Multi-frequency image completion via a biologically-inspired sub-Riemannian model with frequency and phase

TL;DR

This paper introduces a biologically-inspired image completion algorithm that models visual cortex features like orientation, frequency, and phase using a sub-Riemannian geometry, enabling effective image reconstruction.

Contribution

It develops a novel cortically-inspired model incorporating orientation, frequency, and phase for image completion, based on a five-dimensional sub-Riemannian geometry.

Findings

Effective completion of corrupted images with complex features

Model captures orientation, frequency, and phase interactions

Outperforms traditional methods in preserving visual details

Abstract

We present a novel cortically-inspired image completion algorithm. It uses a five dimensional sub-Riemannian cortical geometry modelling the orientation, spatial frequency and phase selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two dimensional corrupted input image via a Gabor transform and represent those values in terms of cortical cell output responses in the model geometry. Then it performs completion via a diffusion concentrated in a neighbourhood along the neural connections within the model geometry. The diffusion models the activity propagation integrating orientation, frequency and phase features along the neural connections. Finally, the algorithm transforms back the diffused and completed output responses back to the two dimensional image plane.