# Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase

@article{Baspinar2021MultiFrequencyIC, title={Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase}, author={Emre Baspinar}, journal={Journal of Imaging}, year={2021}, volume={7} }

We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling 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 represents those values in terms of cortical cell output responses in the model geometry. Then, it performs…

## Figures from this paper

## References

SHOWING 1-10 OF 78 REFERENCES

Minimal Surfaces in Sub-Riemannian Structures and Functional Geometry of the Visual Cortex

- Mathematics
- 2018

We develop geometrical models of vision consistent with the characteristics of the visual cortex and study geometric flows in the relevant model geometries. We provide a novel sub-Riemannian model of…

Sub-Riemannian Mean Curvature Flow for Image Processing

- Mathematics, Computer ScienceSIAM J. Imaging Sci.
- 2016

A formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature is given and results of completion and enhancement on a number of natural images are shown and compared with other models.

A Cortical-Inspired Geometry for Contour Perception and Motion Integration

- Mathematics, BiologyJournal of Mathematical Imaging and Vision
- 2013

The stochastic kernels that are the approximations of two Fokker Planck operators associated to the geometry are computed and implemented as facilitation patterns within a neural population activity model in order to reproduce some psychophysiological findings about the perception of contours in motion and trajectories of points found in the literature.

A Geometric Model of Multi-scale Orientation Preference Maps via Gabor Functions

- Mathematics, BiologyJournal of Mathematical Imaging and Vision
- 2018

A new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features is presented, outlining that the new model is more physiologically motivated.

Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group

- Computer Science, BiologyDifferential Geometry and its Applications
- 2019

The model is extended, proposing that the metric responsible for the cortical connectivity is modulated by the modelled neuro-physiological response of simple cells to the visual stimulus, hence providing a more biologically plausible model that takes into account a presence of visual stimulus.

A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

- Mathematics, Computer ScienceJournal of Mathematical Imaging and Vision
- 2005

We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the…

Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion

- Mathematics, Computer ScienceSIAM J. Control. Optim.
- 2012

A model of geometry of vision due to Petitot, Citti, and Sarti is studied, and a mathematical proof of several important facts for this model is provided.

Image reconstruction via non-isotropic diffusion in Dubins/Reed-Shepp-like control systems

- Mathematics, Computer Science53rd IEEE Conference on Decision and Control
- 2014

We compare the image inpainting results of two models of geometry of vision obtained through control theoretic considerations (the semi-discrete versions of the Citti-Petitot-Sarti and Mumford…

Cortical Spatiotemporal Dimensionality Reduction for Visual Grouping

- Computer Science, MathematicsNeural Computation
- 2015

A spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher-dimensional spaces is defined and how these connectivities can be used to obtain low-level object segmentation is shown.

Representation of local geometry in the visual system

- Mathematics, MedicineBiological Cybernetics
- 2004

It is shown that a convolution with certain reasonable receptive field (RF) profiles yields the exact partial derivatives of the retinal illuminance blurred to a specified degree and how this representation can function as the substrate for “point processors” computing geometrical features such as edge curvature.