scholarly journals Symmetric Networks with Geometric Constraints as Models of Visual Illusions

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 799 ◽  
Author(s):  
Ian Stewart ◽  
Martin Golubitsky
Keyword(s):  
Hopf Bifurcation ◽  
Visual System ◽  
Dynamic Systems ◽  
Necker Cube ◽  
Visual Illusions ◽  
Geometric Constraints ◽  
Consistency Conditions ◽  
Geometric Consistency ◽  
Attribute Levels ◽  
Symmetric Networks

Multistable illusions occur when the visual system interprets the same image in two different ways. We model illusions using dynamic systems based on Wilson networks, which detect combinations of levels of attributes of the image. In most examples presented here, the network has symmetry, which is vital to the analysis of the dynamics. We assume that the visual system has previously learned that certain combinations are geometrically consistent or inconsistent, and model this knowledge by adding suitable excitatory and inhibitory connections between attribute levels. We first discuss 4-node networks for the Necker cube and the rabbit/duck illusion. The main results analyze a more elaborate model for the Necker cube, a 16-node Wilson network whose nodes represent alternative orientations of specific segments of the image. Symmetric Hopf bifurcation is used to show that a small list of natural local geometric consistency conditions leads to alternation between two global percepts: cubes in two different orientations. The model also predicts brief transitional states in which the percept involves impossible rectangles analogous to the Penrose triangle. A tristable illusion generalizing the Necker cube is modelled in a similar manner.

Analysis on Hopf Bifurcation and Complexity of one Kind Financial System

2011 ◽  
Vol 48-49 ◽  
pp. 813-816 ◽  
Author(s):  
Qi Zhang ◽  
Jun Hai Ma
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Financial System ◽  
The Relationship ◽  
At Home

From a mathematical model of one kind complicated financial system, we make a dynamic analysis on this kind of system on the basis of studies of scholars both at home and abroad. We find characteristics of various dynamic systems driven by different parameters, and study possible Hopf bifurcation as well as the relationship between Hopf bifurcation and the values of parameters. Besides, we make use of algorithm to analyze complexity of the system. The results of numerical simulation prove that the theory used in the thesis is correct. This study is regarded with good theoretical and practical value.

Can Illusory Figures Be Transparent and Opaque at the Same Time?

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 321-321
Author(s):  
F Purghé
Keyword(s):  
Visual System ◽  
Necker Cube ◽  
Special Kind ◽  
Illusory Figure ◽  
Cognitive Problem ◽  
Paradoxical Result ◽  
Contrary Evidence

A simple and convincing way of explaining illusory figures is based upon the idea that the visual system would infer the presence of an occluding object when the inducing pattern shows features, such as indentations or interruptions, that can be logically explained as due to an occlusion. This kind of explanation implies (a) that an illusory figure should be prevented from occurring if there is no logical need for it, and (b) that the illusory figure must be opaque to be effective as an occluding object. It can be shown, however, that illusory figures can emerge even when there is contrary evidence to occlusion. A special kind of stereoscopic Kanizsa-like pattern superimposed onto a picture (an Escher engraving) is capable of inducing clear illusory figures (two rectangles). In this pattern, the illusory figures seem to be transparent with respect to the picture on the background, which remains fully visible through them, but act as opaque surfaces with respect to the inducers. The inducers are parts of a Necker cube which can be clearly seen only when its fragments induce the illusory rectangles, but disappears if the same fragments, being only outlined, are not able to induce them. If this outcome can be regarded as a demonstration that the Necker cube can be seen as an amodally completed object only when it virtually completes itself ‘behind’ the illusory rectangles, one would have to conclude that the same illusory surfaces can be transparent and opaque at the same time. This paradoxical result seems to challenge any interpretation of illusory figures as being due to an intelligent solution to a cognitive problem.

scholarly journals Number is not just an illusion: Discrete numerosity is encoded independently from perceived size

