Template Learning from Atomic Representations: A Wavelet-Based Approach to Pattern Analysis
Clayton D. Scott, Robert David Nowak · Rice Research Repository (Rice University) · 2001
Despite the success of wavelet decompositions in other areas of statistical signal and image processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations (e.g., translation, rotation, location of lighting source) inherent in most pattern observations. In this paper we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. This framework takes advantage of the ecient image representations aorded by wavelets, while accounting for unknown pattern transformations. Given a trained model, we can use this framework to synthesize pattern observations. If the model parameters are unknown, we can infer them from labeled training data using TEMPLAR (Template Learning from Atomic Representations), a novel template learning algorithm with linear complexity. TEMPLAR employs minimum description length (MDL) complexity regularization to learn a template with a sparse representation in the wavelet domain. We discuss several applications, including template learning, pattern classication, and image registration.