insight - Computational neuroscience - # Modeling Visual Illusions Induced by Localized Funnel Patterns

Modeling Visual Illusions Induced by Localized Stimuli Using Neural Fields

Q: How can the proposed neural field model be extended to capture the illusory motions that subjects perceived in the after-images reported by Billock and Tsou?

To extend the proposed Amari-type neural field model to capture the illusory motions perceived in the after-images reported by Billock and Tsou, one could incorporate a time-dependent sensory input that simulates the flickering effect observed in the experiments. This would involve modifying the sensory input function ( I(x, t) ) to include temporal variations that mimic the flickering of the complementary regions surrounding the localized stimuli. By introducing a dynamic component to the sensory input, the model could account for the temporal aspects of visual processing, allowing it to simulate the perceived motion in the after-images. Additionally, the model could benefit from integrating a more complex response function ( f ) that captures the nonlinear interactions between excitatory and inhibitory neurons more effectively. This could involve exploring different forms of non-odd nonlinearities that have been shown to reproduce specific visual phenomena. By adjusting the parameters of the response function and the connectivity kernel ( \omega ), the model could be fine-tuned to reflect the dynamics of illusory motion, thereby enhancing its predictive capabilities regarding the temporal aspects of visual perception.

Q: What are the potential implications of the findings in this paper for our understanding of visual processing and perception in the brain?

The findings of this paper have significant implications for our understanding of visual processing and perception in the brain. By demonstrating that both excitatory and inhibitory neuronal activities play crucial roles in the emergence of visual illusions, the study challenges the traditional view that excitatory activity alone drives visual perception. This highlights the importance of considering the interplay between different types of neurons in the primary visual cortex (V1) when modeling visual phenomena. Moreover, the successful reproduction of Billock and Tsou's experimental results using the Amari-type neural field model suggests that mathematical modeling can provide valuable insights into the mechanisms underlying visual perception. This approach may lead to a deeper understanding of how the brain processes complex visual stimuli and how various factors, such as spatial organization and temporal dynamics, influence perceptual outcomes. Ultimately, these insights could inform the development of more effective treatments for visual disorders and enhance our understanding of the neural basis of perception.

Q: Can the insights gained from this study be applied to model other types of visual illusions or perceptual phenomena?

Yes, the insights gained from this study can be applied to model other types of visual illusions and perceptual phenomena. The framework established by the Amari-type neural field model, particularly its ability to incorporate nonlinear dynamics and the interactions between excitatory and inhibitory neurons, can be adapted to explore a wide range of visual illusions beyond those specifically examined in the context of funnel and tunnel patterns. For instance, the model could be extended to investigate other well-documented visual phenomena, such as the Kanizsa triangle or the Hermann grid illusion, by adjusting the sensory input and response functions to reflect the specific characteristics of these illusions. Additionally, the principles of retinotopic organization and the role of spatially distributed neural activity can be leveraged to understand how different visual stimuli interact within the visual cortex, leading to various perceptual outcomes. Furthermore, the mathematical techniques and numerical analysis methods employed in this study can serve as a foundation for future research aimed at uncovering the neural mechanisms underlying more complex perceptual phenomena, such as motion perception, depth perception, and the integration of visual information across different modalities. This versatility underscores the potential of neural field models in advancing our understanding of visual perception as a whole.

Core Concepts

The paper aims to investigate the theoretical modeling of visual illusions observed in Billock and Tsou's experiments, where a localized funnel pattern stimulus induces an orthogonal tunnel pattern in the surrounding region of the visual field. The authors use an Amari-type neural field equation to model the cortical dynamics and explore the role of excitatory and inhibitory neuronal activities in reproducing these nonlinear visual phenomena.

Abstract

The paper focuses on modeling the visual illusions observed in experiments conducted by Billock and Tsou, where a localized funnel pattern stimulus induces an orthogonal tunnel pattern in the surrounding region of the visual field.

The authors use an Amari-type neural field equation to model the cortical dynamics in the primary visual cortex (V1). They make assumptions on the parameters of the model, including the coupling kernel, response function, and the intra-neural connectivity parameter.

The authors mathematically model the visual stimuli associated with funnel patterns localized in the fovea or peripheral visual field, and incorporate them as sensory inputs in the neural field equation. They then analyze the stationary state of the equation to assess its ability to capture the essential features of the visual illusions reported in Billock and Tsou's experiments.

