Detection of incremental and decremental bars at different locations across Mach bands and related stimuli

Fixed versus variable internal noise in contrast transduction: The significance of Whittle's data

A longstanding issue in vision research concerns whether the internal noise involved in contrast transduction is fixed or variable in relation to contrast magnitude. Previous attempts to resolve the issue have focused on the analysis of contrast discrimination data, despite the fact that the effects of internal noise on thresholds are necessarily compounded by the shape of the underlying transducer function. An alternative approach is to compare data obtained from a particular class of scaling experiment - one based on a comparison of perceived contrast differences - with data from discrimination experiments gathered across the full range of contrast. Data from two studies by the late Paul Whittle provide the basis for such an analysis, pointing to the conclusion that contrast internal noise is fixed not variable.

Denoising forced-choice detection data

Observers in a two-alternative forced-choice (2AFC) detection task face the need to produce a response at random (a guess) on trials in which neither presentation appeared to display a stimulus. Observers could alternatively be instructed to use a 'guess' key on those trials, a key that would produce a random guess and would also record the resultant correct or wrong response as emanating from a computer-generated guess. A simulation study shows that 'denoising' 2AFC data with information regarding which responses are a result of guesses yields estimates of detection threshold and spread of the psychometric function that are far more precise than those obtained in the absence of this information, and parallel the precision of estimates obtained with yes-no tasks running for the same number of trials. Simulations also show that partial compliance with the instructions to use the 'guess' key reduces the quality of the estimates, which nevertheless continue to be more precise than those obtained from conventional 2AFC data if the observers are still moderately compliant. An empirical study testing the validity of simulation results showed that denoised 2AFC estimates of spread were clearly superior to conventional 2AFC estimates and similar to yes-no estimates, but variations in threshold across observers and across sessions hid the benefits of denoising for threshold estimation. The empirical study also proved the feasibility of using a 'guess' key in addition to the conventional response keys defined in 2AFC tasks.

Some observations on the masking effects of Mach bands

There are 8 cycle/deg ripples or oscillations in performance as a function of location near Mach bands in experiments measuring Mach bands' masking effects on random polarity signal bars. The oscillations with increments are 180 degrees out of phase with those for decrements. The oscillations, much larger than the measurement error, appear to relate to the weighting function of the spatial-frequency-tuned channel detecting the broadband signals. The ripples disappear with step maskers and become much smaller at durations below 25 ms, implying either that the site of masking has changed or that the weighting function and hence spatial-frequency tuning is slow to develop.

Masking effect produced by Mach bands on the detection of narrow bars of random polarity

Difficulties arise in measuring masking by Mach bands because very-low-contrast signals distort the bands. [J. Opt. Soc. Am. A 17, 1147 (2000).] Adding narrow luminance increments (bright bars) in the dark Mach band widens the dark band; adding decrements (dark bars) narrows the dark band, and conversely in the bright bands. Randomizing signal polarity prevents observers from using the distortion of the Mach bands as a cue to the presence of the signal. We measured (two-alternative-forced-choice) Mach bands' masking of randomly selected bright (incremental) or dark (decremental) bars. Detection was worse in both dark and bright Mach bands than on the neighboring plateaus. Separate analysis of trials containing only one polarity signal revealed 9-cycle/deg oscillations in performance as a function of location. Oscillations in the two polarities were approximately 180 degrees out of phase.

Masking effects of low-frequency sinusoidal gratings on the detection of contrast modulation in high-frequency carriers

A modification and extension of Kortum and Geisler's model [Vision Res. 35, 1595 (1995)] of early visual non-linearities that incorporates an expansive nonlinearity (consistent with neurophysiological findings [Vision Res. 35, 2725 (1995)], a normalization based on a local average retinal illumination, similar to Mach's proposal [F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, Calif, 1965)], and a subsequent compression suggested by Henning et al. [J. Opt. Soc. Am A 17, 1147 (2000)] captures a range of hitherto unexplained interactions between a sinusoidal grating of low spatial frequency and a contrast-modulated grating 2 octaves higher in spatial frequency.

Contrast discrimination with pulse trains in pink noise

Detection performance was measured with sinusoidal and pulse-train gratings. Although the 2.09-cycles-per-degree pulse-train, or line, grating contained at least eight harmonics all at equal contrast, it was no more detectable than its most detectable component. The addition of broadband pink noise designed to equalize the detectability of the components of the pulse train made the pulse train approximately a factor of 4 more detectable than any of its components. However, in contrast-discrimination experiments, with a pedestal or masking grating of the same form and phase as the signal and with 15% contrast, the noise did not affect the discrimination performance of the pulse train relative to that obtained with its sinusoidal components. We discuss the implications of these observations for models of early vision, in particular the implications for possible sources of internal noise.