A Geometric Model of Multi-scale Orientation Preference Maps via Gabor Functions

Baspinar, Emre; Citti, Giovanna; Sarti, Alessandro

doi:10.1007/s10851-018-0803-3

Cited by 22 publications

(18 citation statements)

References 38 publications

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“…We did not elaborate on this in the present paper, leaving it to a potential forthcoming work. Another important question is “how to model a retinal network with cells having different orientation selectivity?” A V1 cortical model has been proposed by Baspinar et al [ 7 ] for the generation of orientation preference maps, considering both orientation and scale features. Each point (cortical column) is characterised by intrinsic variables, orientation and scale, and the corresponding RF is a rotated Gabor function.…”

Section: Discussionmentioning

confidence: 99%

On the potential role of lateral connectivity in retinal anticipation

Souihel

Cessac

2021

J. Math. Neurosc.

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We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can—under conditions analysed in the paper—trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334–338, 1999; Chen et al. in J. Neurosci. 33(1):120–132, 2013). We illustrate these predictions by two examples studied in the experimental literature: differential motion sensitive cells (Baccus and Meister in Neuron 36(5):909–919, 2002) and direction sensitive cells where direction sensitivity is inherited from asymmetry in gap junctions connectivity (Trenholm et al. in Nat. Neurosci. 16:154–156, 2013). We finally present reconstructions of retinal responses to 2D visual inputs to assess the ability of our model to anticipate motion in the case of three different 2D stimuli.

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Section: Discussionmentioning

confidence: 99%

On the potential role of lateral connectivity in retinal anticipation

Souihel

Cessac

2021

J. Math. Neurosc.

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“…Receptive profiles evoke a group structure at each frequency ω ∈ R + . We can describe the group structure underlying the set of receptive profiles by using the transformation law given in (7). First, we notice that the elements (q, θ , φ) induce the group given by…”

Section: The Architecture As a Lie Groupmentioning

confidence: 99%

“…The projection of our generalized model onto can be considered as equivalent to the model provided in [ 25 ]. The procedure we use to obtain the extended framework can be employed for the extension to a model associated with orientation-scale selective simple cells as well (see [ 7 ]).…”

Section: Introductionmentioning

confidence: 99%

A sub-Riemannian model of the visual cortex with frequency and phase

2020

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In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as rotated, frequency modulated, and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling of the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a two-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

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“…Fig. 1), a channel-representation [20], a lift by Gabor wavelets [2], or a fiber orientation density [28], where in general the absolute value |U (x, n)| is a probability density of finding a fiber structure at position x ∈ R d with local orientation n ∈ S d−1 .…”

Section: Figmentioning

confidence: 99%

Total Variation and Mean Curvature PDEs on the Space of Positions and Orientations

Duits

St-Onge²,

Portegies

et al. 2019

Lecture Notes in Computer Science

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Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space M = R d S d−1 of positions and orientations as a Lie group quotient in SE(d). For d = 2 this is called 'total roto-translation variation' by Chambolle & Pock. We extend this to d = 3, by a PDE-approach with a limiting procedure for which we prove convergence. We also include a Mean Curvature Flow (MCF) in our PDE model on M. This was first proposed for d = 2 by Citti et al. and we extend this to d = 3. Furthermore, for d = 2 we take advantage of locally optimal differential frames in invertible orientation scores (OS). We apply our TVF and MCF in the denoising/enhancement of crossing fiber bundles in DW-MRI. In comparison to data-driven diffusions, we see a better preservation of bundle boundaries and angular sharpness in fiber orientation densities at crossings. We support this by error comparisons on a noisy DW-MRI phantom. We also apply our TVF and MCF in enhancement of crossing elongated structures in 2D images via OS, and compare the results to nonlinear diffusions (CED-OS) via OS.

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A Geometric Model of Multi-scale Orientation Preference Maps via Gabor Functions

Cited by 22 publications

References 38 publications

On the potential role of lateral connectivity in retinal anticipation

On the potential role of lateral connectivity in retinal anticipation

A sub-Riemannian model of the visual cortex with frequency and phase

Total Variation and Mean Curvature PDEs on the Space of Positions and Orientations

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