Weber's Law Research Articles

Effect of pre‐receptor filters on chromatic sensitivity and other visual functions in the eye

Spatial and spectral information carried by light emitted from visual displays is filtered as it passes through spectacle lenses in front of the eye as well as by filters within the eye. The image forming and the spectral transmittance properties of the elements involved in image formation in the eye cause changes in both the luminance and colour contrast in retinal images. In addition, the amount of light that reaches the retina is always reduced by pre‐receptor filters and this reduction in retinal illuminance can cause diminished retinal sensitivity to both luminance and colour contrast. Of particular interest are the use of coloured lenses in front of the eye to reduce the short‐wavelength content of the light that reaches the retina and the use of ‘notch’ filters to absorb light selectively in certain wavebands, with inevitable consequences on both the luminance and chromatic contrast of retinal images. The presence of variant cone‐pigments in some subjects or the complete absence of one class of cone pigment in others, can also produce large deviations in both luminance and colour contrast signals that can either enhance or diminish the conspicuity of coloured objects (doi: 10.1364/josaa.22.000017).The purpose of this study was to develop and validate a model of red/green (RG) and yellow/blue (YB) colour discrimination that can also predict how chromatic sensitivity is affected by the use of spectrally‐selective, spectacle lenses or by filters internal to the eye, when viewing visual displays. We examined how RG and YB colour thresholds relate to the corresponding cone contrasts needed for detection of colour differences. The results reveal an invariance of cone contrasts at threshold for different states of chromatic adaptation. In other words, colour contrast signals at threshold follow Weber's law (doi: 10.1111/j.1475‐1313.2010.00773.x). A combination of RG and YB colour signals is needed to predict the colour threshold ellipse. The model relies on these findings and predicts how coloured filters external to the eye as well as pre‐receptor filters within the eye alter the measured RG and YB colour thresholds. Model predictions have been compared against measured colour thresholds using the CAD test (doi: 10.1093/bmb/ldx007). A number of experiments were carried out when the visual display was viewed with no lens in front of the eye or through a number of tinted lenses designed to absorb progressively more blue light.The effects of pre‐receptor filters within the eye such as the lens and the macular pigment have also been investigated. The results show that ‘blue‐blocking’ filters employed in typical spectacle lenses used with daylight illumination cause only small shifts, approximately along the daylight locus, without any significant loss of either RG or YB chromatic sensitivity. ‘Orange’ lenses that absorb greater amounts of short‐wavelength light cause a significant increase in YB thresholds, but have little or no effect on RG thresholds. More surprisingly, the model also predicts that the optical density of the macular pigment has little or no effect on the size of the colour threshold ellipse.Keywords: colour, cone contrasts, blue light, CAD test.

Weber Law Based Approach for Multi-Class Image Forgery Detection

Weber Law Based Approach for Multi-Class Image Forgery Detection

Testing Game Theory of Mind Models for Artificial Intelligence

In this article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines.

Duration perception in peripheral vision: Underestimation increases with greater stimuli eccentricity.

Duration perception plays a fundamental role in our daily visual activities; however, it can be easily distorted, even in the retinal location. While this topic has been extensively investigated in central vision, similar exploration in peripheral vision is still at an early stage. To investigate the influence of eccentricity, a commonly used indicator for quantifying retinal location, on duration perception in peripheral vision, we conducted two psychophysical experiments. In Experiment 1, we observed that the retinal location influenced the Point of Subjective Equality (PSE) but not the Weber Fraction (WF) of stimuli appearing at eccentricities ranging from 30° to 70°. Except at 30°, the PSEs were significantly longer than 416.7 ms (25 frames), which was the duration of standard stimuli. This suggested that participants underestimated duration, and this underestimation increased with greater distance from the central fixation point on the retina. To eliminate the potential interference of the central task used in Experiment 1, we conducted a supplementary experiment (Experiment 2) that demonstrated that this central task did not change the underestimation (PSE) but did influence the sensitivity (WF) at an eccentricity of 50°. In summary, our findings revealed a compressive effect of eccentricity on duration perception in peripheral vision: as stimuli appeared more peripheral on the retina, there was an increasing underestimation of subjective duration. Reasons and survival advantages of this underestimation are discussed. Findings provide new insight on duration perception in peripheral vision, highlighting an expanding compressive underestimation effect with greater eccentricity.

