On the laws of psychophysics

Experiments by S. S. Stevens (Stevens, 1957, and Stevens and Galanter, 1957) and his collaborators indicate that the so-called logarithmic Weber-Fechner Law is not realized in most human perceptions. Instead, a power law seems to emerge over a large number of sensory continua. This is important because for a long time the logarithmic law was looked upon as almost the only possible psychophysical law. The logarithmic law appeared desirable intuitively because it made the sensation depend on the relative values of the stimuli and not on their absolute values. This is, of course, useful for evolutionary reasons. Some other reasons are also discussed by Stevens (1961).     

All Effects of Psychophysical Variables on Color Attributes: A Classification System

This paper reports the research and structuring of a classification system for the effects of psychophysical variables on the color attributes. A basic role of color science is to psychophysically specify color appearance. An early stage is to specify the effects of the psychophysical variables (as singles, pairs, etc) on the color attributes (as singles, pairs, etc), for example to model color appearance. Current data on effects are often scarce or conflicting. Few effects are well understood, and the practice of naming effects after their discoverer(s) is inadequate and can be confusing. The number and types of possible effects have never been systematically analyzed and categorized. We propose a simple and rigorous system of classification including nomenclature. The total range of effects is computed from the possible combinations of three psychophysical variables (luminance, dominant wavelength, purity) and six color attributes (lightness, brightness, hue, chroma, colorfulness, saturation) in all modes of appearance. Omitting those effects that are normally impossible to perceive at any one time (such as four- or five-dimensional colors), the total number perceivable is 161 types of effects for all modes of appearance. The type of effect is named after the psychophysical stimulus (or stimuli) and the relevant color attribute(s), e.g., Luminance-on-hue effect (traditionally known as Bezold-Brucke effect). Each type of effect may include slightly different effects with infinite variations depending on experimental parameters.     

Foveal information processing at photopic luminances

Summary A tentative model of information processing in the human fovea at photopic luminances is described, that handles both luminosity and chromaticity signals. The model consists of a scaling-ensemble, a group of sealers with common scaling-factor that provide an effective compression of the dynamic range of the input signals. The scaling factor adapts in such a way that the model conforms to Weber's law for the detection of short, small flashes on a bright background. The dynamics of the adaptation is such that the model effectively computes the logarithmic time derivative of the input signal. The model predicts the outcome of several psychophysical experiments. The predictions include Weber's law, Bloch's law, the apparent brightness of suprathreshold flashes as a function of adaptation level, the influence of spatial inhomogeneities on the perception of flicker, and the transfer function for moving sinusoidal bar patterns for both luminosity and chromaticity modulations. The influence of involuntary eye-movements on the perception of spatial patterns is also discussed. Finally an attempt is made to locate the components of the model in the anatomical structure of the retina. A tentative scheme of neural connections in the human fovea is presented.     

A neurocomputational model for optimal temporal processing

Humans can estimate the duration of intervals of time, and psychophysical experiments show that these estimations are subject to timing errors. According to standard theories of timing, these errors increase linearly with the interval to be estimated (Weber's law), and both at longer and shorter intervals, deviations from linearity are reported. This is not easily reconciled with the accumulation of neuronal noise, which would only lead to an increase with the square root of the interval. Here, we offer a neuronal model which explains the form of the error function as a result of a constrained optimization process. The model consists of a number of synfire chains with different transmission times, which project onto a set of readout neurons. We show that an increase in the transmission time corresponds to a superlinear increase of the timing errors. Under the assumption of a fixed chain length, the experimentally observed error function emerges from optimal selection of chains for each given interval. Furthermore, we show how this optimal selection could be implemented by competitive spike-timing dependent plasticity in the connections from the chains to the readout network, and discuss implications of our model on selective temporal learning and possible neural architectures of interval timing.     

The validity of the equiratio taste mixture model investigated with sorbitol-sucrose mixtures

The equiratio taste mixture model developed and shown to bevalid for glucose-fructose mixtures was investigated in orderto assess its applicability to two-component mixtures of othersweet substances. A magnitude estimation experiment using thesip and spit procedure determined psychophysical functions forsorbitol, sucrose and three equiratio sorbitol-sucrose mixtures.Mixture functions determined on the basis of the experimentaldata were very similar to those predicted by the model. Thepsychophysical functions for sucrose and the sorbitol-sucrosemixtures showed slight downward curvature. As these deviationsfrom the power law affect the predictive validity of the model,potential factors causing these curvatures are discussed.     

Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex

Whether cognitive representations are better conceived as language-based, symbolic representations or perceptually related, analog representations is a subject of debate. If cognitive processes parallel perceptual processes, then fundamental psychophysical laws should hold for each. To test this, we analyzed both behavioral and neuronal representations of numerosity in the prefrontal cortex of rhesus monkeys. The data were best described by a nonlinearly compressed scaling of numerical information, as postulated by the Weber-Fechner law or Stevens' law for psychophysical/sensory magnitudes. This nonlinear compression was observed on the neural level during the acquisition phase of the task and maintained through the memory phase with no further compression. These results suggest that certain cognitive and perceptual/sensory representations share the same fundamental mechanisms and neural coding schemes.     

A theory for the use of visual orientation information which exploits the columnar structure of striate cortex

A neural model is constructed based on the structure of a visual orientation hypercolumn in mammalian striate cortex. It is then assumed that the perceived orientation of visual contours is determined by the pattern of neuronal activity across orientation columns. Using statistical estimation theory, limits on the precision of orientation estimation and discrimination are calculated. These limits are functions of single unit response properties such as orientation tuning width, response amplitude and response variability, as well as the degree of organization in the neural network. It is shown that a network of modest size, consisting of broadly orientation selective units, can reliably discriminate orientation with a precision equivalent to human performance. Of the various network parameters, the discrimination threshold depends most critically on the number of cells in the hypercolumn. The form of the dependence on cell number correctly predicts the results of psychophysical studies of orientation discrimination. The model system's performance is also consistent with psychophysical data in two situations in which human performance is not optimal. First, interference with orientation discrimination occurs when multiple stimuli activate cells in the same hypercolumn. Second, systematic errors in the estimation of orientation can occur when a stimulus is composed of intersecting lines. The results demonstrate that it is possible to relate neural activity to visual performance by an examination of the pattern of activity across orientation columns. This provides support for the hypothesis that perceived orientation is determined by the distributed pattern of neural activity. The results also encourage the view of neural activity. The results also are determined by the responses of many neurons rather than the sensitivity of individual cells.     

A model for signal detection based on an adaptive filter

A model for the detection of brief stimuli based on a change detection algorithm and a random walk traversed by the residuals generated by an adaptive filter is proposed. A linear relationship between mean RT and response proportion measures obtained in a simulation of the model was consistent with data obtained in psychophysical discrimination tasks using human observers. In this way the role of the sensory system as a detector of change in ambient stimulation could be incorporated into a signal detection model.     

The Effect of Stimulus Duration on Frequency-Response Functions in the Pacinian (P) Channel

Psychophysical experiments on human observers and physiological measurements on Pacinian corpuscles (PCs) isolated from cat mesentery were performed to explain certain discrepancies in the psychophysical—physiological model (Bolanowski et al., 1988) for the sense of touch in the vibrotactle Pacinian (P) channel. The model was based on correlations among the psychophysical frequency response obtained on human glabrous skin and physiological frequency-response functions measured on two PC preparations: PC fibers innervating human glabrous skin (Johansson et al., 1982) and PCs isolated from cat mesentery. The three frequency-response functions were qualitatively similar. However, the low-frequency slope for the human PC fibers differed from the slopes for the psychophysical and cat mesentery PC functions by being 3 dB/octave less steep. This discrepancy can be explained theoretically by differences in methodology involving the effect of stimulus duration and the property of temporal summation known to exist in the P channel (i.e., a 3-dB increase in sensitivity per doubling of stimulus duration). To test this, experiments were performed using two methods of stimulation: (1) a constant stimulus duration for different test frequencies, as generally used in this laboratory; and (2) a constant number of stimulus cycles (n = 5) for each test frequency as used by Johansson et al. The method of least squares was used to calculate the low-frequency (50 to 150-Hz) slopes of individual psychophysical and physiological functions. The mean slopes that resulted from using the two methods of stimulation were consistent with the theoretical expectations.     

