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

arXiv: https://arxiv.org/abs/2110.14330 · HTML: https://mlsanity.com/paper/2110.14330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 76 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Roto-Translation Covariant Convolutional Networks for Medical Image Analysis](https://mlsanity.com/paper/1804.03393/) (2018)
- [Highly corrupted image inpainting through hypoelliptic diffusion](https://mlsanity.com/paper/1502.07331/) (2015)
- [A geometric model of multi-scale orientation preference maps via Gabor functions](https://mlsanity.com/paper/1712.04329/) (2017)
- [Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group](https://mlsanity.com/paper/2002.08063/) (2020)
- [A cortical-inspired geometry for contour perception and motion integration](https://mlsanity.com/paper/1301.3433/) (2013)
- [A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions](https://mlsanity.com/paper/2012.14184/) (2020)
- [Hypoelliptic diffusion and human vision: a semi-discrete new twist](https://mlsanity.com/paper/1304.2062/) (2013)
- [Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging](https://mlsanity.com/paper/1403.3320/) (2014)
- [Cortical spatio-temporal dimensionality reduction for visual grouping](https://mlsanity.com/paper/1407.0733/) (2014)
- [A sub-Riemannian model of the visual cortex with frequency and phase](https://mlsanity.com/paper/1910.04992/) (2019)
- [A neuro-mathematical model for geometrical optical illusions](https://mlsanity.com/paper/1611.08844/) (2016)
- [A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition](https://mlsanity.com/paper/1704.03069/) (2017)
- [Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle](https://mlsanity.com/paper/1907.13004/) (2019)
- [Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling](https://mlsanity.com/paper/1910.06808/) (2019)

## Abstract (arXiv)

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.