Lateral effects in pattern vision

Abstract

There is a large literature on lateral effects in pattern vision but no consensus about them or comprehensive model of them. This paper reviews the literature with a focus on the effects of parallel context in the central fovea. It describes seven experiments that measure detection and discrimination thresholds in annular and Gabor-pattern contexts at different separations. It presents a model of these effects, which is an elaboration of Foley's (1994) model. The model describes the results well, and it shows that lateral context affects the response to the target by both multiplicative excitation and additive inhibition. Both lateral effects extend for several wavelengths beyond the target. They vary in relative strength, producing near suppression and far enhancement of the response to the target. The model describes the detection and discrimination results well, and it also describes the results of experiments on lateral effects on perceived contrast. The model is consistent with the physiology of V1 cells.

Figure 1

A sketch of some TvCp function types for contrast discrimination, without and with lateral context, found in the literature. All are for the case in which context is parallel to and collinear with the target. The horizontal axis is pedestal contrast, and the vertical axis is target contrast threshold. There are logarithmic decibel scales on both axes. The black curve is the TvCp function when there was no lateral context. The other curves correspond to four different function forms found in the literature. The legend indicates the source, year, center-to-center separation in wavelengths, and context contrast. Other factors, including spatial frequency, vary.

Figure 2

Left: patch size experiment. The leftmost stimulus just fills sRFhigh. Right: encroaching annulus experiment. Here the center grating radius was 0.1°, and the innermost radius of the surround was 0.4°. Far surround enhancement was maximum about 6° away. The contrasts on the right are H: 0.7 and L: 0.4. The first symbol is the test contrast, and the second symbol is the annulus contrast. From Ichida et al. (2007). Reprinted with permission.

Figure 3

The response of two sample V1 cells to a center contrast in sRFhigh in the presence of a surround abutting sRFlow. The surround contrasts of 0, 0.03, 0.06, 0.12, 0.25, and 0.5 are indicated by data points from light to dark. As surround contrast increases, the response function decreases and changes shape. From Cavanaugh et al. (2002a). Reprinted with permission.

Figure 4

Examples of the stimuli used in the experiments. Top: disk target with annular context. Bottom: Gabor target with Gabor context. The spatial frequency was 4 c/°. The width of the annuli varied over experiments. The standard deviation of the Gabor patterns was 0.15° (0.6 wavelength) except in Experiment 5. In two of the experiments, the separation between target and context varied.

Figure 5

Experiment 1. Mean target contrast threshold over four observers as a function of surround contrast. The TvCp function (black) is shown for comparison. The parameter is the center-to-center separation of the surround from the target in wavelengths. The mean standard error of these group mean thresholds is 0.57 dB.

Figure 6

Experiment 2. Mean target contrast threshold over four observers as a function of flanker contrast. The parameter is the center-to-center separation of the flankers from the target in wavelengths. The observers were the same as in Experiment 1. The TvCp function (black) is shown for comparison. The threshold for each observer was measured in four to six QUEST sequences. The mean standard error of these group mean thresholds is 0.47 dB.

Figure 7

Experiment 3. Mean target threshold over five observers as a function of pedestal contrast. The parameter is annulus contrast. Data points correspond to the mean threshold over five observers, all different from the observers in the first two experiments. The threshold for each observer was measured in seven Quest sequences. The standard error of these group mean thresholds is 1.1 dB.

Figure 8

Experiment 4. Mean target threshold over four observers as a function of pedestal contrast. The observers were the same four that were in Experiments 1 and 2. The parameter is annulus contrast. Data points correspond to the mean threshold over the four observers. The threshold for each observer was measured in five to seven Quest sequences. The mean standard error of these group mean thresholds is 0.40 dB.

Figure 9

Experiment 5. Mean target threshold over four observers as a function of pedestal contrast. The observers were the same four that were in Experiments 1 and 2. The parameter is flanker contrast. Data points correspond to the mean threshold over the four observers. The threshold for each observer was measured in five to seven Quest sequences. The mean standard error of these data points is 0.57 dB.

Figure 10

Experiment 6. Mean target threshold over three observers as a function of annulus contrast. The parameter is annulus width in cycles of the grating frequency. The corresponding mid-radii are 0.75, 1.25, and 2.75 wavelengths. Data points correspond to the mean threshold over three of the four observers in Experiment 1. The threshold for each observer was measured in four to six Quest sequences. The pedestal alone TvCp function is shown for comparison. The standard error of these group mean thresholds is 0.85 dB. The pedestal data are from Experiment 1.

Figure 11

Experiment 7. Mean target contrast threshold as a function of disk mask contrast for three sizes of disk mask. The smallest disk mask is the same size as the target. There were six observers, all different from the observers in the other experiments. For each observer, each threshold was measured in four to six Quest sequences. The mean standard error was 0.57 dB.

Figure 12

Sensitivity parameters and as a function of separation. Left: Experiment 1, disk and annulus. Right: Experiment 2, Gabor pattern with Gabor flankers.

Figure 13

Response functions in the four experiments in which both pedestal contrast and context contrast vary. The response function changes form as the context moves away from the target. Abutting context is suppressive except at high pedestal contrasts. Remote context is enhancing. In Experiment 7, the disk mask consists of a pedestal and an abutting annulus of the same contrast. Here and the response to the target varies with this contrast. The Experiment 7 graph shows the response to a target superimposed on a mask of contrast 0.3.

Figure 14

Response functions for the Xing and Heeger model. The parameters are a = 0.01, p = 2.4, q = 2.0, = 0.1, pe = 0.1, = 0.6, and qi = 1. Here contrast is expressed as percentage contrast. The parameter k sets the response scale. Here, it is arbitrarily set to 0.4.