Modelling fast forms of visual neural plasticity using a modified second-order motion energy model

The Adelson-Bergen motion energy sensor is well established as the leading model of low-level visual motion sensing in human vision. However, the standard model cannot predict adaptation effects in motion perception. A previous paper Pavan et al.(Journal of Vision 10:1–17, 2013) presented an extension to the model which uses a first-order RC gain-control circuit (leaky integrator) to implement adaptation effects which can span many seconds, and showed that the extended model’s output is consistent with psychophysical data on the classic motion after-effect. Recent psychophysical research has reported adaptation over much shorter time periods, spanning just a few hundred milliseconds. The present paper further extends the sensor model to implement rapid adaptation, by adding a second-order RC circuit which causes the sensor to require a finite amount of time to react to a sudden change in stimulation. The output of the new sensor accounts accurately for psychophysical data on rapid forms of facilitation (rapid visual motion priming, rVMP) and suppression (rapid motion after-effect, rMAE). Changes in natural scene content occur over multiple time scales, and multi-stage leaky integrators of the kind proposed here offer a computational scheme for modelling adaptation over multiple time scales.     

Receptor noise as a determinant of colour thresholds.

Inferences about mechanisms at one particular stage of a visual pathway may be made from psychophysical thresholds only if the noise at the stage in question dominates that in the others. Spectral sensitivities, measured under bright conditions, for di-, tri-, and tetrachromatic eyes from a range of animals can be modelled by assuming that thresholds are set by colour opponency mechanisms whose performance is limited by photoreceptor noise, the achromatic signal being disregarded. Noise in the opponency channels themselves is therefore not statistically independent, and it is not possible to infer anything more about the channels from psychophysical thresholds. As well as giving insight into mechanisms of vision, the model predicts the performance of colour vision in animals where physiological and anatomical data on the eye are available, but there are no direct measurements of perceptual thresholds. The model, therefore, is widely applicable to comparative studies of eye design and visual ecology.     

A model of the perception of area.

A psychophysical experiment was performed to measure the ability of human observers to compare the areas of two geometrical figures (squares and rectangles). The results show a systematic overestimation of rectangle area with respect to that of the squares. A formal model of area perception and its consequent estimation is proposed, which is based on the concept of an 'image function'. It assumes that not the original figure but some specific isocline defined on the image function surface determines area perception. The systematic error observed in the experiment is explained by the model. We discuss the role of different definitions of the image function as well as its parameters on the model performance.     

Signal transmission through a metabolic cycle follows the compression hypothesis or a weak Weber's law

Biological signal transduction often involves a metabolic cycle in which the flux at one point is driven by the input signal and the concentration of one of the metabolites of the cycle serves as the output signal. A kinetic analysis of such a metabolic cycle is made under an assumption that the law of mass action applies. The resultant kinetic model can produce a response that overshoots, quickens, and eventually saturates as the input intensity is increased. The possible model behavior ranges parametrically from non-adaptive (compression hypothesis) to weakly adaptive (limited Weber's law).     

Determination of saltiness from the laws of thermodynamics--estimating the gas constant from psychophysical experiments

One can relate the saltiness of a solution of a given substance to the concentration of the solution by means of one of the well-known psychophysical laws. One can also compare the saltiness of solutions of different solutes which have the same concentration, since different substances are intrinsically more salty or less salty. We develop here an equation that relates saltiness both to the concentration of the substance (psychophysical) and to a distinguishing physical property of the salt (intrinsic). For a fixed standard molar entropy of the salt being tasted, the equation simplifies to Fechner's law. When one allows for the intrinsic 'noise' in the chemoreceptor, the equation generalizes to include Stevens's law, with corresponding decrease in the threshold for taste. This threshold reduction exemplifies the principle of stochastic resonance. The theory is validated with reference to experimental data.     

A transduction model of the Meissner corpuscle

I propose a transduction model of the Meissner corpuscle that integrates ideas put forth by Freeman and Johnson and results obtained by Looft. The principal development in the present model is its specification that RA receptor potentials are updated as a linear function of stimulus velocity above baseline; the model thus readily accommodates non-sinusoidal input. It also incorporates modifications to Freeman and Johnson's model proposed by Slavík and Bell, namely a period of refractoriness lasting 1 ms followed by a period of hyperexcitability lasting 13.5 ms. The model is applied to various psychophysical and physiological situations: psychophysical threshold vs. frequency, RA afferent impulse rates vs. intensity, impulse regularity vs. frequency, phase retardation vs. frequency, and responses to non-repeating noise and to complex stimuli. Model output closely matches psychophysical and neurophysiological data. The proposed model thus reliably predicts RA afferent responses to arbitrary stimuli and may facilitate the development of theories relating psychophysical phenomena to their underlying neural representations.     

