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

TL;DR

This paper reviews and compares algorithms inspired by the visual cortex for image inpainting, demonstrating that incorporating corruption location information leads to state-of-the-art results, supporting biological plausibility.

Contribution

It introduces and evaluates multiple hypoelliptic diffusion algorithms for image inpainting, highlighting the importance of corruption location data for superior reconstruction.

Findings

Algorithms without corruption info reconstruct recognizable images.

Algorithms with corruption info achieve state-of-the-art inpainting results.

Biological plausibility of the algorithms is supported by their performance.

Abstract

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.