# Computational role of eccentricity dependent cortical magnification

arXiv: https://arxiv.org/abs/1406.1770 · HTML: https://mlsanity.com/paper/1406.1770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2014.

## Built on by (most cited first, 2 of 2)

- [On the use of Cortical Magnification and Saccades as Biological Proxies for Data Augmentation](https://mlsanity.com/paper/2112.07173/) (2021)
- [Finding Biological Plausibility for Adversarially Robust Features via Metameric Tasks](https://mlsanity.com/paper/2202.00838/) (2022)

## Abstract (arXiv)

We develop a sampling extension of M-theory focused on invariance to scale and translation. Quite surprisingly, the theory predicts an architecture of early vision with increasing receptive field sizes and a high resolution fovea -- in agreement with data about the cortical magnification factor, V1 and the retina. From the slope of the inverse of the magnification factor, M-theory predicts a cortical "fovea" in V1 in the order of 40 by 40 basic units at each receptive field size -- corresponding to a foveola of size around 26 minutes of arc at the highest resolution, ≈ 6 degrees at the lowest resolution. It also predicts uniform scale invariance over a fixed range of scales independently of eccentricity, while translation invariance should depend linearly on spatial frequency. Bouma's law of crowding follows in the theory as an effect of cortical area-by-cortical area pooling; the Bouma constant is the value expected if the signature responsible for recognition in the crowding experiments originates in V2. From a broader perspective, the emerging picture suggests that visual recognition under natural conditions takes place by composing information from a set of fixations, with each fixation providing recognition from a space-scale image fragment -- that is an image patch represented at a set of increasing sizes and decreasing resolutions.