Visual Background Extractor (VIBE) consisting in a method for detecting a background in an image selected from a plurality of related images. But in case of PCA it is used to reduce the dimension of an matrix. There is no directly relationship between them. ViBe method is used in feature extraction but PCA is feature reduction technique.
ViBe was evaluated on the changedetection.net (See on the related website) and RPCA methods on the BMC 2012 dataset (See my paper in CVIU 2014).
T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Issue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014
The source of ViBe is now available for academic use on the ViBe website. The best is to evaluate it on the BMC 2012 dataset that allow us to compare with RPCA methods.