The generation of handwriting with delta-lognormal synergies

This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy trade-offs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law. Received: 22 July 1996 / Accepted in revised form: 15 September 1997     

Population-response model for vibrotactile spatial summation

A computational model based on previous physiological and psychophysical data is presented for the human Pacinian (P) psychophysical channel. The model can predict the probability of detection in simple psychophysical tasks, and hence psychometric functions and thresholds. The model simulates stimulating variable and fixed glabrous skin sites with different-sized contactors and includes spatial variation of monkey P-fiber sensitivities. Therefore, it is especially suitable for studying spatial summation, i.e. the improvement of threshold with increasing contactor area. Selective contributions of neural integration (n.i.) and probability summation (p.s.) are also incorporated into the model. Model predictions are compared to psychophysical results of Gescheider et al. (). The performance of the model regarding the effects of contactor size is very good. In addition to predicting approximately 3?dB improvement of thresholds when the contactor area is doubled, the model also reveals nonlinear contributions of p.s. and n.i. Furthermore, the model asserts that thresholds are largely governed by neural integration when small contactors are used. These and other findings discussed in the article show that the presented model is a helpful tool for formulating testable hypotheses. Although the model can also simulate some temporal summation effects, simulation results do not conform well to previous data on temporal response properties. Thus, the model needs to be refined in that respect.     

Population-response model for vibrotactile spatial summation

A computational model based on previous physiological and psychophysical data is presented for the human Pacinian (P) psychophysical channel. The model can predict the probability of detection in simple psychophysical tasks, and hence psychometric functions and thresholds. The model simulates stimulating variable and fixed glabrous skin sites with different-sized contactors and includes spatial variation of monkey P-fiber sensitivities. Therefore, it is especially suitable for studying spatial summation, i.e. the improvement of threshold with increasing contactor area. Selective contributions of neural integration (n.i.) and probability summation (p.s.) are also incorporated into the model. Model predictions are compared to psychophysical results of Gescheider et al. (2005). The performance of the model regarding the effects of contactor size is very good. In addition to predicting approximately 3 dB improvement of thresholds when the contactor area is doubled, the model also reveals nonlinear contributions of p.s. and n.i. Furthermore, the model asserts that thresholds are largely governed by neural integration when small contactors are used. These and other findings discussed in the article show that the presented model is a helpful tool for formulating testable hypotheses. Although the model can also simulate some temporal summation effects, simulation results do not conform well to previous data on temporal response properties. Thus, the model needs to be refined in that respect.     

An Equiratio Mixture Model for Non-additive Components: A Case Study for Aspartame/Acesulfame-K Mixtures

The Equiratio Mixture Model predicts the psychophysical functionfor an equiratio mixture type on the basis of the psychophysicalfunctions for the unmixed components. The model reliably estimatesthe sweetness of mixtures of sugars and sugar-alchohols, butis unable to predict intensity for aspartame/sucrose mixtures.In this paper, the sweetness of aspartame/acesulfame-K mixturesin aqueous and acidic solutions is investigated. These two intensivesweeteners probably do not comply with the model's originalassumption of sensory dependency among components. However,they reveal how the Equiratio Mixture Model could be modifiedto describe and predict mixture functions for non-additive substances. To predict equiratio functions for all similar tasting substances,a new Equiratio Mixture Model should yield accurate predictionsfor components eliciting similar intensities at widely differingconcentration levels, and for substances exhibiting hypo- orhyperadditivity. In addition, it should be able to correct violationsof Stevens's power law. These three problems are resolved ina model that uses equi-intense units as the measure of physicalconcentration. An interaction index in the formula for the constantaccounts for the degree of interaction between mixture components.Deviations from the power law are corrected by a nonlinear responseoutput transformation, assuming a two-stage model of psychophysicaljudgment. Chem. Senses 21: 1–11, 1996.