The paper presents several key findings:

A linear response function in the neural field equation is not sufficient to reproduce the orthogonal response observed in the experiments.
Certain nonlinear response functions with strong inhibitory or excitatory influences and a weak slope, or a balance between excitatory and inhibitory influences, are also unable to capture the experimental observations.
However, if the response function exhibits a good interplay between excitatory and inhibitory influence and a weak slope, the stationary output of the neural field equation can reproduce the essential features of the visual illusions reported by Billock and Tsou.

The authors also provide numerical simulations to support their theoretical analysis. The paper highlights the importance of considering the complex interplay between excitatory and inhibitory neuronal activities in modeling certain nonlinear visual phenomena.

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Stats

The paper does not contain any explicit numerical data or statistics to support the key findings. The analysis is primarily theoretical, with some numerical simulations presented.

Quotes

"The matter of why neurons behave this way is outside the scope of this article, albeit being a very active topic of investigation in theoretical neuroscience [10, 26, 32]."
"Notice that while sensory inputs in Billock and Tsou's experiments are time-varying, our study finds that a temporal flicker of the complementary region where the stimulus is not localized is not necessary to reproduce these intriguing visual phenomena (an observation already made in [30])."
"Our interpretation is that Billock and Tsou's phenomena result wholly from the underlying non-local and nonlinear properties of neural activity in V1 rather than the temporal flickering of the complementary region where the stimulus is not localized."

Key Insights Distilled From

Reproducibility via neural fields of visual illusions induced by localized stimuli

by Cyprien Tame... at arxiv.org 10-03-2024

https://arxiv.org/pdf/2401.09108.pdf

Reproducibility via neural fields of visual illusions induced by localized stimuli

Deeper Inquiries

How can the proposed neural field model be extended to capture the illusory motions that subjects perceived in the after-images reported by Billock and Tsou?

To extend the proposed Amari-type neural field model to capture the illusory motions perceived in the after-images reported by Billock and Tsou, one could incorporate a time-dependent sensory input that simulates the flickering effect observed in the experiments. This would involve modifying the sensory input function ( I(x, t) ) to include temporal variations that mimic the flickering of the complementary regions surrounding the localized stimuli. By introducing a dynamic component to the sensory input, the model could account for the temporal aspects of visual processing, allowing it to simulate the perceived motion in the after-images.
Additionally, the model could benefit from integrating a more complex response function ( f ) that captures the nonlinear interactions between excitatory and inhibitory neurons more effectively. This could involve exploring different forms of non-odd nonlinearities that have been shown to reproduce specific visual phenomena. By adjusting the parameters of the response function and the connectivity kernel ( \omega ), the model could be fine-tuned to reflect the dynamics of illusory motion, thereby enhancing its predictive capabilities regarding the temporal aspects of visual perception.

What are the potential implications of the findings in this paper for our understanding of visual processing and perception in the brain?

The findings of this paper have significant implications for our understanding of visual processing and perception in the brain. By demonstrating that both excitatory and inhibitory neuronal activities play crucial roles in the emergence of visual illusions, the study challenges the traditional view that excitatory activity alone drives visual perception. This highlights the importance of considering the interplay between different types of neurons in the primary visual cortex (V1) when modeling visual phenomena.
Moreover, the successful reproduction of Billock and Tsou's experimental results using the Amari-type neural field model suggests that mathematical modeling can provide valuable insights into the mechanisms underlying visual perception. This approach may lead to a deeper understanding of how the brain processes complex visual stimuli and how various factors, such as spatial organization and temporal dynamics, influence perceptual outcomes. Ultimately, these insights could inform the development of more effective treatments for visual disorders and enhance our understanding of the neural basis of perception.

Can the insights gained from this study be applied to model other types of visual illusions or perceptual phenomena?

Yes, the insights gained from this study can be applied to model other types of visual illusions and perceptual phenomena. The framework established by the Amari-type neural field model, particularly its ability to incorporate nonlinear dynamics and the interactions between excitatory and inhibitory neurons, can be adapted to explore a wide range of visual illusions beyond those specifically examined in the context of funnel and tunnel patterns.
For instance, the model could be extended to investigate other well-documented visual phenomena, such as the Kanizsa triangle or the Hermann grid illusion, by adjusting the sensory input and response functions to reflect the specific characteristics of these illusions. Additionally, the principles of retinotopic organization and the role of spatially distributed neural activity can be leveraged to understand how different visual stimuli interact within the visual cortex, leading to various perceptual outcomes.
Furthermore, the mathematical techniques and numerical analysis methods employed in this study can serve as a foundation for future research aimed at uncovering the neural mechanisms underlying more complex perceptual phenomena, such as motion perception, depth perception, and the integration of visual information across different modalities. This versatility underscores the potential of neural field models in advancing our understanding of visual perception as a whole.