# A Critical Connectivity Radius for Segmenting Randomly-Generated, High Dimensional Data Points

arXiv: https://arxiv.org/abs/1602.03822 · HTML: https://mlsanity.com/paper/1602.03822/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2016.

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

- [Image Segmentation, Compression and Reconstruction from Edge Distribution Estimation with Random Field and Random Cluster Theories](https://mlsanity.com/paper/2104.10762/) (2021)

## Abstract (arXiv)

Motivated by a 2-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are calculated that indicate strong correlation between randomly-generated, high dimensional data points that have been projected into structures in a partition of a bounded, 2-dimensional area, of which, an image is a special case. A neighbor concept for structures in the partition is defined and a critical radius is uncovered. Measured from a central structure in localized regions of the partition, the radius indicates strong, long and short range correlation in the count of occupied structures. The size of a short interval of radii is estimated upon which the transition from short-to-long range correlation is virtually assured, which defines a demarcation of when an image ceases to be "interesting".