A stochastic model for eye movements during fixation on a stationary target

Vasudevan, R.; Phatak, A. V.; Smith, James D.

doi:10.1007/bf00267762

Cited by 6 publications

(2 citation statements)

References 16 publications

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“…The idea that FEMs is a stochastic process and may be described as a random walk has a long history, [ 29 , 30 , 31 , 32 , 33 , 42 ].…”

Section: Information Processing In Dynamicsmentioning

confidence: 99%

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Microsaccades, Drifts, Hopf Bundle and Neurogeometry

Alekseevsky

2022

J. Imaging

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The first part of the paper contains a short review of the image processing in early vision is static, when the eyes and the stimulus are stable, and in dynamics, when the eyes participate in fixation eye movements. In the second part, we give an interpretation of Donders’ and Listing’s law in terms of the Hopf fibration of the 3-sphere over the 2-sphere. In particular, it is shown that the configuration space of the eye ball (when the head is fixed) is the 2-dimensional hemisphere SL+, called Listing hemisphere, and saccades are described as geodesic segments of SL+ with respect to the standard round metric. We study fixation eye movements (drift and microsaccades) in terms of this model and discuss the role of fixation eye movements in vision. A model of fixation eye movements is proposed that gives an explanation of presaccadic shift of receptive fields.

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“…The idea that FEMs is a stochastic process and may be described as a random walk has a long history, [ 29 , 30 , 31 , 32 , 33 , 42 ].…”

Section: Information Processing In Dynamicsmentioning

confidence: 99%

“…Fixational eye movements are stochastic in nature. There were proposed various stochastic models of FEM as a random walk, see [ 29 , 30 , 31 ]. We especially note the works [ 32 , 33 ].…”

Section: Introductionmentioning

confidence: 99%

Microsaccades, Drifts, Hopf Bundle and Neurogeometry

Alekseevsky

2022

J. Imaging

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Exploring the Characteristics of Secret Eye Movements During Fixation: a New Approach of Chaotic Time Series

Schuchard

Lim

1997

Documenta Ophthalmologica Proceedings Series

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A theory of the pattern induced flight orientation of the fly Musca domestica

1973

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The theory presented here describes the visual orientation behavior of fixed flying insects (the fly Musca domestica) in the presence of elementary patterns. The theory, which is based on a number of experimental results, Reichardt (1973), is a phenomenological one whose main purpose is to provide an organizational framework for treating a complex phenomenon without the need of detailed assumptions about the neural mechanisms actually involved. A simple hypothesis concerning the basic structure of the pattern fixation process leads to an equivalent stochastic equation of the Langevin type, which can be linearized for simple single-stripe panoramas. A critical experiment supports these theoretical assumptions. In addition, the effect on pattern fixation behavior of adding contrast noise to the background of the panorama, is quantitatively predicted by the theory. In the more general case of a panorama consisting of many vertical stripes, the Fokker-Planck equation associated with the Langevin equation, no longer linear, is solved. Making use of an experimentally proven ldquosuperposition principlerdquo, the stationary pattern fixation behavior of the fly in an arbitrary panorama consisting of a collection of vertical stripes is predicted. In this context, concepts like pseudo-invariance and phase-transition can be applied to the insects orientation behavior. The theory presented here seems to contain rich classification properties, which might provide the foundations for an understanding of more complex pattern discrimination processes. Possible extensions of the theory, as well as some similarities to human eye fixation, are also discussed

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A stochastic model for eye movements during fixation on a stationary target

Cited by 6 publications

References 16 publications

Microsaccades, Drifts, Hopf Bundle and Neurogeometry

Microsaccades, Drifts, Hopf Bundle and Neurogeometry

Exploring the Characteristics of Secret Eye Movements During Fixation: a New Approach of Chaotic Time Series

A theory of the pattern induced flight orientation of the fly Musca domestica

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