title: Statistical model of natural stimuli predicts edge-like pooling of spatial frequency channels in V2.
abstract: BACKGROUND
  It has been shown that the classical receptive fields of simple and complex cells in the primary visual cortex emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse or independent. We investigate how to learn features beyond the primary visual cortex from the statistical properties of modelled complex-cell outputs. In previous work, we showed that a new model, non-negative sparse coding, led to the emergence of features which code for contours of a given spatial frequency band.
  
  
  RESULTS
  We applied ordinary independent component analysis to modelled outputs of complex cells that span different frequency bands. The analysis led to the emergence of features which pool spatially coherent across-frequency activity in the modelled primary visual cortex. Thus, the statistically optimal way of processing complex-cell outputs abandons separate frequency channels, while preserving and even enhancing orientation tuning and spatial localization. As a technical aside, we found that the non-negativity constraint is not necessary: ordinary independent component analysis produces essentially the same results as our previous work.
  
  
  CONCLUSIONS
  We propose that the pooling that emerges allows the features to code for realistic low-level image features related to step edges. Further, the results prove the viability of statistical modelling of natural images as a framework that produces quantitative predictions of visual processing.
authors.affiliation: HIIT Basic Research Unit and Dept of Computer Science, University of Helsinki, Finland. ahyvarin@cc.helsinki.fi
authors.forename: Aapo
authors.initials: A
authors.lastname: Hyvärinen
authors.forename: Michael
authors.initials: M
authors.lastname: Gutmann
authors.forename: Patrik O
authors.initials: PO
authors.lastname: Hoyer
mesh_terms: D015233:Models, Statistical; D016571:Neural Networks, Computer; D016011:Normal Distribution; D010775:Photic Stimulation / Q000379:methods; D011237:Predictive Value of Tests; D014793:Visual Cortex / Q000502:physiology*
references.citation: Proc Biol Sci. 1998 Mar 7;265(1394):359-66
references.pmid: 9523437
references.citation: Nature. 1999 Oct 21;401(6755):788-91
references.pmid: 10548103
references.citation: J Vis. 2002;2(4):324-53
references.pmid: 12678582
references.citation: Vision Res. 2004 Feb;44(4):407-21
references.pmid: 14659967
references.citation: Vision Res. 2002 Jun;42(12):1593-605
references.pmid: 12074953
references.citation: Network. 2001 Aug;12(3):331-50
references.pmid: 11563533
references.citation: Vision Res. 2001 Mar;41(6):711-24
references.pmid: 11248261
references.citation: Perception. 1997;26(9):1101-20
references.pmid: 9509146
references.citation: Nat Neurosci. 2001 Aug;4(8):819-25
references.pmid: 11477428
references.citation: Nature. 1996 Jun 13;381(6583):607-9
references.pmid: 8637596
references.citation: Proc Biol Sci. 1998 Dec 7;265(1412):2315-20
references.pmid: 9881476
references.citation: Vision Res. 2002 Apr;42(8):1017-33
references.pmid: 11934453
references.citation: Nat Neurosci. 1998 Jun;1(2):150-4
references.pmid: 10195131
references.citation: J Opt Soc Am A Opt Image Sci Vis. 2001 Jan;18(1):65-77
references.pmid: 11152005
references.citation: J Neurophysiol. 2002 Nov;88(5):2557-74
references.pmid: 12424294
references.citation: Neural Comput. 2003 Mar;15(3):663-91
references.pmid: 12620162
references.citation: J Opt Soc Am A Opt Image Sci Vis. 2003 Jul;20(7):1237-52
references.pmid: 12868630
references.citation: Network. 2000 Aug;11(3):191-210
references.pmid: 11014668
references.citation: Vision Res. 1997 Dec;37(23):3327-38
references.pmid: 9425547
references.citation: Nat Neurosci. 1999 Mar;2(3):277-82
references.pmid: 10195222
references.citation: Proc Natl Acad Sci U S A. 2001 Feb 13;98(4):1935-40
references.pmid: 11172054
references.citation: J Neurophysiol. 1998 Dec;80(6):2811-23
references.pmid: 9862886
references.citation: J Neurophysiol. 2004 Jun;91(6):2859-73
references.pmid: 14749316
references.citation: IEEE Trans Neural Netw. 1999;10(3):626-34
references.pmid: 18252563
references.citation: Vision Res. 1999 Mar;39(5):887-95
references.pmid: 10341942
references.citation: Neural Comput. 2000 Jul;12(7):1705-20
references.pmid: 10935923
references.citation: Vision Res. 1985;25(3):365-74
references.pmid: 3895724