The algebra and statistics of generalized principal component analysis We consider the problem of simultaneously segmenting data samples drawn from multiple linear subspaces and estimating model parameters for those subspaces. This subspace segmentation problem naturally arises in many computer vision applications such as motion and video segmentation, and in the recognition of human faces, textures, and range data. Generalized Principal Component Analysis (GPCA) has provided an effective way to resolve the strong coupling between data segmentation and model estimation inherent in subspace segmentation. Essentially, GPCA works by first finding a global algebraic representation of the unsegmented data set, and then decomposing the model into irreducible components, each corresponding to exactly one subspace. We provide a summary of important algebraic properties and statistical facts that are crucial for making GPCA both efficient and robust, even when the given data are corrupted with noise or contaminated by outliers. We demonstrate the effectiveness of GPCA using a large testbed of synthetic and real experiments.

A robustified hidden markov model for visual tracking with subspace representation This paper describes a new, robustified Hidden Markov Model for target tracking using a subspace representation. The Hidden Markov Model (HMM) provides a powerful framework for the probabilistic modelling of observations and states. Visual tracking problems are often cast as an inference problem within the HMM framework. Probabilistic Principal Component Analysis (PPCA), a classic subspace representation method, is a popular tool for appearance modelling because it provides a compact representation for highdimensional data. Previous subspace based tracking algorithms assume the image observations were generated from a Gaussian distribution parameterized by principal components. One drawback of using Gaussian density model is that atypical observations cannot be modelled well. Hence, they are very sensitive to outliers. To address this problem, we propose to augment the HMM by adding a set of latent variables w i  i  t 1 to adjust the shape of the observation distribution. By carefully choosing the distribution of w i  i  t 1, we obtain a more robust observation distribution with heavier tails than a Gaussian. Numerical experiments demonstrate the effectiveness of this new framework in cases where the target objects are corrupted by noise or occlusion.