Background Estimation Using Principal Component Analysis Based on Limited Memory Block Krylov Subspace Optimization

Abstract

Given a video of 𝑀 frames of size ℎ × 𝑤. Background components of a video are the elements matrix which relative constant over 𝑀 frames. In PCA (principal component analysis) method these elements are referred as “principal components”. In video processing, background subtraction means excision of background component from the video. PCA method is used to get the background component. This method transforms 3 dimensions video (ℎ × 𝑤 × 𝑀) into 2 dimensions one (𝑁 × 𝑀), where 𝑁 is a linear array of size ℎ × 𝑤. The principal components are the dominant eigenvectors which are the basis of an eigenspace. The limited memory block Krylov subspace optimization then is proposed to improve performance the computation. Background estimation is obtained as the projection each input image (the first frame at each sequence image) onto space expanded principal component. The procedure was run for the standard dataset namely SBI (Scene Background Initialization) dataset consisting of 8 videos with interval resolution [146 150, 352 240], total frame [258,500]. The performances are shown with 8 metrics, especially (in average for 8 videos) percentage of error pixels (0.24%), the percentage of clustered error pixels (0.21%), multiscale structural similarity index (0.88 form maximum 1), and running time (61.68 seconds).