A QR decomposition based mixture model algorithm for background modeling

Abstract

This paper presents a new algorithm for background modeling in a sequence of images, even if there are foreground objects in each frame. We develop a QR decomposition based algorithm to remove foreground pixels from the image and then we construct the background model using Mixture of Gaussian algorithm, MoG. We split the image into small blocks and construct the background blocks using R-values taken from QR decomposition which indicate the degree of significance of the decomposed parts. The simulation results show the better performance of the proposed algorithm in compare with conventional methods on modeling static background images.

Eigenbackground Revisited: Can We Model the Background with Eigenvectors?

“…This is actually the same as the concept of eigenfaces, which models the faces and not the background. In our previous papers [25], [26] we demonstrated the efficiency of the usage of eigenvectors related to weak eigenvalues, by QR factorization; here our claim is extended and mathematically proved.…”

“…As before, the red circles demonstrate foreground frames and blue crosses show background frames. Subfigures (a)-(e) show the subspaces corresponding to the following eigenvectors' pairs: (1,2), (25,26), (49,50), (73,74) and (97,98), respectively.…”

“…Figure 6(a) shows the first 120 rows of the mentioned matrix, with their original order. Reordering these frames based on the R-values of its QR decomposition, leads to figure 6(b) [25], [26]. The diagonal elements of matrix R are called R-values.…”

Foreground Detection in Dynamic Scenes using Singular Value Decomposition Algorithm in Comparison with Gaussian Mixture Model to measure F-score

“…The background motion induced by orthographic cameras is found in a low rank subspace, and pixels corresponding to a single trajectory are found in a low rank subspace (Cui et al 2012). This work has a wide range of applications, ranging from compression to scene interpretation for recognising moving objects in films captured by stationary cameras (Amintoosi, Farbiz, and Fathy 2007).…”