scholarly journals Local edge detectors using a sigmoidal transformation for piecewise smooth data

2013 ◽  
Vol 26 (2) ◽  
pp. 270-276
Author(s):  
Beong In Yun ◽  
Kyung Soo Rim
Keyword(s):  
Piecewise Smooth ◽  
Edge Detectors ◽  
Local Edge ◽  
Smooth Data

On the organization of receptive fields of retinal spot detectors projecting to the fish tectum: Analogies with the local edge detectors in frogs and mammals

2020 ◽  
Vol 528 (8) ◽  
pp. 1423-1435
Author(s):  
Elena M. Maximova ◽  
Alexey T. Aliper ◽  
Ilija Damjanović ◽  
Alisa A. Zaichikova ◽  
Paul V. Maximov
Keyword(s):  
Receptive Fields ◽  
Edge Detectors ◽  
Local Edge

scholarly journals Distinct Roles for Inhibition in Spatial and Temporal Tuning of Local Edge Detectors in the Rabbit Retina

PLoS ONE ◽  
2014 ◽  
Vol 9 (2) ◽  
pp. e88560 ◽  
Author(s):  
Sowmya Venkataramani ◽  
Michiel Van Wyk ◽  
Ilya Buldyrev ◽  
Benjamin Sivyer ◽  
David I. Vaney ◽  
...  
Keyword(s):  
Rabbit Retina ◽  
Edge Detectors ◽  
Local Edge

Neuronal Processing of Contours

Physiology ◽  
1990 ◽  
Vol 5 (4) ◽  
pp. 152-155 ◽  
Author(s):  
R Von der Heydt ◽  
E Peterhans ◽  
G Baumgartner
Keyword(s):  
Visual Cortex ◽  
Surface Contour ◽  
Edge Detectors ◽  
Neuronal Processing ◽  
Local Edge

The visual cortex looks at things in a strange way: perception of the white of a sheet of paper is related to activity of the neurons stimulated by its edges, not its surface;contour is a product of a cortical mechanism that integrates various "occlusion cues," not an intensity step that excites local edge detectors.

Filters, mollifiers and the computation of the Gibbs phenomenon

Acta Numerica ◽  
2007 ◽  
Vol 16 ◽  
pp. 305-378 ◽  
Author(s):  
Eitan Tadmor
Keyword(s):  
Physical Space ◽  
Gibbs Phenomenon ◽  
Delta Function ◽  
High Accuracy ◽  
Piecewise Smooth ◽  
Spectral Information ◽  
Smooth Functions ◽  
Exponential Accuracy ◽  
Local Loss ◽  
Edge Detectors

We are concerned here with processing discontinuous functions from their spectral information. We focus on two main aspects of processing such piecewise smooth data: detecting the edges of a piecewise smooth f, namely, the location and amplitudes of its discontinuities; and recovering with high accuracy the underlying function in between those edges. If f is a smooth function, say analytic, then classical Fourier projections recover f with exponential accuracy. However, if f contains one or more discontinuities, its global Fourier projections produce spurious Gibbs oscillations which spread throughout the smooth regions, enforcing local loss of resolution and global loss of accuracy. Our aim in the computation of the Gibbs phenomenon is to detect edges and to reconstruct piecewise smooth functions, while regaining the high accuracy encoded in the spectral data.To detect edges, we utilize a general family of edge detectors based on concentration kernels. Each kernel forms an approximate derivative of the delta function, which detects edges by separation of scales. We show how such kernels can be adapted to detect edges with one- and two-dimensional discrete data, with noisy data, and with incomplete spectral information. The main feature is concentration kernels which enable us to convert global spectral moments into local information in physical space. To reconstruct f with high accuracy we discuss novel families of mollifiers and filters. The main feature here is making these mollifiers and filters adapted to the local region of smoothness while increasing their accuracy together with the dimension of the data. These mollifiers and filters form approximate delta functions which are properly parametrized to recover f with (root-) exponential accuracy.

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