Redundancies of the natural environment are a key feature for understanding biological vision but the multivariate probability density function (pdf) of natural images has not yet been identified in detail. We compare several source models for this pdf and analyze their explanatory power with respect to the basic operations performed in early vision. The most common models, like the Gauss-Markov source, are based on second-order correlations. They can describe properties like the 1/f^2 decay of the power spectral density and we show that they may even provide a limited explanation for the advantages of self-similar band-pass decompositions. However, we will also show that they are definitely unable to represent the common occurrence of oriented features in natural images, and can thus provide no convincing explanation of cortical orientation selectivity. This, as well as certain aspects of sparse coding might be better understood within the framework of a more recent concept: the separable Laplace source. This source, however, is incompatible with certain circular symmetries, as induced by the stationarity of the statistics. The latter are relevant for an understanding of the advantages of a polar feature space as provided by complex cells and/or cortical gain control mechanisms. We show that a better description of the local pdf can be obtained by the assumption of a hierarchy of intrinsic dimensionality. This leads to a low-dimensional manifold which can be approximated by a compound of quasi-orthogonal subspaces. We finally provide measurements which extend the local description and reveal dependencies between spatially separated aligned orientations. These may be related to an nonlinear predictive encoding by cortical end-stopped cells.