**7. Conclusion**

This chapter presented a novel density comparison method, given two sets of points sampled from two distributions. The method does not require explicit density estimation as an intermediate step. Instead it works directly on the data points to compute the similarity measure. The proposed similarity measure is robust to noise and outliers. Possible applications of the proposed density comparison method in computer vision are visual tracking, segmentation, image registration, and stereo registration. We used the technique for visual tracking and provided a variational localization procedure.

**0**

**12**

*France*

**Robust Principal Component Analysis for**

Charles Guyon, Thierry Bouwmans and El-hadi Zahzah

**and Comparative Analysis**

*Lab. MIA - Univ. La Rochelle*

**Background Subtraction: Systematic Evaluation**

The analysis and understanding of video sequences is currently quite an active research field. Many applications such as video surveillance, optical motion capture or those of multimedia need to first be able to detect the objects moving in a scene filmed by a static camera. This requires the basic operation that consists of separating the moving objects called "foreground" from the static information called "background". Many background subtraction methods have been developed (Bouwmans et al. (2010); Bouwmans et al. (2008)). A recent survey (Bouwmans (2009)) shows that subspace learning models are well suited for background subtraction. Principal Component Analysis (PCA) has been used to model the background by significantly reducing the data's dimension. To perform PCA, different Robust Principal Components Analysis (RPCA) models have been recently developped in the literature. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. However, authors compare their algorithm only with the PCA (Oliver et al. (1999)) or another RPCA model. Furthermore, the evaluation is not made with the datasets and the measures currently used in the field of background subtraction. Considering all of this, we propose to evaluate RPCA models in the field of video-surveillance. Contributions of this chapter can be

**1. Introduction**

summarized as follows:

established in Section 4.

• A survey regarding robust principal component analysis

**2. Robust principal component analysis: A review**

applications in background subtraction:

• An evaluation and comparison on different video surveillance datasets

The rest of this paper is organized as follows: In Section 2, we firstly provide the survey on robust principal component analysis. In Section 3, we evaluate and compare robust principal component analysis in order to achieve background subtraction. Finally, the conclusion is

In this section, we review the original PCA and five recent RPCA models and their

• Principal Component Analysis (PCA) (Eckart & Young (1936); Oliver et al. (1999))

#### **8. References**

