Low-dimensional representations are key to solving problems in high(cid:173) level vision, such as face compression and recognition. Factorial coding strategies for reducing the redundancy present in natural images on the basis of their second-order statistics have been successful in account(cid:173) ing for both psychophysical and neurophysiological properties of early vision. Class-specific representations are presumably formed later, at the higher-level stages of cortical processing. Here we show that when retinotopic factorial codes are derived for ensembles of natural objects, such as human faces, not only redundancy, but also dimensionality is re(cid:173) duced. We also show that objects are built from parts in a non-Gaussian fashion which allows these local-feature codes to have dimensionalities that are substantially lower than the respective Nyquist sampling rates.