Weighted Low Rank Approximation for Background Estimation Problems
This work addresses computational efficiency in background estimation for computer vision, but it is incremental as it builds on existing robust PCA techniques.
The paper tackles the problem of robust background estimation by proposing a weighted low rank (WLR) method to avoid computationally expensive ℓ₁ norm algorithms, achieving the same or better performance as existing methods.
Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the $\ell_1$ norm in the Robust PCA (RPCA) method successfully eliminates the weakness of PCA in separating the sparse outliers. In this paper, by sticking a simple weight to the Frobenius norm, we propose a weighted low rank (WLR) method to avoid the often computationally expensive algorithms relying on the $\ell_1$ norm. As a proof of concept, a background estimation model has been presented and compared with two $\ell_1$ norm minimization algorithms. We illustrate that as long as a simple weight matrix is inferred from the data, one can use the weighted Frobenius norm and achieve the same or better performance.