Abstract
In a broad range of computer vision applications, the purpose of Low-rank matrix approximation (LRMA) models is to recover the underlying low-rank matrix from its degraded observation. The latest LRMA methods - Robust Principal Component Analysis (RPCA) resort to using the nuclear norm minimization (NNM) as a convex relaxation of the non-convex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank components equally, limiting its flexibility in practical applications. We use a more flexible model, namely the Weighted Schatten p-Norm Minimization (WSNM), to generalize the NNM to the Schatten p-norm minimization with weights assigned to different singular values. The proposed WSNM not only gives a better approximation to the original low-rank assumption but also considers the importance of different rank components. In this paper, a comparison of the low-rank recovery performance of two LRMA algorithms- RPCA and WSNM is brought out on occluded human facial images. The analysis is performed on facial images from the Yale database and over own database , where different facial expressions, spectacles, varying illumination account for the facial occlusions. The paper also discusses the prominent trends observed from the experimental results performed through the application of these algorithms. As low-rank images sometimes might fail to capture the details of a face adequately, we further propose a novel method to use the image-histogram of the sparse images thus obtained to identify the individual in any given image. Extensive experimental results show, both qualitatively and quantitatively, that WSNM surpasses RPCA in its performance more effectively by removing facial occlusions, thus giving recovered low-rank images of higher PSNR and SSIM.
Abstract (translated)
URL
https://arxiv.org/abs/2007.12362
