Subspace analysis of arbitrarily many linear filter responses with an application to face tracking

Multi-scale/orientation local image analysis methods are valuable tools for obtaining highly distinctive image-based representations. Very often, these features are generated from the responses of a bank of linear filters corresponding to different scales and orientations. Naturally, as the number of filters increases, so does the feature dimensionality. Further processing is often feasible only when dimensionality reduction is performed by subspace learning techniques, such as Principal Component analysis (PCA) or Linear Discriminant Analysis (LDA). The major problem stems from the fact that as the number of features increases, so does the computational complexity of these methods which, in turn, limits the number of scales and orientations examined. In this paper, we show how linear subspace analysis on features generated by the response of linear filter banks can be efficiently re-formulated such that complexity does not depend on the number of filters used. We describe computationally efficient and exact versions of PCA while the extension to other subspace learning algorithms is straightforward. Finally, we show how the proposed methods can boost the performance of algorithms for appearance based tracking algorithm.