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Sparse approximation of images inspired from the functional architecture of the primary visual areas


Abstract
Several drawbacks of critically sampled wavelets can be solved by overcomplete multiresolution transforms and sparse approximation algorithms. Facing the difficulty to optimize such nonorthogonal and nonlinear transforms, we implement a sparse approximation scheme inspired from the functional architecture of the primary visual cortex. The scheme models simple and complex cell receptive fields through log-Gabor wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells. Functionally these interactions allow to extract edges and ridges, providing an edge-based approximation of the visual information. The edge coefficients are shown sufficient for closely reconstructing the images, while contour representations by means of chains of edges reduce the information redundancy for approaching image compression. Additionally, the ability to segregate the edges from the noise is employed for image restoration.

fig_architecure.png

Figure1: Schematic structure of the primary visual cortex implemented in Fischer (2007). Simple cortical cells are modeled through log-Gabor functions. They are organized in pairs in quadrature of phase (dark-gray circles). For each position the set of different orientations compose a pinwheel (large light-gray circles). The retinotopic organization induces that adjacent spatial positions are arranged in adjacent pinwheels. Inhibition interactions occur towards the closest adjacent positions which are in the directions perpendicular to the cell preferred orientation and toward adjacent orientations (light-red connections). Facilitation occurs towards coaligned cells up to a larger distance (dark-blue connections).

reference


related bibliography on edge detection

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  • Jean Petitot. The neurogeometry of pinwheels as a sub-Riemannian contact structure, URL . Journal of Physiology (Paris), 97(2-3):265--309, 2003 abstract.
  • Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Efficient representation of natural images using local cooperation. In Perception, pages 241. 2005 abstract.
  • Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Sparse Gabor wavelets by local operations. In Proceedings SPIE, pages 75--86. 2005 abstract.
  • Rafael Redondo, Sylvain Fischer, Laurent Perrinet, Gabriel Crist\'obal. Modeling of simple cells through a sparse overcomplete gabor wavelet representation based on local inhibition and facilitation. In Perception, pages 238. 2005 abstract.
  • Sylvain Fischer, Gabriel Crist\'obal, Rafael Redondo. Sparse Overcomplete Gabor Wavelet Representation Based on Local Competitions. IEEE Transactions in Image Processing, 15(2):265, 2006 abstract.
  • Laurent Perrinet, Frédéric V. Barthélemy, Guillaume S. Masson. Input-output transformation in the visuo-oculomotor loop: modeling the ocular following response to center-surround stimulation in a probabilistic framework. In 1ère conférence francophone NEUROsciences COMPutationnelles - NeuroComp, 2006 abstract.
  • Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Sparse approximation of images inspired from the functional architecture of the primary visual areas, URL . EURASIP Journal on Advances in Signal Processing, 2007(1):122, 2007 abstract.
  • Sylvain Fischer, Filip Sroubek, Laurent Perrinet, Rafael Redondo, Gabriel Crist\'obal. Self-invertible 2D log-Gabor wavelets. International Journal of Computer Vision, 2007 abstract.

All material (c) L. Perrinet. Please check the copyright notice.


TagYear07 TagPublicationsArticles TagSparse TagImageProcessing

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