From neural oscillations to variational problems in the visual cortex

Sarti, Alessandro; Citti, Giovanna; Manfredini, Maria

doi:10.1016/j.jphysparis.2003.09.014

Cited by 21 publications

(10 citation statements)

References 37 publications

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“…We want responses to interact if they are linked by the association field displayed in Figure 2 (left). The exact solution leads to the computation of geodesics in a space with sub-Riemannian geometry [20,19].…”

Section: Detection Algorithmmentioning

confidence: 99%

Contours, Corners and T-Junctions Detection Algorithm

Buades¹,

Gioi²,

Navarro³

2018

Image Processing on Line

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This article describes the implementation of the method proposed by Buades, Grompone and Navarro in 2017 for the detection of line segments, contours, corners and T-junctions. The method is inspired by the mammal visual system. The detection of corners and T-junctions plays a role as part of the process in contour detection. An a contrario validation is applied to select the most meaningful contours without the need of fixing any critical parameter. Source CodeThe reviewed source code and documentation for this algorithm are available from the web page of this article 1 . Compilation and usage instruction are included in the README.txt file of the archive.

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Section: Detection Algorithmmentioning

confidence: 99%

Contours, Corners and T-Junctions Detection Algorithm

Buades¹,

Gioi²,

Navarro³

2018

Image Processing on Line

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“…The connections are usually directed and model inhibitory/excitatory interactions between the regions. Examples of such networks include interactions of the amacrine and the ganglion cells in the retina [48,49], hypercolumns in the visual cortex [50,51] and glomeruli interactions in the olfactory bulb [52,53].…”

Section: Synchronous Subregionsmentioning

confidence: 99%

Neural Activity Measures and Their Dynamics

Shlizerman¹,

Schröder²,

Kutz³

2012

SIAM J. Appl. Math.

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Abstract. We provide an asymptotically justified derivation of activity measure evolution equations (AMEE) for a finite size neural network. The approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model, i.e. Hodgkin-Huxley equations or their reductions. By representing the interacting network as self and pairwise interactions, we propose a general definition of spatial projections of the network, called activity measures, that quantify the activity of a network. We show that the evolution equations that govern the dynamics of the activity measure shadow the activity measure of the network (i.e. the two quantities stay close to each other for all times) for general interactions and various asymptotic dynamics. The AMEE effectively serve as a dimensionality reduction technique for the complex network when spatial synchrony and coherence are present and allow to a priori predict network dynamics that would not be guessed from individual neuron behavior. To demonstrate an explicit derivation of such a reduction, we consider the mean measure for a network of interacting FitzHugh-Nagumo neurons.Computational results comparing the full network dynamics with the mean AMEE model of identical and nonidentical FitzHugh-Nagumo and FitzHugh-Rinzel neurons validate the shadowing theorems and expose the various resulting AMEE models that allow to describe the mean of the network.

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“…A similar approach was independently developed by [30], [31] who developed a Lie group theory for image analysis. This cortical method was later adapted to the problem of perceptual unit identification in [32], based on a previous study on neural synchronization [33]. In our previous work [34], we applied an instrument inspired by the geometry of the primary visual cortex (V1) and the approach of [32] to group and separate the blood vessels as individual perceptual units, even though there were informations missing due to poor segmentations.…”

Section: Introductionmentioning

confidence: 99%

Curvature Integration in a 5D Kernel for Extracting Vessel Connections in Retinal Images

Abbasi-Sureshjani

Favali

Citti

et al. 2018

IEEE Trans. on Image Process.

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Tree-like structures, such as retinal images, are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite several segmentation and tracking methods proposed in the literature, there still exist several limitations specifically when two or more curvilinear structures cross or bifurcate, or in the presence of interrupted lines or highly curved blood vessels. In this paper, we propose a novel approach based on multi-orientation scores augmented with a contextual affinity matrix, which both are inspired by the geometry of the primary visual cortex (V1) and their contextual connections. The connectivity is described with a 5D kernel obtained as the fundamental solution of the Fokker-Planck equation modeling the cortical connectivity in the lifted space of positions, orientations, curvatures, and intensity. It is further used in a self-tuning spectral clustering step to identify the main perceptual units in the stimuli. The proposed method has been validated on several easy as well as challenging structures in a set of artificial images and actual retinal patches. Supported by quantitative and qualitative results, the method is capable of overcoming the limitations of current state-of-the-art techniques.

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From neural oscillations to variational problems in the visual cortex

Cited by 21 publications

References 37 publications

Contours, Corners and T-Junctions Detection Algorithm

Contours, Corners and T-Junctions Detection Algorithm

Neural Activity Measures and Their Dynamics

Curvature Integration in a 5D Kernel for Extracting Vessel Connections in Retinal Images

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