Abstract : The structure of receptive fields in the visual cortex is believed to be shaped by unsupervised learning. A simple variant of unsupervised learning is the extraction of principal components. In this paper, we derived analytically the form of the principal components of natural images. This derivation relies on results about the covariance matrix of natural images. Our results predict both the shapes and the phases of the receptive fields. We also compared our results to numerical simulation results. Finally the biological relevance of our results is discussed.