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| Paper IPM / Cognitive / 13436 |
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Natural scenes contain rich information in their local phase structure compared to their amplitudes. Nevertheless, conventional models of visual systems represent the natural images using superposition of receptive fields (RFs) based on the information contained only in the amplitudes. As a result, the redundancy in the images is not completely removed. Typically, the responses of the RFs after training exhibit circular dependencies. Thus recent studies suggested decomposing images using amplitude and phase coefficients of a complex representation. However, these studies assume uniform phase distributions. Here, we report the presence of structured bimodal distributions for the phase variables of the complex RFs responding to natural scenes, suggesting that the uniform distribution is insufficient to reduce the redundancy of natural scenes. To show this, we first construct a complex RF defined as a pair of Gabor-like RFs possessing the same features such as scales, orientations, and frequencies, but are in quadrature phase. Next, we obtain a phase distribution of its responses to patches selected from whitened natural scenes. The phase distribution was then fitted by a mixture of two von Mises distributions and a uniform circular distribution, using the expectation-maximization algorithm developed for this study. Finally, we apply the complex RFs possessing different features to the natural image patches to investigate variation of the phase distributions with these features. The analysis revealed a half of the complex RFs exhibited bimodal distributions. The distances between two peaks of the distributions were about 180 degree. Importantly, the shape of the distributions significantly varied when the scale or frequency of the complex RFs changed: The complex RFs possessing low frequencies or small scales yielded the bimodal distributions. Our results suggest that the redundancy in the natural images can be further removed if we consider bimodal phase distributions, in particular, for low-frequency / small-scale complex RFs.
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