Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System

This paper summarizes results of a sequence of works related to usage of sub-Riemannian (SR) geometry in image processing and modeling of the human visual system. In recent research in psychology of vision (J. Petitot, G.Citti, A. Sarti) it was shown that SR geodesics appear as natural curves that model a mechanism of the primary visual cortex V1 of a human brain for completion of contours that are partially corrupted or hidden from observation. We extend the model to include data adaptivity via a suitable external cost in the SR metric. We show that data adaptive SR geodesics are useful in real image analysis applications and provide a refined model of V1 that takes into account the presence of a visual stimulus.