scholarly journals A Mathematical Principle of Art and Human Vision

2020 ◽  
Author(s):  
Xin Zhang
Keyword(s):  
Fourier Analysis ◽  
Mathematical Theory ◽  
Visual Illusions ◽  
Human Vision ◽  
Mathematical Principle ◽  
Frequency Filtering ◽  
Human Visual Perception ◽  
Visual Objects ◽  
Geometrical Illusions ◽  
Shed Light

The study of visual illusions is an old subject and an important part of the psychology of human visual perception, but hitherto there has been no single principle able to explain radically different kinds of visual illusions conjointly. Such a principle does exist, as is to be shown, and has the virtue of being rigorous: it is the mathematical theory of Fourier analysis. A great many visual illusions are what happen when the visual objects involved undergo certain frequency filtering, a concept deduced from Fourier analysis. Phenomena thus explained belong in these distinct categories: brightness illusions, colour illusions, geometrical illusions, and motion illusions, all of which have been simulated with computer programmes based on this mathematical principle. Visual illusions obeying this principle have in fact been depicted in Western painting for centuries, and art can in certain ways shed light on the quest for the understanding of human vision.

Making the Black Box Transparent

1999 ◽  
Vol 92 (9) ◽  
pp. 780-784
Author(s):  
Lawrence M. Lesser
Keyword(s):  
Mathematical Theory ◽  
Black Box ◽  
Mathematical Understanding ◽  
Complete Graphs ◽  
Interpolating Polynomials ◽  
Mathematics Curricula ◽  
Best Fit ◽  
Shed Light

Although introducing technology into our mathematics curricula allows us to tackle problems of size and complexity as never before, we face a danger of introducing tools to students before they have a sufficient understanding of how mathematics content within their reach can be used to shed light on the algorithms within the tools or on the use of the tools themselves. Fortunately, we can view mathematical theory and technology not as opponents but rather as partners that make the whole of mathematical understanding richer than the sum of its parts. Indeed, bringing technology into our classrooms can encourage new questions that technology-free mathematics must answer. This article focuses mainly on a common example in technology-rich mathematics curricula, namely, the line of best fit, followed by a discussion of two additional examples—interpolating polynomials and complete graphs. In each case, connections between theory and technology do not appear to be as widely known and used as they could be.

Relationships between Channels for Colour and Spatial Frequency in Human Vision

Perception ◽  
1973 ◽  
Vol 2 (1) ◽  
pp. 31-40 ◽  
Author(s):  
V Virsu ◽  
S Haapasalo
Keyword(s):  
Spatial Frequency ◽  
Visual System ◽  
Human Visual System ◽  
Human Vision ◽  
Visual Objects ◽  
The Third ◽  
Simultaneous Integration ◽  
Two Systems ◽  
Channel Systems

Five forms of relationships and four types of channels are possible between two systems of sensory channels. The relationships between channels for colour and spatial frequency were studied in three adaptation experiments. In the first, a new colour-specific spatial aftereffect was found, which indicates the existence of channels that are specific both to colour and to spatial frequency. The second showed that the spatial-frequency aftereffect of Blakemore and Sutton is not colour specific, which indicates that there are channels for spatial frequency that are not colour specific. The third demonstrated that coloured afterimages are not spatial-frequency specific immediately after adaptation, although they become so later. This indicates that there are channels for colour that are not spatial-frequency specific. The existence of these three types of channels implies that the channel systems for colour and spatial frequency overlap partially and mutually in the human visual system. This kind of organisation of channel systems, if it exists, may form the psychophysical structure that is required for the capacity of simultaneous integration and differentiation in the perception of colour and size of visual objects.

scholarly journals Information Theory: Deep Ideas, Wide Perspectives, and Various Applications

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 232
Author(s):  
Irad Ben-Gal ◽  
Evgeny Kagan
Keyword(s):  
Information Theory ◽  
Data Transmission ◽  
Mathematical Theory ◽  
Mathematical Principle ◽  
Information Communication ◽  
Famous Paper ◽  
History Of ◽  
History Of Information