2021 ◽  
Author(s):  
Andrea Adriano ◽  
Luisa Girelli ◽  
Luca Rinaldi
Keyword(s):  
Convex Hull ◽  
Visual System ◽  
Object Segmentation ◽  
Ponzo Illusion ◽  
Visual Illusions ◽  
Continuous Variables ◽  
Discrete Elements ◽  
Comparison Task ◽  
Low Level ◽  
Number Comparison

AbstractWhile seminal theories suggest that nonsymbolic visual numerosity is mainly extracted from segmented items, more recent views advocate that numerosity cannot be processed independently of nonnumeric continuous features confounded with the numerical set (i.e., such as the density, the convex hull, etc.). To disentangle these accounts, here we employed two different visual illusions presented in isolation or in a merged condition (e.g., combining the effects of the two illusions). In particular, in a number comparison task, we concurrently manipulated both the perceived object segmentation by connecting items with Kanizsa-like illusory lines, and the perceived convex-hull/density of the set by embedding the stimuli in a Ponzo illusion context, keeping constant other low-level features. In Experiment 1, the two illusions were manipulated in a compatible direction (i.e., both triggering numerical underestimation), whereas in Experiment 2 they were manipulated in an incompatible direction (i.e., with the Ponzo illusion triggering numerical overestimation and the Kanizsa illusion numerical underestimation). Results from psychometric functions showed that, in the merged condition, the biases of each illusion summated (i.e., largest underestimation as compared with the conditions in which illusions were presented in isolation) in Experiment 1, while they averaged and competed against each other in Experiment 2. These findings suggest that discrete nonsymbolic numerosity can be extracted independently from continuous magnitudes. They also point to the need of more comprehensive theoretical views accounting for the operations by which both discrete elements and continuous variables are computed and integrated by the visual system.

scholarly journals Predictive coding as a unifying principle for explaining a broad range of brightness phenomena

2020 ◽  
Author(s):  
Alejandro Lerer ◽  
Hans Supèr ◽  
Matthias S.Keil
Keyword(s):  
Visual System ◽  
Computational Model ◽  
Predictive Coding ◽  
Gain Control ◽  
Physical World ◽  
Input Image ◽  
Visual Illusions ◽  
Contrast Effects ◽  
Dynamic Filtering ◽  
The Brain

AbstractThe visual system is highly sensitive to spatial context for encoding luminance patterns. Context sensitivity inspired the proposal of many neural mechanisms for explaining the perception of luminance (brightness). Here we propose a novel computational model for estimating the brightness of many visual illusions. We hypothesize that many aspects of brightness can be explained by a predictive coding mechanism, which reduces the redundancy in edge representations on the one hand, while non-redundant activity is enhanced on the other (response equalization). Response equalization is implemented with a dynamic filtering process, which (dynamically) adapts to each input image. Dynamic filtering is applied to the responses of complex cells in order to build a gain control map. The gain control map then acts on simple cell responses before they are used to create a brightness map via activity propagation. Our approach is successful in predicting many challenging visual illusions, including contrast effects, assimilation, and reverse contrast.Author summaryWe hardly notice that what we see is often different from the physical world “outside” of the brain. This means that the visual experience that the brain actively constructs may be different from the actual physical properties of objects in the world. In this work, we propose a hypothesis about how the visual system of the brain may construct a representation for achromatic images. Since this process is not unambiguous, sometimes we notice “errors” in our perception, which cause visual illusions. The challenge for theorists, therefore, is to propose computational principles that recreate a large number of visual illusions and to explain why they occur. Notably, our proposed mechanism explains a broader set of visual illusions than any previously published proposal. We achieved this by trying to suppress predictable information. For example, if an image contained repetitive structures, then these structures are predictable and would be suppressed. In this way, non-predictable structures stand out. Predictive coding mechanisms act as early as in the retina (which enhances luminance changes but suppresses uniform regions of luminance), and our computational model holds that this principle also acts at the next stage in the visual system, where representations of perceived luminance (brightness) are created.

