The Integration of Color-Selective Mechanisms in Symmetry Detection

We studied how the visual system detects multicolor symmetric patterns by manipulating the number of colors in an image in both isoluminance and luminance conditions. With a two-interval forced choice noise masking paradigm, we presented a noise mask in both intervals of each trial. A vertically symmetric target was randomly presented in one interval while a noise control was presented in the other. The task of the observers was to determine which interval contained the target. The target detection threshold was measured at various noise mask densities, which was found to decrease 1.4- to 2.5-fold as the number of colors in the image went up at median to high noise densities across different conditions. In addition, this color facilitation effect was greater in luminance conditions than in isoluminance conditions. Our data cannot be explained by the probability summation theory or simple signal-to-noise ratio. We therefore propose a computational model that incorporates a linear chromatic symmetry register, a nonlinear transducer response, noise manipulation and a multiple channel decision making process. This model suggests that the increment of the number of colors reduces the interference to the symmetry channels produced by noise, and in turn facilitates symmetry detection.

observer to detect symmetry in a two-color pattern with a signal-to-noise ratio of 0.84*k/2 in each color. Sum up the color components, and the threshold for the 2color pattern at a given noise density should be about 0.84 times, or 0.076 log units, lower than for the 1-color pattern. Similarly, the threshold for the 4-color pattern should be about 0.15 log units lower than for the 1-color pattern.

Supplementary Method
Threshold Measurement 2 To ensure that our result would not be contaminated by a difference in salience or sensitivity to early visual features, we set the contrast of each color component at three times its detection threshold. We used a temporal 2IFC paradigm to measure the contrast threshold for symmetry detection in the colors used in the experiment for each observer. In each trial, a vertical symmetric target was randomly presented in one of the two intervals while a balancing control was presented in the other. The density of both images was 1%. The duration was 233ms and the inter-stimulus interval (ISI) was 600ms. An audio tone indicated the beginning of each interval. The observers' task was to judge which interval contained a vertical symmetric pattern.
An audio feedback was provided for the response. The PSI threshold-seeking algorithm 5 was used to determine the contrast level for each trial and to measure the threshold at 75% correct level. There were 40 trials for each threshold measurement.
The threshold was an average of 4 to 10 measurements. The order of the tested colors was randomized.
With this measurement, we got the contrast threshold for each color for each observer. In the experiment, we set the contrast of each color at three times its threshold for each observer based on this measurement.

Model Implementation
Our experiment used a 2IFC design, in which one interval contained a symmetric target and a noise mask (target interval), while the other interval contained a balancing control and a noise mask (non-target interval). In an n-color condition, the target, balancing control, and noise mask contained an equal density of dots in each 3 color. Let the density of the symmetric target and balancing control in the image be D t ', and that of the noise mask be D m '. In the n-color condition, the density of the symmetric target or balancing control of a specific color is thus expressed as D t '/n and that of the noise mask as D m '/n.
The j-th color-selective symmetry channel is excited by a symmetric target or signal of its preferred color. The noise of its preferred color inevitably contains spurious symmetric pairs which occur completely by chance. These spurious pairs should also produce its excitation. However, the density of these pairs is the square of the density of the noise, which is negligible compared to either the symmetric target or noise itself. Therefore, for the sake of simplicity, we did not take the effect of these pairs into consideration in our model. Hence, in the target interval, including the target itself and the mask, the excitation of the j-th symmetry channel in equation (2) was expressed as while in the non-target interval, including the balancing control and the mask, , was zero.
All the image components produce inhibition to the j-th channel, including the symmetric target or signal of its preferred color, the symmetric component of its nonpreferred color, the noise component of its preferred color, and the noise component 4 of its non-preferred color. Here, we set the inhibitory sensitivity to a channel from the image components of its non-preferred color as zero, since our previous paper showed that the presence of dots of one color had little, if any, influence on detecting a symmetric pattern of another color 6 . We also used a typical value of 2 for the power q for the divisive inhibition term [7][8][9] . Hence, equation (5) in the target interval was expressed by while in the non-target interval it was expressed by We fixed the internal noise in the j-th channel,  a