The history of information theory, as a mathematical principle for analyzing data transmission and information communication, was formalized in 1948 with the publication of Claude Shannon’s famous paper “A Mathematical Theory of Communication” [...]

scholarly journals Simulating Human Visual Perception in Tunnel Portals

2021 ◽  
Vol 13 (7) ◽  
pp. 3741
Author(s):  
Changjiang Liu ◽  
Qiuping Wang
Keyword(s):  
Experimental Data ◽  
Visual Perception ◽  
Dark Adaptation ◽  
Light Adaptation ◽  
Human Vision ◽  
Adaptation Process ◽  
Human Visual Perception ◽  
Recognition Time ◽  
Design Data ◽  
Adaptation Time

To study the characteristics of light and dark adaptation in tunnel portals, and to determine the influencing factors in light–dark vision adaptation, basic tunnel lighting and linear design data were obtained. In this study, we used a light-shielded tent to simulate the dark environment of a tunnel, observe the driver recognition time for target objects during the light–dark adaptation process, and analyze the light–dark adaptation time of human vision. Based on the experimental data, we examined the relationships between age, gender, illuminance, and light and dark adaptation times, and established a model for these relationships. The experimental results show that the dark adaptation time is generally longer than the light adaptation time. The dark adaptation time is positively related to age and exhibits a cubic relationship. There is no significant correlation between the light adaptation time and age, but the overall trend is for the light adaptation time to gradually increase with increasing age. There is no correlation between gender and light and dark adaptation times, but there is a notable correlation between light and dark adaptation times and illuminance. When the illuminance ranges from 11,000 to 13,000 lux, the light and dark adaptation times are the longest.

scholarly journals Twos in human visual perception

2020 ◽  
Author(s):  
Liuba Papeo
Keyword(s):  
High Efficiency ◽  
Spatial Relations ◽  
Human Vision ◽  
Human Visual Perception ◽  
Body Perception ◽  
Face To Face ◽  
The Social ◽  
Visual Areas ◽  
Social Entities ◽  
Increased Activity

Human vision serves the social function of detecting and discriminating with high efficiency conspecifics and other animals. The social world is made of social entities as much as the relations between those entities. Recent work demonstrates that vision encodes visuo-spatial relations between bodies with the same efficiency and high specialization of face/body perception. Specifically, perception of face-to-face (vs. non-facing) bodies evokes effects compatible with the most robust markers of face-specificity such as the behavioral inversion effect and increased activity in selective visual areas. Another set of results suggests that face-to-face bodies are processed as a grouped unit, analogously to facial features in a face. The facing dyad in the visual cortex may be the earliest rudimentary representation of social interaction.

Image Machine

2017 ◽  
Author(s):  
Andreas Broeckmann
Keyword(s):  
Visual Media ◽  
Human Vision ◽  
Visual Artists ◽  
Human Visual Perception ◽  
Vision Systems ◽  
Early Computer ◽  
Technical Vision ◽  
And Control ◽  
Human Eyes ◽  
Nam June Paik

This chapter deals with the role that vision and images play in the conjunction of technics and aesthetics in the twentieth century. Based on an analysis of the fundamental technicity of human visual perception, it discusses the complicated notion of the “image” and that of the “medium” in art. The chapter begins with a detailed analysis of the concept of “operational images,” which pinpoints the tension between images that are produced to be seen by human eyes, and technical vision systems that are independent of human vision and human intervention. The author then presents artworks by artists including Nam June Paik, Steina Vasulka, and Julien Maire which articulate the complex aesthetics of visual media techniques. A discussion of early computer graphics artists like Vera Molnar, and more recent works by Antoine Schmitt, JODI, and others, exemplifies how issues like seriality, chance, and control have concerned visual artists working with different media supports ever since the 1920s. Finally, an analysis of works by David Rokeby, Wolfgang Staehle, and David Tomas serve to further outline the particular aesthetics of machine images and automated vision systems.

