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Abstract

A long standing hypothesis is that neural representations are adapted to environmental statistical regularities
(Attneave 1954, Barlow 1959), yet the relation between the primate visual system’s functional properties and the
statistical structure of natural images is still unknown. The central problem is that the high-dimensional space of
natural images is difficult to model. While many statistical models of small image patches that have been
suggested share certain neural response properties with the visual system (Atick 1990, Olshausen&Field 1996,
Schwarz&Simoncelli 2001), it is unclear how informative they are about the functional properties of visual
perception. Previously, we quantitatively evaluated how different models capture natural image statistics using
average log-loss (e.g. Eichhorn et al, 2009). Here we assess human sensitivity to natural image structure by
measuring how discriminable images synthesized by statistical models are from natural images. Our goal is to
improve the quantitative description of human sensitivity to natural image regularities and evaluate various
models’ relative efficacy in capturing perceptually relevant image structure.
Methods
We measured human perceptual thresholds to detect statistical deviations from natural images. The task was two
alternative forced choice with feedback. On a trial, two textures were presented side-by-side for 3 seconds: one a
tiling of image patches from the van Hateren photograph database, the other of model-synthesized images (Figure
1A). The task was to select the natural image texture.
We measured sensitivity at 3 patch sizes (3x3, 4x4, & 5x5 pixels) for 7 models. Five were natural image models: a
random filter model capturing only 2nd order pixel correlations (RND), the independent component analysis model
(ICA), a spherically symmetric model (L2S), the Lp-spherical model (LpS), and the mixture of elliptically
contoured distributions (MEC) with cluster number varied at 4 levels (k = 2, 4, 8, & 16). For MEC, we also used
patch size 8x8. We also tested perceptual sensitivity to independent phase scrambling in the Fourier basis (IPS)
and to global phase scrambling (GPS) which preserves all correlations between the phases and between the
amplitudes but destroys statistical dependences between phases and amplitudes. For each type, we presented 30
different textures to 15 naïve subjects (1020 trials/subject).
Results
Figure 1B shows performance by patch size for each model. Low values indicate better model performance as the
synthesized texture was harder to discriminate from natural. Surprisingly, subjects were significantly above chance
in all cases except at patch size 3x3 for MEC. This shows that human observers are highly sensitive to local
higher-order correlations as the models insufficiently reproduced natural image statistics for the visual system.
Further, the psychometric functions’ ordering parallels nicely the models’ average log-loss ordering, beautifully so
within MEC depending on cluster number, suggesting that the human visual system may have near perfect
knowledge of natural image statistical regularities and that average log-loss is a useful model comparison measure
in terms of perceptual relevance. Next, we will determine the features human observers use to discriminate the
textures’ naturalness which can help improve statistical modeling of perceptually relevant natural image structure.