Weighted Low-Rank Approximation of Matrices and Background Modeling

TL;DR

This paper introduces a weighted low-rank approximation approach for background modeling in videos, offering algorithms that are robust to outliers and do not require training data, outperforming existing methods.

Contribution

It proposes novel batch and incremental algorithms for weighted low-rank approximation tailored to background modeling, including a robust technique that learns background frames without prior training.

Findings

Algorithms outperform state-of-the-art methods in accuracy.

Robust technique effectively handles outliers.

Methods are computationally efficient and versatile.

Abstract

We primarily study a special a weighted low-rank approximation of matrices and then apply it to solve the background modeling problem. We propose two algorithms for this purpose: one operates in the batch mode on the entire data and the other one operates in the batch-incremental mode on the data and naturally captures more background variations and computationally more effective. Moreover, we propose a robust technique that learns the background frame indices from the data and does not require any training frames. We demonstrate through extensive experiments that by inserting a simple weight in the Frobenius norm, it can be made robust to the outliers similar to the $\ell_1$ norm. Our methods match or outperform several state-of-the-art online and batch background modeling methods in virtually all quantitative and qualitative measures.