Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/21911
Title: The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images
Contributor(s): Loxley, Peter  (author)orcid 
Publication Date: 2017
DOI: 10.1162/neco_a_00997
Handle Link: https://hdl.handle.net/1959.11/21911
Abstract: The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.
Publication Type: Journal Article
Source of Publication: Neural Computation, 29(10), p. 2769-2799
Publisher: MIT Press
Place of Publication: United States of America
ISSN: 1530-888X
Field of Research (FOR): 010506 Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter
080108 Neural, Evolutionary and Fuzzy Computation
010202 Biological Mathematics
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
970106 Expanding Knowledge in the Biological Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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