Ecological statistics continues to serve as an important source of information and inspiration for vision research. In this work, we seek feature types that are induced by the statistics of natural images. As point of departure, we use the Gaussian derivative filters as a model of V1 simple cell ensembles. Specifically, we focus on 2nd order derivative filters. 2nd order differential structure can be re-parameterised and qualitatively described through the shape index. Following Koenderink, we group image patches that are metamerically equivalent - in this case have identical shape index. For each metamery class, a class representative is selected as the most likely among all collected patches and thus is not tainted by any models other than that implicitly dictated by the distribution of natural image patches. Although the shape index spans a continuous real interval, our results show that maximum likelihood 2nd order natural image structure falls in one of only five qualitatively distinct categories: dark blobs, dark bars, saddles, light bars, and light blobs. Control experiments performed on Gaussian noise images and phase randomised natural images give results that are in accordance with theoretical predictions and suggest that the main result is specific to natural images.