Although the higher order mechanisms behind object representation and classification in the visual system are still not well understood, there are hints that simple shape primitives such as “curviness” might activate neural activation and guide this process. Drawing on elementary invariance principles, we propose that a statistical geometric object, the probability distribution of the normalized contour curvatures (NCC) in the intensity field of a planar image, has the potential to represent and classify categories of objects. We show that NCC is sufficient for discriminating between cognitive categories such as animacy, size and type, and demonstrate the robustness of this metric to variation in illumination and viewpoint, consistent with neurobiological constraints, psychological experiments, and aspects of computer vision. A generative model for producing artificial images with the observed NCC distributions highlights the key features that our metric captures and just as importantly, those that it does not. More broadly, our study points to the need for statistical geometric approaches that build in the invariances of the natural world.
A pre-print of our paper, “Image classification and cognition using contour curvature statistics”, can be found on bioRxiv.