Efficient representation of natural images using local cooperation
Abstract
Low-level perceptual computations may be understood in terms of efficient codes (Simoncelli and Olshausen, 2001, Annual Review of Neuroscience 24 1193-216). Following this argument, we explore models of representation for natural static images as a way to understand the processing of information in the primary visual cortex. This representation is here based on a generative linear model of the synthesis of images using an over-complete multi-resolution dictionary of edges. This transform is implemented using log-Gabor filters and permits an exact reconstruction of any image. However, this linear representation is redundant and since to any image may correspond different representations, we explore more efficient representations of the image. The problem is stated as an ill-posed inverse problem and we compare first different known strategies by computing the efficiency of the solutions given by Matching Pursuit (Perrinet, 2004, IEEE Trans. Neural Networks 15 1164-75) and sparse edge coding (Fischer, in press, Trans. Image Processing) with classical representation methods such as JPEG. This comparison allows us to provide a synthesized approach using a probabilistic representation which would progressively construct the neural representation by using lateral cooperations. We propose an algorithm which dynamically diffuses information to correlated filters so as to yield a progressively disambiguated representation. This approach takes advantage of the computational properties of spiking neurons such as Integrate-and-Fire neurons and provides an efficient yet simple model for the representation of natural images. This representation is directly linked with the edge content of natural images and we show applications of this method to edge extraction, denoising and compression. We also show that this dynamical approach fits with neuro-physiological observations and may explain the non-linear interactions between neighboring neurons which may be observed in the cortex.
- relies on log-Gabor filters:(2007). Self-Invertible 2D Log-Gabor Wavelets. International Journal of Computer Vision.
Schematic structure of the primary visual cortex implemented in the present study. 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 direc-tions perpendicular to the cell preferred orientation and toward adjacent orientations (light-red connections). Facilitation occurs to-wards co-aligned cells up to a larger distance (dark-blue connections).
Laurent U Perrinet
Researcher in Computational Neuroscience
My research interests include Machine Learning and computational neuroscience applied to Vision.