4.4.1 Contrast sensitivity across the central visual field
-18 -12 -6 0 Normalised sensitivity (dB) e) f) DHB -18 -12 -6 0 6 12 18
Eccentricity (carrier cycles)
-18 -12 -6 0 g) -18 -12 -6 0 6 12 18 h) Horizontal Left oblique Right oblique Vertical -18 -12 -6 0 Normalised sensitivity (dB) a) b) ASB -18 -12 -6 0 6 12 18
Eccentricity (carrier cycles)
-18 -12 -6 0 c) -18 -12 -6 0 6 12 18 d) Horizontal Left oblique Right oblique Vertical
Figure 4.3: Contrast sensitivity data from Experiment 1 for observers ASB (left) and DHB (right), normalised to the observer’s sensitivity at fixation. The separate plots show the sensitivity data for the detection of a 4 c/deg log-Gabor patch for each meridian, as indicated by the diagram in each plot. The four sets of symbols show data from the different stimulus orientations (as indicated in the legend). Eccentricity is expressed in stimulus carrier cycles, the visual angle of the range shown here is +4.5 degrees to -4.5 degrees along each meridian. Error bars in this figure (and in all subsequent figures) show ±1 standard error where visible. Where they are not visible this is due to their being smaller than the symbol size.
The contrast sensitivity along the eight tested hemi-meridians for two observers can be seen in Figure 4.3. In agreement with previous findings, the sensitivity is greatest at fixation, and
Individual hemi-meridian fall-off fits (dB/cycle)
Angle 0◦ 180◦ 90◦ 270◦ 45◦ 135◦ 225◦ 315◦
ASB 0.72 0.65 0.55 0.55 0.61 0.64 0.65 0.59
DHB 0.79 0.92 0.79 0.74 0.70 0.90 0.86 0.84
Average Vertical Horizontal Diagonal
ASB 0.69 ±0.04 0.55 ±0.00 0.62 ±0.01
DHB 0.86 ±0.07 0.77 ±0.03 0.83 ±0.04
Table 4.2: Log-contrast sensitivity decline gradient (in dB) for linear fits to Experiment 1 data. Averages are given as the mean ±1 standard error.
the decline is steeper along the vertical meridian than along the horizontal meridian. The di- agonal meridians appear to show declines in sensitivity that are intermediate between those for the horizontal and vertical meridians (a point which will be returned to in the modelling). The overall declines were slightly steeper than those found in previous studies, the gradients from a linear fit (y = mx + c, with both m and c allowed to vary freely) are shown in Table 4.2. To test for the absolute and relative orientation effects, a pair of 3-way repeated-measures ANOVA tests was performed using PASW Statistics (version 18.0, IBM) for each observer. The first test was for factors of: eccentricity, hemi-meridian, and absolute patch orientation. The second test was the same, but with patch orientation defined relative to the meridian that the stimulus was placed on. For example, a right oblique patch placed on the 225◦to 45◦meridian
(see Figure 4.3) would have an absolute orientation of 45◦, but a relative orientation of 0◦. Re-
sults from Mauchly’s test of sphericity showed that the ANOVAs that found significant results did not suffer from a violation of sphericity, therefore no correction was required.
4.4.2 Absolute orientation effects
Significant effects of absolute patch orientation were found for both ASB (Mauchly’s test n.s. χ2(5) = 5.45, p = 0.43; ANOVA F
3,9= 11.50, p < 0.01) and DHB (Mauchly’s test n.s. χ2(5) = 4.01,
p= 0.61; ANOVA F3,9 = 5.52, p = 0.02), but were small and not consistent across observers.
ASB was most sensitive to vertical patches and least sensitive to horizontal patches (compare blue and red symbols in panels a-d of Figure 4.3), whereas DHB was most sensitive to horizon- tal patches and least sensitive to left-oblique patches (compare red and magenta symbols in the panels e-h of Figure 4.3).
