Exploitation of natural image statistics by biological vision systems: 1/f/sup 2/ power spectra and self-similar bandpass decompositions

The second-order statistics of natural images can be well characterized by a "self-similar" 1/F/sup 2/ power spectrum and the bandpass decomposition in biological vision systems is characterized by a self-similar, wavelet-like structuring of the "frequency channels". It has thus often been suggested that there might exist a systematic interrelationship between these two properties, but a complete formal derivation of this relation has not yet been provided. Using rate-distortion arguments and a complexity measure, we first show that a self-similar bandpass decomposition can achieve a desired level of distortion with a less complex system structure than required for a decomposition in bands of equal linear bandwidth. A closer analysis reveals that the true optimum decomposition is approximately self-similar but shows a systematic decrease of the log-bandwidths with increasing center frequency of the subbands. Since this effect has also been observed in neurophysiological experiments, we conclude that the typical properties of visual neurons may in fact result from an optimized exploitation of the statistical redundancies of the natural environment.

[1]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[2]  Bernhard Wegmann,et al.  The importance of intrinsically two-dimensional image features in biological vision and picture coding , 1993 .

[3]  G. Krieger,et al.  Neural network models and the visual cortex: the missing link between orientation selectivity and the natural environment , 1997, Neuroscience Letters.

[4]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[5]  J. Movshon,et al.  Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex. , 1978, The Journal of physiology.

[6]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[7]  S. Laughlin,et al.  Predictive coding: a fresh view of inhibition in the retina , 1982, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[8]  D. G. Albrecht,et al.  Spatial frequency selectivity of cells in macaque visual cortex , 1982, Vision Research.

[9]  Joseph J. Atick,et al.  What Does the Retina Know about Natural Scenes? , 1992, Neural Computation.

[10]  David J. Field,et al.  What Is the Goal of Sensory Coding? , 1994, Neural Computation.

[11]  J. O. Limb,et al.  Intraframe coding for picture transmission , 1972 .

[12]  William A. Pearlman,et al.  Performance Bounds for Subband Coding , 1991 .

[13]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[14]  R. Haddad,et al.  Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets , 1992 .

[15]  A.V. Oppenheim,et al.  The importance of phase in signals , 1980, Proceedings of the IEEE.

[16]  F. Attneave.  Some informational aspects of visual perception. , 1954, Psychological review.

[17]  David J. Field,et al.  Wavelet-Like Receptive Fields Emerge From a Network That Learns Sparse Codes for Natural Images , 1996 .

[18]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  R Linsker,et al.  From basic network principles to neural architecture: emergence of orientation-selective cells. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[20]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[21]  J. H. Hateren,et al.  Independent component filters of natural images compared with simple cells in primary visual cortex , 1998 .