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 Learning dictionary statistics from natural images


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A wavelet dictionary comprising a set of Gabor functions is learned from natural images using a sparse image code. Gabor functions describe the receptive field properties of simple cells in the primary visual cortex, and form a basis for efficiently coding natural image patches. Each Gabor function is completely specified by five parameters, and each parameter is treated as a random variable. I derive a learning rule and use it to learn a joint probability distribution over the Gabor parameters. Gabor parameters corresponding to receptive-field size and spatial frequency are found to be strongly correlated, and Pareto distributed: revealing that Gabor functions in the dictionary are scale invariant over a range of length scales. Parametric models of the joint probability distribution are estimated. Synthetic dictionaries sampled from these parametric models are shown to perform well on image-patch reconstruction, and highlight the importance of taking into account Gabor-parameter correlations. This approach generalizes uniform sampling of wavelet parameters, to sampling of wavelet parameters from non-uniform distributions learned from natural image data - thereby adapting wavelets to the statistics of the data.



Autor: Peter Loxley

Fuente: https://archive.org/







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