# A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition

arXiv: https://arxiv.org/abs/1704.03069 · HTML: https://mlsanity.com/paper/1704.03069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Multi-frequency image completion via a biologically-inspired sub-Riemannian model with frequency and phase](https://mlsanity.com/paper/2110.14330/) (2021)

## Abstract (arXiv)

In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for the primary visual cortex of mammals. This model is neurophysiologically justified. Further developments of this theory lead to efficient algorithms for image reconstruction, based upon the consideration of an associated hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or certain of its improvements) is a left-invariant structure over the group SE(2) of rototranslations of the plane. Here, we propose a semi-discrete version of this theory, leading to a left-invariant structure over the group SE(2,N), restricting to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to SE(2). Based upon this semi-discrete model, we improve on previous image-reconstruction algorithms and we develop a pattern-recognition theory that leads also to very efficient algorithms in practice.