Neuroanatomy and function in two visual systems

2000 ◽  
Vol 23 (4) ◽  
pp. 535-536
Author(s):  
Bruce Bridgeman
Keyword(s):  
Visual System ◽  
Cross Talk ◽  
Visual Illusions ◽  
Sensorimotor System ◽  
Reverse Link ◽  
Visual Systems ◽  
Two Visual Systems ◽  
Direct Cross ◽  
Normal Humans ◽  
And Function

Neuroanatomy and neurophysiology are insufficient to specify function. Modeling is essential to elucidate function, but psychophysics is also required. An example is the cognitive and sensorimotor branches of the visual system: anatomy shows direct cross talk between the branches. Psychophysics in normal humans shows links from cognitive to sensorimotor, but the reverse link is excluded by visual illusions affecting the cognitive system but not the sensorimotor system.

scholarly journals The Aftereffects of Müller-Lyer and Ponzo Illusions: Differences Revealed in Sensorimotor Domain

2017 ◽  
Vol 71 (5) ◽  
pp. 352-358
Author(s):  
Vsevolod Lyakhovetskii ◽  
Valeriia Karpinskaia
Keyword(s):  
Visual System ◽  
Visual Illusion ◽  
Ponzo Illusion ◽  
Touch Screen ◽  
Visual Illusions ◽  
Motor Tasks ◽  
Right Hand ◽  
Long Time ◽  
Visual Domain ◽  
Different Levels

Abstract Either effects or aftereffects of visual illusions are well studied at the visual domain while there are few studies of aftereffects at the motor tasks such as grasping or pointing at the illusory. The aftereffects of Müller-Lyer and Ponzo illusions in the sensorimotor domain were studied. We used four illusions: two versions of Müller-Lyer illusions (upper/bottom shafts appear longer) and two versions of Ponzo illusions (classical and inverted, upper/bottom shafts appear longer). They were presented to four experimental groups, each type to one of the groups. A fifth group was shown neutral stimuli (two horizontal lines, one under another). At first, one of the above described stimuli was presented ten times. Then, for testing the aftereffect, the neutral stimuli were presented thirty times. After the disappearance of each stimulus, the participant moved his/her right hand across the touch screen along its upper and lower shafts. The participants of all experimental groups experienced significant illusions, but only the classical Ponzo illusion caused significant long-time assimilative aftereffect. These results reveal the existence of an illusory aftereffect in the sensorimotor domain. Moreover, it depends on the type of visual illusion, thereby supporting the hypothesis of origin of the different visual illusions at different levels of the visual system.

scholarly journals Your Visual System Provides all the Information You Need to make Moral Judgments about Generic Visual Events

2017 ◽  
Author(s):  
Julian De Freitas
Keyword(s):  
Visual System ◽  
Contextual Factors ◽  
Visual Illusions ◽  
Moral Judgments ◽  
Motion Processing ◽  
Specific Task ◽  
Visual Events ◽  
Task Irrelevant

To what extent are people's moral judgments susceptible to subtle factors of which they are unaware? Here we show that we can change people’s moral judgments outside of their awareness by subtly biasing perceived causality. Specifically, we used subtle visual manipulations to create visual illusions of causality in morally relevant scenarios, and this systematically changed people’s moral judgments. After demonstrating the basic effect using simple displays involving an ambiguous car collision that ends up injuring a person (E1), we show that the effect is sensitive on the millisecond timescale to manipulations of task-irrelevant factors that are known to affect perceived causality, including the duration (E2a) and asynchrony (E2b) of specific task-irrelevant contextual factors in the display. We then conceptually replicate the effect using a different paradigm (E3a), and also show that we can eliminate the effect by interfering with motion processing (E3b). Finally, we show that the effect generalizes across different kinds of moral judgments (E3c). Combined, these studies show that obligatory, abstract inferences made by the visual system directly influence moral judgments.

Hopf Bifurcation in Symmetric Networks of Coupled Oscillators with Hysteresis

2012 ◽  
Vol 24 (4) ◽  
pp. 713-759 ◽  
Author(s):  
Z. Balanov ◽  
W. Krawcewicz ◽  
D. Rachinskii ◽  
A. Zhezherun
Keyword(s):  
Hopf Bifurcation ◽  
Coupled Oscillators ◽  
Symmetric Networks
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