When independent component analysis (ICA) is applied to color natural images, the representation it learns has spatiochromatic properties similar to the responses of neurons in primary visual cortex. Existing models of ICA have only been applied to pixel patches. This does not take into account the space-variant nature of human vision. To address this, we use the space-variant log-polar transformation to acquire samples from color natural images, and then we apply ICA to the acquired samples. We analyze the spatiochromatic properties of the learned ICA filters. Qualitatively, the model matches the receptive field properties of neurons in primary visual cortex, including exhibiting the same opponent-color structure and a higher density of receptive fields in the foveal region compared to the periphery. We also adopt the “self-taught learning” paradigm from machine learning to assess the model’s efficacy at active object and face classification, and the model is competitive with the best approaches in computer vision. 1. Introduction In humans and other simian primates, central foveal vision has an exceedingly high spatial resolution (acuity) compared to the periphery. This space-variant scheme enables a large field of view, while allowing visual processing to be efficient. The human retina contains about six million cone photoreceptors but sends only about one million axons to the brain [1]. By employing a space variant representation, the retina is able to greatly reduce the dimensionality of the visual input, with eye movements allowing fine details to be resolved if necessary. The retina’s space-variant representation is reflected in early visual cortex’s retinotopic map. About half of primary visual cortex (V1) is devoted solely to processing the central 15 degrees of visual angle [2, 3]. This enormous overrepresentation of the fovea in V1 is known as cortical magnification [4]. Neurons in V1 have localized an orientation sensitive receptive fields (RFs). V1-like RFs can be algorithmically learned using independent component analysis (ICA) [5–8]. ICA finds a linear transformation that makes the outputs as statistically independent as possible [5], and when ICA is applied to achromatic natural image patches, it produces basis functions that have properties similar to neurons in V1. Moreover, when ICA is applied to color image patches, it produces RFs with V1-like opponent-color characteristics, with the majority of the RFs exhibiting either dark-light opponency, blue-yellow opponency, or red-green opponency [6–8]. Filters learned from unlabeled
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