In addition to the ANOVA, the absolute orientation effects were further investigated by three paired Bonferroni-corrected t-tests per observer. In the first two tests the thresholds for or- thogonal patch orientations were compared to each other (horizontal against vertical, and left-oblique against right-oblique), paired by eccentricity and hemi-meridian (i.e. comparing the thresholds for orthogonal patches at the same location in the visual field). For these analy- ses, ASB showed significant differences in sensitivity for both comparisons (p < 0.01), whereas
DHB showed no significant difference in either the horizontal vs. vertical (p = 0.24) or the left- vs. right-oblique (p = 0.09) tests. In the third test the results for the two cardinal stimulus orientations (horizontal and vertical) were compared against those for the two oblique ori- entations by averaging the pairs of thresholds from each repetition (i.e. a t-test comparing the average of the horizontal and vertical thresholds against the average of the two oblique thresholds at each of the tested locations in the visual field). For ASB there was a small dif- ference (0.13 dB) between the thresholds of the cardinal and oblique patches, however this was not significant (p = 0.23). For DHB the oblique effect was larger (0.66 dB) and achieved significance (p < 0.01).
The oblique effect reported here is smaller than that found previously at higher spatial fre- quencies (e.g. Campbell et al., 1966, found effects of 2 - 6 dB for spatial frequencies in the range of 10 - 30 c/deg) but consistent with that found at similar spatial frequencies to those tested here (see also Long & Tuck, 1991). Based on the findings here it is concluded that for these stimulus conditions the absolute orientation effects were of little concern, since when they were statistically significant they were inconsistent across observers and small in size.
4.4.3 Relative orientation effects
Comparing the mean contrast detection threshold of patches aligned with the meridian they were placed on with that of patches having the orthogonal orientation, I found a small radial advantage for both ASB (0.25 dB) and DHB (0.56 dB). The ANOVA that tested relative orienta- tion (across all four orientations) found this effect to be non-significant for ASB (ANOVA F3,9
= 1.54, p = 0.27), but significant for DHB (Mauchly’s test n.s. χ2(5) = 0.44, p > 0.99; ANOVA F 3,9
= 4.07, p = 0.04). However, despite the overall significant result on the ANOVA for DHB there were no significant pairwise comparisons across aligned and orthogonal patches.
Previous studies that have reported an effect of relative orientation (e.g. Rovamo et al., 1982; Sasaki et al., 2006) investigated greater eccentricities (25 deg and 15.5 deg, respectively) than those tested here, so it is possible that relative orientation effects might become stronger with increasing eccentricity. If this were the case within the tested eccentricity range for Exper- iment 1, then it would appear in the two-way interaction between eccentricity and relative orientation. The results of this analysis however did not show a significant effect for either observer (ASB: ANOVA F6,18= 0.59, p = 0.74; DHB: ANOVA F6,18= 2.09, p = 0.11).
4.4.4 Results for vertical stimuli
The lack of substantial and consistent differences in sensitivity to patches of different orien- tations means that the contrast sensitivity findings for just one patch orientation can be gen- eralised across all patch orientations within the region of interest. Two additional observers
a)
b)
Figure 4.4: Contrast sensitivity across the cardinal meridians for all four observers. Ver- tical log-Gabor stimuli with a spatial frequency of 4 c/deg were used. The black dashed lines presented here for comparison are the gradients for the vertical (0.5 dB/cycle) and horizontal (0.33 dB/cycle) meridians reported by Pointer and Hess (1989).
(SAW and TSM) performed a subset of conditions from Experiment 1. Their data, for vertical patches in the horizontal and vertical meridians, can be seen in Figure 4.4 along with the data from ASB and DHB for those conditions (replotted from Figure 4.3). The sensitivity decline gradients reported previously by Pointer and Hess (1989) are shown by the dashed lines in Figure 4.4. A comparison of these lines with the data from this study shows that the rate of decline found here is considerably steeper than that reported by Pointer and Hess (1989). In Figures 4.3 and 4.4 it appears that the decline in log contrast sensitivity with distance from fixation is non-linear. For most observers and hemi-meridians there is a steep initial decline followed by a shallower slope. However the sampling for this dataset is not sufficiently fine to either support this interpretation over other nonlinear declines, or to pin down the location of the transition between these two slopes (the “knee-point”, see the Modelling section) beyond placing it within the first 18 cycles (4.5 degrees). The shape of the decline, the location of the knee-point, and whether the position of the transition is based on periods of the stimulus or absolute position on the retina will be investigated in the results from Experiments 2 and 3.