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Aaron P Johnson, Curtis L Baker, Jr.; Response of first- and second-order filters to natural images. Journal of Vision 2003;3(9):520. doi: 10.1167/3.9.520.
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© ARVO (1962-2015); The Authors (2016-present)
Previous analyses of natural image statistics have mainly dealt with their Fourier power spectra. Here we explore image statistics by examining responses to biologically motivated filters which are spatially localized, and respond to first-order (luminance-defined), and second-order (contrast- or texture-defined) characteristics. We begin by comparing the distribution of natural image responses across filter parameters for first and second order information, and whether the two kinds of response are correlated. First-order filtering was implemented as convolutions with oriented Gabor functions, with gains scaled to give equal amplitude response across spatial frequency for random fractal images (Field & Brady, Vision Res. 37:3367–3383). Second-order operators were a pair of such Gabors in a filter-rectify-filter arrangement. Responses were obtained for many combinations of parameters (spatial frequency: 2–64 cycles/image, orientation: 0–180 deg, phase: sine and cosine) in early and late filters. In agreement with previous spectral analyses, the first-order results show approximately equal responses at all spatial frequencies, but a pronounced orientational anisotropy in favor of vertical and horizontal, which was particularly evident at high spatial frequencies. Phase had no significant effect. Second-order responses also exhibited nearly equal responses across spatial frequencies; however, they show only a small bias towards the horizontal orientation, probably due to foreshortening. Magnitudes of first- and second-order responses were usually uncorrelated; however for particular combinations of filter parameters, they were very highly correlated for natural images but not for random fractals. These results indicate that second-order information in natural scenes shows the same self-similarity previously described for first-order statistics, and that the two kinds of information are correlated in a highly structured manner.
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