Characteristics of cell motility during cell collision

Quantitative examination of cellular motion and intercellullar interactions possesses substantial relevance for both biology and medicine. However, the effects of intercellular interactions during cellular locomotion remain under-explored in experimental research. As such, this study seeks to bridge this research gap, adopting Dictyostelium discoideum (Dicty) cells as a paradigm to investigate variations in cellular motion during reciprocal collisions. We aim to attain a comprehensive understanding of how cell interactions influence cell motion. By observing and processing the motion trajectories of colliding cells under diverse chemical environments, we calculated the diffusion coefficient (D) and the persistence time (τ), using mean square displacement. Our analysis of the relationship dynamics between D and τ prior to the collisions reveals intricate and non-monotonic alterations in cell movements during collisions. By quantitatively scrutinizing the τ trend, we were able to categorize the cellular responses to interactions under different conditions. Importantly, we ascertained that the effect of cell interactions during collisions in Dicty cells emulates a classical sigmoid function. This discovery suggests that cellular responses might comply with a pattern akin to the Weber–Fechner law.

The Analysis of Weber's Law in Product Marketing Strategy: Taking Coca Cola as Evidence

Transaction marketing is a business strategy that focuses on a single "point of sale" transaction. A transaction marks a financial agreement between two parties in which one party receives a financial benefit from the sale of goods and services to the other party. The way to obtain goods in modern society is usually inseparable from transactions, maximizing profits and obtaining more property has become the goal of many businessmen. However, obtaining benefits is not a simple science. It needs to be analyzed from different fields such as cost, research and development, publicity and the focus of this research: buyer psychology. This research paper analyzes the combination of mental accounting and the application of Weber's law in the market through examples of The Coca-Cola Company's development in the Chinese market. Using data and statistical methods to analyze the sales market and sales channels. Finally, it summarizes the suggestions and strategies of Coca-Cola's price increase, price reduction, sales methods and sales channels to provide a reference for sellers, so as to maximize the seller's benefits.

The role of numerical and nonnumerical magnitudes in pigeons' conditional discrimination behavior.

Research on approximate numerical estimation suggests that numerical representations can be influenced by nonnumerical magnitudes. Current theories of numerical cognition differ on the nature of this interaction. The present project evaluated the effect of task requirements on the stimulus control exerted by numerical and nonnumerical magnitudes on pigeons' numerical discrimination behavior. In a series of experiments, we explored the effects of cumulative area and item size on pigeons' numerical discrimination. The effect of cumulative area was assessed by presenting visual displays in which cumulative area and item number were either positively correlated, uncorrelated, or negatively correlated. The effect of item size was evaluated by presenting displays in which the size of individual items was varied across trials. Results confirmed that pigeons' numerical discrimination behavior accorded with Weber's law, a prime indicator of nonsymbolic numerical representation. The results further indicated that pigeons did not use numerical information when nonnumerical magnitudes also provided reliable information to solve the discrimination task. However, task manipulations that rendered the information provided by nonnumerical magnitudes unreliable successfully shifted stimulus control toward numerical magnitudes. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Weber’s Law

Bullough et al. introduce Weber's Law and proportional processing during perception.

Model aspect of the study of the processes of sustainable development of socio-economic systems

The triune concept of sustainable development takes into account environmental, social and economic issues in general. At the same time, the solution of the problems of resource conservation and socio-economic development do not contradict each other, but contribute to mutual reinforcement. The purpose of this study is to build, describe, test and analyze economic and mathematical models of the processes of self-organization of the socio-economic system within the framework of the concept of sustainable development. The considered models take into account both quantitative and qualitative characteristics. The research methodology is based on the assumption that the system under consideration is dynamic. The study makes it possible to evaluate the process of sustainable development of the socio-economic system in terms of the formation and influence of its characteristics on the overall result. Various options for formalizing the level of motivation of economic activity are described and analyzed, one of which is based on the economic interpretation of the Weber-Fechner psychophysiological law. The assumption of the continuous development of innovative technologies made it possible to reveal the existence of a “fatigue point”, the onset of which indicates the possibility of increasing the growth rate of production activities due to its technological transformation.

