Chapter 2 Visual-Haptic Compliance Perception

Traditional psychophysical methods are so-called because some physical dimension is carefully manipulated while people make judgments of its psychological impact (see Chap.1). Typical psychophysical measures are: the detection threshold (minimumstimulus intensity required for conscious perception), the discrimination threshold or Just Noticeable Difference (JND; minimum difference in intensity required for discrimination), and parameters of the function relating perceived intensity to physical intensity across a range of values on the target dimension. Early attempts to measure these psychophysical variables tended to focus on univariate quantities. Thus, for example, one can find values for the threshold intensity of physical dimensions such as length, brightness, or weight, as well as other quantitative dimensions with less obvious physical interpretations such as salt dilution or voltage of a current applied to the skin (see Woodworth and Schlossberg 1960). One can also find, from so-called magnitude estimation tasks, that perceived stimulus magnitude tends to be related to physical signal intensity in the form of a logarithmic function (Fechner 1860) or a power function, the exponent of which provides a summary measure of the perceptual transduction output for a given dimension (Stevens 1975). The present chapter focuses on stiffness, the mathematical inverse of compliance. Stiffness is inherently a higher-order property, in the sense that it is computed from the relation between two underlying quantities. By Hooke’s Law, stiffness (denoted k) is the relation between displacement (d, change in position or length) and the force that produces that displacement (F), as specified by the equation, F = kd. Given that stiffness is defined by the ratio of two physical variables, force and posi-