Image inpainting via a control-theoretical model of human vision

Ugo Boscain (1, 2, 3) , Jean-Paul Gauthier (4) , Dario Prandi (3, 5)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CaGE - Control And GEometry
3 CNRS - Centre National de la Recherche Scientifique
4 UTLN UFR Droit - Université de Toulon - Faculté de Droit de Toulon
5 L2S - Laboratoire des signaux et systèmes

In this paper we consider 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.

Mots clés: Image inpainting; sub-Riemannian geometry; neurogeometry; hypoelliptic diffusionmage inpainting; sub- Riemannian geometry; hypoelliptic diffusion

Domaines: Optimisation et contrôle [math.OC]; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Ugo Boscain, Jean-Paul Gauthier, Dario Prandi. Image inpainting via a control-theoretical model of human vision. 2018 IEEE 14th International Conference on Control and Automation (ICCA), Jun 2018, Anchorage, AK, United States. ⟨10.1109/icca.2018.8444289⟩. ⟨hal-02394678⟩