scholarly journals Modified tangential frequency filtering decomposition and its fourier analysis

2010 ◽  
Vol 116 (1) ◽  
pp. 123-148 ◽  
Author(s):  
Qiang Niu ◽  
Laura Grigori ◽  
Pawan Kumar ◽  
Frédéric Nataf
Keyword(s):  
Fourier Analysis ◽  
Frequency Filtering

scholarly journals Two Types of Visual Objects

Studia Humana ◽  
2015 ◽  
Vol 4 (2) ◽  
pp. 26-38
Author(s):  
Błażej Skrzypulec
Keyword(s):  
Cognitive Psychology ◽  
Visual Persistence ◽  
Human Vision ◽  
Visual Objects ◽  
Visual Organization ◽  
The One

Abstract While it is widely accepted that human vision represents objects, it is less clear which of the various philosophical notions of ‘object’ adequately characterizes visual objects. In this paper, I show that within contemporary cognitive psychology visual objects are characterized in two distinct, incompatible ways. On the one hand, models of visual organization describe visual objects in terms of combinations of features, in accordance with the philosophical bundle theories of objects. However, models of visual persistence apply a notion of visual objects that is more similar to that endorsed in philosophical substratum theories. Here I discuss arguments that might show either that only one of the above notions of visual objects is adequate in the context of human vision, or that the category of visual objects is not uniform and contains entities properly characterized by different philosophical conceptions.

Color Image Region Growth Segmentation Integration of Normalized Cut

2010 ◽  
Vol 143-144 ◽  
pp. 139-142
Author(s):  
Xiao Ying Wu ◽  
Li Juan Ma ◽  
Zhao Feng Li ◽  
Shi Tao Yan
Keyword(s):  
Color Image ◽  
Image Features ◽  
Human Vision ◽  
Segmentation Result ◽  
Segmentation Method ◽  
Human Visual Perception ◽  
Normalized Cut ◽  
Image Region ◽  
Region Growth ◽  
Selection Of

This paper solves that image segmentation result is not consistent with human visual perception or too broken. First of all, based on the continuity of image features, appropriate human vision, calculated the similarity of color image pixel as Eq.2 in HSV space to grow region, then made the regional merge, using normalized-cut segmentation method as Eq.4 and Eq.5 to eliminate over-segmentation phenomenon. In this paper, experimental results shows that the segmentation can be achieved very good results as Fig.1, and parts of the method can be applied in other segmentation to solve over segmentation. This method on color images as the research object is different from other methods on gray images, the selection of seeds and achieves these automatic that differ from general algorithms, presents a new implementation to solve over-segmentation.

God’s Dice: Bayesian Probability and Providence

2015 ◽  
Vol 27 (1) ◽  
pp. 4-24
Author(s):  
William R. Clough ◽  
Keyword(s):  
Mathematical Theory ◽  
Bayes Theorem ◽  
Bayesian Probability ◽  
Religion And Science ◽  
Central Thesis ◽  
Mathematical Theorem ◽  
Providence Of God ◽  
Probabilistic Nature ◽  
Shed Light

The Reverend Thomas Bayes has recently become best known for his mathematical Theorem, but Bayes’ vocation, and primary identity, was that of minister. Bayes’ writings include a tract on divine benevolence and an essay on the philosophy of calculus as well as what has come to be known as Bayes’ Theorem. Two and a half centuries ago, Bayes affirmed both the Providence of God and the probabilistic nature of reality. This essay explores some implications of Bayes’ Theorem in light of his theology. The central thesis is that it is fruitful to make the connection between Bayes’ mathematical theory of probability, its implications when extended in time, and his view of God as the continuous in-breaking of the good tending to the benefit of all creation. In so doing, Bayes suggests ways to shed light on current theological and philosophical discussions, including theodicy, religion and science, and chance and Providence.

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