# Why are images smooth?

arXiv: https://arxiv.org/abs/1406.5035 · HTML: https://mlsanity.com/paper/1406.5035/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2014.

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

- [The JEPA Paradox in Language: The Geometry of Linguistic Alternatives](https://mlsanity.com/paper/2607.23531/) (2026)
- [Online Prediction with Limited Selectivity](https://mlsanity.com/paper/2508.09592/) (2025)

## Abstract (arXiv)

It is a well observed phenomenon that natural images are smooth, in the sense that nearby pixels tend to have similar values. We describe a mathematical model of images that makes no assumptions on the nature of the environment that images depict. It only assumes that images can be taken at different scales (zoom levels). We provide quantitative bounds on the smoothness of a typical image in our model, as a function of the number of available scales. These bounds can serve as a baseline against which to compare the observed smoothness of natural images.