SENSORIAL TECHNIQUES OF ODOUR MEASUREMENTS – A RELATIONSHIP BETWEEN ODOUR CONCENTRATION AND ODOUR INTENSITY FOR A SELECTED WASTE MANAGEMENT FACILITY

Sensory analyses are one of the most frequently used odour research methods that allowestablishing the most important odour characteristics, i.e. odour concentration and odourintensity, characterised by a high degree of interrelationship. During an11-month study odourconcentration and intensity were measured at selected mechanical-biological solid municipalwaste treatment plant at 35 measuring locations to assess the degree of correlation between thosetwo parameters. Commonly used Weber-Fechner law was applied to assess the correlation. Resultsindicate a high degree of correlation between odour concentration and intensity, for example, R2valued for two different approaches at 0.87, and 0.95, while Pearson’s r valued at 0.93, and 0.97.Following the results this proves that odour concentration and odour intensity could potentially beused interchangeably for odour assessment. However, applying Weber-Fechner law for predictionof odour concentration based on odour intensity measurements gives imprecise results. Suchapproach could be potentially applied when limited measurements of odour concentration areavailable as determination of odour intensity that could be performed even by Facility employees.

Infrared visibility and infrared visibility range: the practical signif cance and method for measuring

New physical quantities are presented – infrared visibility and infrared visibility range. The relevance and demand for measurements of these quantities is shown. Their physical meaning is revealed, formula ratios for the calculation are given, and the practical signifi cance. The presented calculation ratios are obtained on the basis of the transformation of the real thermal portrait of the object into an equivalent thermal geometric model. It is shown that the numerical values of the infrared visibility index for various real objects can vary over a wide range: from zero for absolutely non-thermal contrast objects to values of several units for high-contrast objects, i.e. within 0.5–2.5. The ratio for the infrared visibility range is obtained in based on the Lambert-Bouguer-Beer law and Fechner's law, used in the theory of sensory sensitivity. A detailed description and procedure for measuring the indicated physical quantities is presented, examples are given, and the measurement uncertainty is estimated. The introduced values are aimed at ensuring the unity of the assessment of thermal protection of various man-made and biological objects and allow developing preventive measures for their thermal protection at the stage of commissioning.

Non-Uniform-Illumination Image Enhancement Algorithm Based on Retinex Theory

To address the issues of fuzzy scene details, reduced definition, and poor visibility in images captured under non-uniform lighting conditions, this paper presents an algorithm for effectively enhancing such images. Firstly, an adaptive color balance method is employed to address the color differences in low-light images, ensuring a more uniform color distribution and yielding a low-light image with improved color consistency. Subsequently, the image obtained is transformed from the RGB space to the HSV space, wherein the multi-scale Gaussian function is utilized in conjunction with the Retinex theory to accurately extract the lighting components and reflection components. To further enhance the image quality, the lighting components are categorized into high-light areas and low-light areas based on their pixel mean values. The low-light areas undergo improvement through an enhanced adaptive gamma correction algorithm, while the high-light areas are enhanced using the Weber–Fechner law for optimal results. Then, each block area of the image is weighted and fused, leading to its conversion back to the RGB space. And a multi-scale detail enhancement algorithm is utilized to further enhance image details. Through comprehensive experiments comparing various methods based on subjective visual perception and objective quality metrics, the algorithm proposed in this paper convincingly demonstrates its ability to effectively enhance the brightness of non-uniformly illuminated areas. Moreover, the algorithm successfully retains details in high-light regions while minimizing the impact of non-uniform illumination on the overall image quality.

Pleasant emotional feelings follow one of the most basic psychophysical laws (weber's law) as most sensations do.

