Efficient representation of natural images using local cooperation
- Using structure and functions inspired by the primary visual areas to construct efficient image processing algorithms.
Figure: Exemple of denoising using Matching Pursuit: denoising.avi (upper left) noisy image. red dots correspond to spikes (upper right) absolute coefficient value (down left) Squared error (down right) reconstructed image
See also Publications/Fischer07
For the underlying image reprensation using log-Gabor filters, see Publications/Fischer07cv
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, 2007, 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.
- Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Cristobal. Efficient representation of natural images using local cooperation. In Perception, pages 238. 2005, abstract
additional related publications
- Rafael Redondo, Sylvain Fischer, Laurent Perrinet, Gabriel Cristobal. Simple cells modeling through a sparse overcomplete gabor wavelet representation based on local inhibition and facilitation.. In Perception, pages 238. 2005 abstractWe present a biologically plausible model of simple cortical cells as 1) a linear transform representing edges and 2) a non-linear iterative stage of inhibition and facilitation between neighboring coefficients. The linear transform is a complex log-Gabor wavelet transform which is overcomplete (i.e. there are more coefficients than pixels in the image) and has exact reconstruction. The inhibition consists in diminishing down the coefficients which are not at a local-maxima along the direction normal to the edge filter orientation, whereas the facilitation enhances the collinear and co-aligned local-maximum coefficients. At each iteration and after the inhibition and facilitation stages, the reconstructed error is subtracted in the transform domain for keeping an exact reconstruction. Such process concentrates the signal energy on a few coefficients situated along the edges of the objects, yielding a sparse representation. The rationale for such procedure is: (1) th e overcompleteness offers flexibility for activity reassignment; (2) images can be coded by sparse Gabor coefficients located on object edges; (3) image contours produce aligned and collinear local-maxima in the transform domain; (4) the inhibition/facilitation processes are able to extract the contours.The sparse Gabor coefficients are mostly connected each other and located along object contours. Such layout makes chain coding suitable for compression purposes. Specially adapted to Gabor wavelets features, our chain coding represents every chain by its end-points (head and tail) and the elementary movements necessary to walk along the chain from head to tail. Moreover it predicts the module and phase of each Gabor coefficient according to the previous chain coefficient. As a result, redundancy of the transform domain is further reduced. Used for compression, the scheme limits particularly the high-frequency artifacts. The model performs also efficiently in tasks the Human Visual System is supposed to deal with, as for instance edge extraction and image denoising..
- Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Cristobal. Sparse Gabor wavelets by local operations, URL . In Proceedings SPIE, pages 75--86. 2005 abstract
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