The precision of size constancy

The precision of objective size judgments, made when target disparity changed at random from trial-to-trial, was compared to the precision of angular size judgments made under the same condition. Subjects judged incremental changes in the vertical distance separating a pair of horizontal lines. For the objective judgments (in cm), the angle subtended by the target separation decreased with increasing depth consistent with the natural geometry of physical objects. For the angular judgments (in arc min), the angular separation did not change with disparity. For separations subtending an angle < 10 arc min, objective thresholds were considerably higher than angular thresholds, indicating that size constancy does not function well at small scales. At larger scales (> 20 arc min), the Weber fractions for angular and objective thresholds were nearly equal (approximately 6%) for two of the three subjects. These same two subjects also learned to judge "objective size" when angular subtense systematically increased with increasing depth in an exact inversion of the natural relationship. Although their "anti-constancy" judgments were less precise (approximately 9%) than their constancy judgments, the fact that subjects could learn this task with little practice suggests that constancy itself may be a learned response. Angular thresholds for targets presented only in the fixation plane were significantly lower than the angular thresholds measured with random changes in disparity, showing that observers with normal stereopsis do not have direct access to information about the angle subtended at the retina.