Emotion episodes may include a conscious aspect of the emotion, namely being aware of our own emotional experience. Despite explosion in research over previous years, it remains unclear how emotions reach awareness and become feelings. Already in 1884, William James argued that emotional feelings resemble ordinary sensations in this respect. Here, using a novel model-based ratio scale of emotion intensity, we provide one of the strongest pieces of evidence supporting James' perceptual theory by showing that emotion awareness obeys one of the most fundamental laws of perception, Weber's law. According to this law, stimulus encoding accuracy decreases with intensity. In this work, we asked participants to provide binary pleasant-versus-unpleasant reports of their experience when watching normed emotion-eliciting pictures (NAPS; Marchewka et al., 2014). The results validate our model's measure of emotion intensity by showing its monotonous relation to picture norms. Most importantly, they show, for the first time, that in humans, pleasant emotion experiences follow Weber's classical psychophysical law-indicating decreased encoding precision with increasing pleasantness. This result supports James' theory, suggesting that (pleasant) emotions reach awareness just as ordinary sensations do. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Neurorehabilitation Method for Preventing the Collapse of Internal Model: Verification of Unconscious Motor Change Caused by Implicit Error Involved in Multimodal Sensory FBs(Feedbacks).

It remains challenging for patients with stroke to regain the proper gait they had before stroke onset. In this study, one of the significant reasons for the problem is assumed to be the collapse of patients' internal model. Therefore, this study aimed to propose a method for lower-limb rehabilitation in the acute phase to prevent the collapse of the internal model and simultaneously promote voluntariness.To verify the effect of the proposed method and determine the optimal FB conditions, a supine pseudo-walking system has been developed providing multimodal sensory FBs, including somatosensory FB (walking on the walking robot), load transfer FB (plantar vibration provided by the robot), and visual FB (walking scene shown in virtual reality).First, the implicit error range of each sensory FB that was unable to recognize was investigated according to Weber's law. Subsequently, 12 participants were asked to perform 12 steps of walking exercise in the system to evaluate the unconscious motor-changing effect due to different/multimodal FBs. Errors were presented at the 7th step in either three FBs in the ratio determined or their combinations (two or three types of FBs simultaneously changing).Second, to examine whether the effect can last and influence the motion after the training, a pre-post comparison test was performed with the training in the middle, wherein implicit errors were presented in the three kinds of FBs.The results show that presenting implicit error can cause motor change, and multiple types of FBs may have a better effect. The statistical data of 12 participants of the pre-post comparison test show that the average integrated electromyogram in the post-test appears significantly larger than that in the pre-test. The result indicates that the motor-changing effect of the proposed method has a subsequent influence on motion and shows the possibility of the future application of the proposed method to the rehabilitation field.

A Weberized Total Variance Regularization-based Image Multiplicative Noise Model

This paper considers Weber's law and proposes a new non-convex model for images contaminated by Gaussian noise and Rayleigh noise. The alternating direction method of multipliers (abbreviated as ADMM) is a recent popular method that can handle convex and non-convex problems well. This paper compares denoising effect between ADMM and the Euler-Lagrange equation method applied to the non-convex model. The numerical experimental results show that ADMM performs better and has a higher Peak Signal to Noise Ratio.

Female preference for males with lower pattern contrast follows Weber's law of proportional processing in jumping spiders

Abstract According to Weber's law of proportional processing, perceptual discrimination between stimuli of different magnitudes is based on their proportional differences in magnitude (not absolute differences). Proportional processing operates in various sensory modalities and behavioural contexts. However, whether female mate preference for colour patterns in animals follows Weber's law of proportional processing remains untested. We addressed this research gap using the jade jumping spider, Siler semiglaucus, whose males exhibit remarkable sexually selected colour patterns and whose females show preferences for males with low abdomen pattern contrast (pattern contrast is defined as the spatial feature of the relative abundance of two adjacent colour patches). By manipulating the dorsal abdomen colour patterns of S. semiglaucus males, we created males with varying abdomen pattern contrasts. We then assessed female preference for males that varied in both absolute and proportional differences in pattern contrast. We found that females preferred males with lower abdomen pattern contrasts and discriminated between males based on both absolute and proportional differences in pattern contrast. While proportional difference alone was not a significant predictor of female mate‐choice, discrimination based on proportional difference coupled with absolute difference had a greater influence on female mate preference than absolute difference alone. Hence, our findings suggest that S. semiglaucus female preference for males with lower pattern contrast follows Weber's law, and female discrimination may have the potential to limit the exaggeration of sexually selected colour patterns. Read the free Plain Language Summary for this article on the Journal blog.

