June 2004
Volume 4, Issue 8
Vision Sciences Society Annual Meeting Abstract  |   August 2004
Sparse Coding in First- and Second-Order Filtered Images.
Author Affiliations
  • Aaron P. Johnson
    McGill Vision Research, Canada
Journal of Vision August 2004, Vol.4, 542. doi:https://doi.org/10.1167/4.8.542
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      Aaron P. Johnson, Curtis L. Baker; Sparse Coding in First- and Second-Order Filtered Images.. Journal of Vision 2004;4(8):542. doi: https://doi.org/10.1167/4.8.542.

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      © ARVO (1962-2015); The Authors (2016-present)

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Most natural images contain regions of interest, interspersed with redundant uniform information. This redundancy may be reduced by using a sparsely-coded image representation, in which only a small number of neurons are activated. Here we simulate the responses of filters for first-order (luminance-modulated) and second-order (texture and contrast-modulated) information to examine the sparseness of their activation. First-order linear filtering was implemented as convolutions of cosine-windowed images with oriented Gabor functions, with gains scaled to give equal amplitude response across spatial frequency to random fractal images. Second-order operators were a pair of such Gabors in a filter-rectify-filter cascade. We obtained unsigned responses across a range of filter parameters (spatial frequency: 2–64 cycles/image, orientation: 0–180 deg., phase: sine and cosine). The sparseness of each filter's response was measured as its kurtosis (fourth-order cumulant). Both first- and second-order outputs exhibit a high kurtosis to natural but not phase-scrambled images. For first-order information, high spatial frequency filters (>32 cycles/image) orientated around the horizontal and vertical show the greatest sparseness. This effect can be removed by inverse-scaling the cosine window size with spatial frequency, as previously hypothesized (Thompson, 2001). For second-order information, there is no orientation or spatial frequency dependence, but kurtosis is always significantly larger for natural images than for their phase-scrambled counterparts. A number of different nonlinearities in the FRF cascade were studied, with sparseness being maximized using a power function with an n= 3 or 4. Finally, for a given image, those filters which respond strongest to first- and second-order information, also show the strongest correlation, and are the best at maximizing sparseness.

Johnson, A. P., Baker, C. L.Jr.(2004). Sparse Coding in First- and Second-Order Filtered Images[Abstract]. Journal of Vision, 4( 8): 542, 542a, http://journalofvision.org/4/8/542/, doi:10.1167/4.8.542. [CrossRef]
 Funded by CIHR (Grant No. MOP-9685)

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