4.3 Experiment 1b
4.3.3 Method
The apparatus, stimuli and procedures for Experiment 1b were identical to those used in Experi- ment 1a with the exception that a low-pass 1/f3 power law noise background was used instead of
a white noise background (Figure 4.5). A set of 150 pairs of power law images was generated for pairwise correlation value. These were generated by ltering pairs of correlated Gaussian white noise images. The actual correlation of each resulting noise pair was measured, and pairs having correlation values more than 0.01 away from the nominal level were discarded. The standard devi- ation of the noise in the images was the same as for the white noise, 0.22. On each trial, a random pair of images was selected from the pool, and a Gaussian blob was added to one of them.
4.3.4 Observers
Six observers participated in Experiment 1b (two male and four female). Four were inexperienced observers (JR, CA, JN, and AW) but received training prior to commencing the study. GR and WS were the author and author's PhD supervisor and both were experienced psychophysical observers. No observer had a background in radiology or medical physics. All observers had normal or corrected-to-normal vision and each observer conducted a minimum of four sessions, where each session included both symmetry modes and all six correlation levels and took approximately one hour to complete.
4.3.5 Results and discussion
Contrast thresholds for detecting a Gaussian blob were measured as a function of the cross- correlation between the two noise elds presented to the observer. The cross-correlation was a
Figure 4.5: Example mirror-symmetric synthetic mammogram image pairs with low-pass 1/f3
power spectrum noise. From top to bottom, the inter-image correlations are 0, .75, and 1. A Gaussian blob having contrast well above threshold is shown on the left or right.
measure of the level of symmetry present. Thresholds for each correlation value were calculated from the 75% correct point of each observer's psychometric function tted using probit regression. The response on each trial was correct or incorrect, and the probit regression used these binary values. Thus each threshold represents a t to at least 4 blocks of 60 trials = 240 points. Using the relative values of contrast threshold, determined as shown in section 4.2.1.2, the experiment aimed to investigate whether symmetry, either mirror or repeat, aids the observer in the detection of a signal in correlated power law noise elds.
4.3.5.1 Mirror symmetric displays - does symmetry aid the observer in the detection of a signal in mirror symmetric noise elds?
Figure 4.6 shows the relative threshold contrast plotted against correlation for the detection of a signal in mirror symmetric paired power law noise backgrounds for the six observers. The thresholds and 95% con dence intervals obtained by probit regression are shown. Curves were tted using least squares regression of Equation 4.12 and the tted parameters are given in Table 4.3. It is clear from Figure 4.6 that, whilst observers JR and GR do show some improvement, for most real observers' performance does not improve as the correlation between the noise elds increases. Their tted curves are very at compared to the performance of the ideal observer, as shown by the dotted curves.
Power Law Noise Mirror Symmetric Display
Observer k LCL UCL AW 0.10 0.02 0.18 JR 0.39 0.31 0.47 CA -0.03 -0.09 0.03 GR 0.52 0.45 0.59 JN -0.03 -0.09 0.03 WS -0.11 -0.21 -0.01
Table 4.3: The symmetry improvement factor k and 95% con dence limits for the mirror and repeat conditions with a signal in low-pass 1/f3 power law noise for six observers.
As with Gaussian white noise in Experiment 1a, the symmetry improvement factors are much lower than the ideal value of k = 1. As shown in Table 4.3, the tted parameter k has a value that is not statistically dierent from zero for observers JN and CA (k = −0.03 and −0.03 respectively, 95% CIs [-0.09, 0.03] and [-0.09, 0.03], respectively) and slightly positive for AW ((k = 0.1, 95% CIs [0.02, 0.18]). Observers JR and GR show moderately positive values (k = 0.39 and 0.52 respectively, 95% CIs [0.31, 0.47] for observer JR and [0.45, 0.59] for observer GR, and observer WS shows a slightly negative (k = −0.11, 95% CIs [-0.21, -0.01]). A negative value of k means that performance gets worse as the correlation increases. From these data it is clear that mirror
0.0 0.5 1.0 1.5
AW
JR
0.0 0.5 1.0 1.5CA
GR
0.0 0.5 1.0 1.5 0.0 0.5 1.0JN
0.0 0.5 1.0WS
Correlation
Relativ
e Threshold Contr
ast
Figure 4.6: Contrast thresholds for detecting a Gaussian blob relative to that obtained when the correlation is zero plotted as a function of the correlation between the two power law noise elds. The solid curves are least squares ts of Equation 4.12. The noise elds in the image pair had mirror symmetry. Results for six observers are shown. Error bars show 95% con dence intervals. The dotted curve shows the performance for the ideal observer. The real observers' thresholds do not decline as correlation increases, unlike those of the ideal observer.
symmetry provides, at best modest, but in most cases, little or no help when trying to detect a signal in paired noise elds.
4.3.5.2 Repeat symmetric displays - does symmetry aid the observer in the detection of a signal in repeat symmetric noise elds?
The experiment also looked at the eect of symmetry for the repeat displays in the same way as described above. The results of the repeat symmetric condition are shown in gure 4.7. The pattern of results is similar to that in gure 4.6 for the mirror symmetric noise, with ts of Equation 4.12 being markedly at compared to that of the ideal observer (dotted curve).
The values of the symmetry improvement factor (k), derived from the linear regression analysis of the variation of relative threshold contrast with correlation for the detection of a signal in paired power law noise elds displayed in a repeat symmetric format are shown in Table 4.4.
Power Law Noise Repeat Symmetric Display
Observer k LCL UCL AW 0.09 0.04 0.14 JR 0.48 0.27 0.69 CA 0.06 0.00 0.12 GR 0.48 0.38 0.58 JN -0.13 -0.21 -0.05 WS 0.11 0.08 0.14
Table 4.4: The symmetry improvement factor k and 95% con dence limits for the mirror and repeat conditions with a signal in low-pass 1/f3 power law noise for six observers.
Once again, the symmetry improvement factors are much lower than the ideal value of k = 1. As shown in Table 4.4, the tted parameter k has a value that is not statistically dierent from zero for observer CA (k = 0.06 , 95% CIs [0.00, 0.12]) and slightly positive for AW and WS ((k = 0.09 and 0.11 respectively, 95% CIs [0.04, 0.14] and [0.08, 0.14] respectively). Observers JR and GR show moderately positive values (k = 0.48 for both observers, 95% CIs [0.27, 0.69] and [0.38, 0.58], respectively and observer JN shows a slightly negative (k = −0.13, 95% CIs [-0.21, -0.05]). A negative value of k means that performance gets worse as the correlation increases. In all cases, the k values are well below the ideal observer's value of 1. From these data it is clear that repeat symmetry provides, at best modest, but in most cases, little or no help when trying to detect a signal in paired power law noise elds. This tells us that symmetry, be it mirror or repeat, does not provide much help to the observer for the detection of a signal in one of the images.
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AW
JR
0.0 0.5 1.0 1.5CA
GR
0.0 0.5 1.0 1.5 0.0 0.5 1.0JN
0.0 0.5 1.0WS
Correlation
Relativ
e Threshold Contr
ast
Figure 4.7: Contrast thresholds for detecting a Gaussian blob relative to that obtained when the correlation is zero plotted as a function of the correlation between the two power law noise elds. The solid curves are least squares ts of Equation 4.12. The noise elds in the image pair had repeat symmetry. Results for six observers are shown. Error bars show 95% con dence intervals. The dotted curve shows the performance for the ideal observer. The real observers' thresholds do not decline as correlation increases, unlike those of the ideal observer.