain parameter, and

*M*is the uncertainty parameter. We used a maximum rule whereby the observer is assumed to choose the interval that contains the maximum response. The first term gives the probability that the channel with the signal has the maximum output; the second term is the probability that a noise channel in the signal interval has maximum output. The data were fit by a method similar to that used for fitting the Weibull function. There were as many gain parameters (gain is the theoretical sensitivity when

*M*= 1) as there were repeated runs for a given surround condition. An additional parameter specified

*M*, the number of attended channels on each stimulus presentation. The weighted mean of the gain parameters and uncertainty parameters for each observer are listed in the right half of Table 2. Figure 5c shows each observer’s mean percent correct data and the simulated psychometric functions based on each observer’s mean gain and

*M*values. Results show unchanged

*M*(2.0 ± 1.2 vs. 1.9 ± 1.1) for J.E. and insignificantly reduced

*M*(6.0 ± 3.6 vs. 1.9 ± 1.0) for M.L. because of the large errors, again not supporting a significant uncertainty reduction in cross surround facilitation. Meanwhile, the gain is increased for observer J.E. (from 0.50 ± 0.03 to 0.65 ± 0.04) but unchanged for observer M.L. (0.64 ± 0.04 vs. 0.65 ± 0.03).