Improved ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ell }^{1}}$$\end{document}-tracker using robust PCA and random projection

In this paper, we propose an improved ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ell }^{1}}$$\end{document}-tracker in a particle filter framework using robust principal component analysis (robust PCA) and random projection. At first we redesign the template set and its update scheme. Three target templates and several background templates combined with the trivial templates are used to represent the candidate images sparsely. One fixed target template is generated from the image patch in the first frame. The other two are dynamic target templates, called stable target template, and fast changing one used for long time and short time, respectively. Robust PCA is used to generate and update the stable target template, and fast changing target template is initialized by the stable one at certain times. The background templates are used to strengthen the ability of distinguishing background and foreground. Then, the large set of Haar-like features are extracted and compressively sensed with a very sparse measurement matrix for the ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ell }^{1}}$$\end{document}-tracker framework. The compressive sensing theories ensure that the sensed features preserve almost all the information of the original features. Our proposed method is more robust than the original ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ell }^{1}}$$\end{document}-method. Experiments have been done on numerous sequences to demonstrate the better performance of our improved tracker.