Highly corrupted image inpainting through hypoelliptic diffusion

We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging Sci., vol. 7, no. 2, pp. 669--695, 2014] and based upon a semi-discrete variation of the Citti-Petitot-Sarti model of the primary visual cortex V1. The AHE algorithm is based on a suitable combination of sub-Riemannian hypoelliptic diffusion and ad-hoc local averaging techniques. In particular, we focus on reconstructing highly corrupted images (i.e. where more than the 80% of the image is missing), for which we obtain reconstructions comparable with the state-of-the-art.

Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information of where the image is corrupted, and others that do it. While the first algorithm is able to reconstruct only images that our visual system is still capable of recognize, we show that those of the second type completely transcend such limitation providing reconstructions at the state-of-the-art in image inpainting. This can be interpreted as a validation of the fact that our visual cortex actually encodes the first type of algorithm.