We previously showed that the human visual system is exquisitely sensitive to local natural image regularities (Gerhard et al, 2011 Perception 40 ECVP Supplement, 18). However, luminance histogram features were a very salient cue. Here we focus instead on sensitivity to the local shape regularities in natural images. Stimuli were textures made of image patches sampled either from natural images or from a natural image model, where observers had to discriminate the two kinds of textures in a forced choice task. We used a variety of natural image models that capture varying degrees of higher-order correlations. We removed salient luminance cues from the textures and measured discriminability of the models from natural images when shape was the only cue. Above chance performance with patches 4x4 pixels in size and larger indicated sensitivity to higher-order natural image correlations associated with shape. A surprising pattern of discriminability also emerged which indicated an advantage of the independent components analysis model in capturing salient shape content, even though it captures less of the overall higher-order correlations than other models tested. We also analyzed the contribution of different principle components to discrimination performance in order to develop a preliminary mechanistic explanation using responses of spatial frequency filter banks.