Background Recovery by Fixed-Rank Robust Principal Component Analysis

Abstract

Abstract. Background recovery is a very important theme in computer vision applications. Recent research shows that robust principal component analysis (RPCA) is a promising approach for solving problems such as noise removal, video background modeling, and removal of shadows and specularity. RPCA utilizes the fact that the background is common in multiple views of a scene, and attempts to decompose the data matrix constructed from input images into a low-rank matrix and a sparse matrix. This is possible if the sparse matrix is sufficiently sparse, which may not be true in computer vision applications. Moreover, algorithmic parameters need to be fine tuned to yield accurate results. This paper proposes a fixed-rank RPCA algorithm for solving background recovering problems whose low-rank matrices have known ranks. Comprehensive tests show that, by fixing the rank of the low-rank matrix to a known value, the fixed-rank algorithm produces more reliable and accurate results than existing low-rank RPCA algorithm.

Think big, solve small: Scaling up robust PCA with coupled dictionaries

“…For photometric stereo, Oh et al [10] show that their rank-aware RPCA method is more robust in removing large-amplitude noise than generic RPCA [18] and standard least squares [17]. For reflection removal, we show that our FRPCA method [7] is more robust than RPCA in removing global reflections. These methods are compared with FRPCA-CD in Section 4.…”

“…In [7], we show that FPRCA offers better performance than RPCA, especially when the noise in the data matrix is not sparse.…”

“…Several methods have exploited the known rank to improve their accuracy. For example, our fixed-rank RPCA (FRPCA) methods [6,7] constrain the rank of A to the known rank via exact augmented Lagrange multiplier (ALM) method. The method of [6] speeds up FRPCA by applying incremental SVD, but it is still restricted to lowresolution images.…”

“…In contrast, our FRPCA-CD method adopts the fixedrank RPCA method of [7] but changes exact ALM to inexact ALM, which is more efficient than and has comparable accuracy as exact ALM [8,21]. Moreover, FRPCA-CD is designed to handle high-resolution images, although it can be applied to low-resolution images as well.…”

“…Recent advances in robust PCA (RPCA) offers a powerful method for solving a wide variety of low-level vision problems such as batch alignment of images [10,12], recovery of video background [6,7], background modeling for high dynamic range images [10], noise reduction in photometric stereo [10], and removal of shadows, specularity [2,18], and reflections [7] in images. RPCA solves these problems by arranging images as columns in a data matrix M, and decomposing it into a lowrank matrix A that contains the desired solutions and a sparse matrix E that contains noise or errors.…”