Magnetic Navigation in Animals, Visual Contrast Sensitivity and the Weber–Fechner Law

Magnetic Navigation in Animals, Visual Contrast Sensitivity and the Weber–Fechner Law

How to define thresholds for level and interaural-level-difference discrimination: Insights from scedasticities and distributions

Sensitivity to changes in the stimulus level at one or at both ears and to changes in the interaural level difference (ILD) between the two ears has been studied widely. Several different definitions of threshold and, for one of them, two different ways of averaging single-listener thresholds have been used (i.e., arithmetically and geometrically), but it is unclear which definition and which way of averaging is most suitable. Here, we addressed this issue by examining which of the differently defined thresholds yielded the highest degree of homoscedasticity (homogeneity of the variance). We also examined how closely the differently defined thresholds followed the normal distribution. We measured thresholds from a large number of human listeners as a function of stimulus duration in six experimental conditions, using an adaptive two-alternative forced-choice paradigm. Thresholds defined as the logarithm of the ratio of the intensities or amplitudes of the target and the reference stimulus (i.e., as the difference in their levels or ILDs; the most commonly used definition) were clearly heteroscedastic. Log-transformation of these latter thresholds, as sometimes performed, did not result in homoscedasticity. Thresholds defined as the logarithm of the Weber fraction for stimulus intensity and thresholds defined as the logarithm of the Weber fraction for stimulus amplitude (the most rarely used definition) were consistent with homoscedasticity, but the latter were closer to the ideal case. Thresholds defined as the logarithm of the Weber fraction for stimulus amplitude also followed the normal distribution most closely. The discrimination thresholds should therefore be expressed as the logarithm of the Weber fraction for stimulus amplitude and be averaged arithmetically across listeners. Other implications are discussed, and the obtained differences between the thresholds in different conditions are compared to the literature.

Numerosity Comparison in Three Dimensions in the Case of Low Numerical Values.

This study investigated the perception of numbers in humans in 3D stimuli. Recent research has shown that number processing relies on "number sense" for small values, in line with Weber's law. While previous studies have reported 3D numerosity overestimation mainly in higher numerical values, our experiment examined whether this phenomenon occurs at lower numerical values. We also explored whether the Weber ratio follows Weber's law when comparing 2D and 3D stimuli in terms of the number of elements. Observers were presented with pairs of stimuli on a monitor and were asked to identify the stimulus with a larger number of elements. Using the constant method, we calculated the point of subjective equality (PSE), just noticeable difference (JND), and Weber ratios from the collected data. As a result, it was confirmed that the phenomenon of over-estimation of 3D numerical values occurs even when the numerical values are small. Additionally, we observed that the Weber fraction adhered to Weber's law within the measured range. These findings contribute to the existing body of research, supporting the existence of distinct mechanisms for perceiving numerosity and density.

A Fechner multiscale local descriptor for face recognition.

Inspired by Fechner's law, we propose a Fechner multiscale local descriptor (FMLD) for feature extraction and face recognition. Fechner's law is a well-known law in psychology, which states that a human perception is proportional to the logarithm of the intensity of the corresponding significant differences physical quantity. FMLD uses the significant difference between pixels to simulate the pattern perception of human beings to the changes of surroundings. The first round of feature extraction is performed in two local domains of different sizes to capture the structural features of the facial images, resulting in four facial feature images. In the second round of feature extraction, two binary patterns are used to extract local features on the obtained magnitude and direction feature images, and four corresponding feature maps are output. Finally, all feature maps are fused to form an overall histogram feature. Different from the existing descriptors, the FMLD's magnitude and direction features are not isolated. They are derived from the "perceived intensity", thus there is a close relationship between them, which further facilitates the feature representation. In the experiments, we evaluated the performance of FMLD in multiple face databases and compared it with the leading edge approaches. The results show that the proposed FMLD performs well in recognizing images with illumination, pose, expression and occlusion changes. The results also indicate that the feature images produced by FMLD significantly improve the performance of convolutional neural network (CNN), and the combination of FMLD and CNN exhibits better performance than other advanced descriptors.