Classification is an important mechanism in many pattern recognition applications. In many of these application, such as object recognition, there are several classes from which the data originates. In such cases many traditional classification methods such as Artificial Neural Networks or Support Vector Machines are used. However, in some applications the training data may belong to only one class. In this case, the classification is performed by finding whether a test sample belongs to the known class or not. The main criteria in single-class classification (also known as novelty detection) is to perform the classification without any information about other classes. This chapter presents a classic problem in video processing applications and addresses the issues through novelty detection techniques. The problem at hand is to detect foreground objects in a video with quasi-stationary background. The video background is called quasistationary if the camera is static but the background itself changes due to waving tree branches, flags, water surfaces, etc. Detection of foreground region in such scenarios requires a pixel-wise background model for each pixel in the scene. Once the pixel models are built, there should be a mechanism to decide whether pixels in new frames belong to their corresponding background model or not. The generation of pixel models from their history and the decision making mechanism is a novelty detection problem. In order to address the foreground detection problem, two main approaches to novelty detection, namely statistical and analytical, are presented in this chapter. The advantage and disadvantages of these approaches are discussed. Moreover, the suitability of each approach to specific scenarios in video processing applications are evaluated.