Luminance discrimination, color contrast, and multiple mechanisms

Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties

Visual detection and discrimination thresholds are often measured using adaptive staircases, and most studies use transformed (or weighted) up/down methods with fixed step sizes--in the spirit of Wetherill and Levitt (Br J Mathemat Statist Psychol 1965;18:1-10) or Kaernbach (Percept Psychophys 1991;49:227-229)--instead of changing step size at each trial in accordance with best-placement rules--in the spirit of Watson and Pelli (Percept Psychophys 1983;47:87-91). It is generally assumed that a fixed-step-size (FSS) staircase converges on the stimulus level at which a correct response occurs with the probabilities derived by Wetherill and Levitt or Kaernbach, but this has never been proved rigorously. This work used simulation techniques to determine the asymptotic and small-sample convergence of FSS staircases as a function of such parameters as the up/down rule, the size of the steps up or down, the starting stimulus level, or the spread of the psychometric function. The results showed that the asymptotic convergence of FSS staircases depends much more on the sizes of the steps than it does on the up/down rule. Yet, if the size delta+ of a step up differs from the size delta- of a step down in a way that the ratio delta-/delta+ is constant at a specific value that changes with up/down rule, then convergence percent-correct is unaffected by the absolute sizes of the steps. For use with the popular one-, two-, three- and four-down/one-up rules, these ratios must respectively be set at 0.2845, 0.5488, 0.7393 and 0.8415, rendering staircases that converge on the 77.85%-, 80.35%-, 83.15%- and 85.84%-correct points. Wetherill and Levitt's transformed up/down rules--which require delta-/delta+ = 1--and the general version of Kaernbach's weighted up/down rule--which allows any delta-/delta+ ratio--fail to reach their presumed targets. The small-sample study showed that, even with the optimal settings, short FSS staircases (up to 20 reversals in length) are subject to some bias, and their precision is less than reasonable, but their characteristics improve when the size delta+ of a step up is larger than half the spread of the psychometric function. Practical recommendations are given for the design of efficient and trustworthy FSS staircases.

Color and luminance detection and discrimination asymmetries and interactions

We investigated the nature of color and luminance processes under threshold and suprathreshold conditions in normal trichromatic observers. Detection and discrimination contours as well as threshold-vs-contrast (Tvc) functions were measured in the Derrington-Krauskopf-Lennie (DKL) color space using a masking paradigm. Such contours revealed substantial threshold asymmetries along the three cardinal axes for excursions of opposite polarity along a single axis (e.g. "red" vs "green"). The detection threshold asymmetry was significant for the "blue" and "yellow" (P < 0.05) and luminance increments and decrements (P < 0.01). For suprathreshold discrimination contours the polarity of these asymmetries reversed but remained significant for "blue" and "yellow" (P < 0.001) and luminance increments and decrements (P < 0.01). No significant differences were found between the "red" and "green" cardinal axes under either condition. The discrimination contours also indicated that suprathreshold performance had variable masking along the different axes. A characteristic Tvc curve was found in all cardinal directions except "yellow". The Tvc for "yellow" differed from the other cardinal directions by showing no masking after the initial facilitation and by giving a greater saturating response as a function of contrast. We considered whether the state of retinal adaptation had any role in producing the asymmetries.

Colour and luminance interact to improve pattern recognition

The authors have previously hypothesised that colour vision has evolved not only to encode colour per se but also, perhaps principally, to enhance luminance-based visual processing so that for colour information to be fully effective, luminance as well as chromatic variations should be present in visual targets. Results of previous experiments, testing detection of spatial gratings and detection and perceived brightness of Mach bands support the hypothesis. Further experiments are reported in which the hypothesis was tested by using a higher-level task of pattern recognition. Subjects had to discriminate between luminance (isochromatic), isoluminant (chromatic), or combined colour/luminance ellipses and circles. It was found that the ability to discriminate between a circle and an ellipse was greatly enhanced when both colour and luminance variations were present as compared with the pure luminance or colour presentations. Summation-square analysis shows linear colour-luminance summation which can be modeled by a single-analyser model.