In the study, we added external Gaussian noise of various intensities to the target (
Figure 4a, see figure legend for details of noise properties) and measured TvN (thresholds vs. noise) functions (
Figure 4b) with and without the presence of cross surrounds. Results (
Figure 4b) indicate contrast facilitation at all levels of external noise, though the effects are smaller when noise is intense. To characterize internal noise and efficiency changes, we fit the data with the function Th = k(N
i2 + N
e2)
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.