# Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation

arXiv: https://arxiv.org/abs/1907.04409 · HTML: https://mlsanity.com/paper/1907.04409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

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

- [Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate](https://mlsanity.com/paper/2203.03899/) (2022)

## Abstract (arXiv)

In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of sparse and low-rank matrices. The resulting formulation, a nonnegative variant of robust principal component analysis, is more computationally tractable than its commonly employed convex relaxation, although not generally solvable to global optimality. In spite of this limitation, we derive intuitive and interpretable conditions on the video data under which the uniqueness and global optimality of the object segmentation are guaranteed using local search methods. We illustrate these novel optimality criteria through example segmentations using real video data.