TEMPLAR: A Wavelet-Based Framework for Pattern Learning and Analysis.

Recovering a pattern or image from a collection of noisy and misaligned observations is a challenging problem that arises in image processing and pattern recognition. This paper presents an automatic, wavelet-based approach to this problem. Despite the success of wavelet decompositions in other areas of statistical signal and image processing, most 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 pattern observations. Our framework takes advantage of the efficient image representations afforded by wavelets while accounting for unknown translations and rotations. In order to learn the parameters of our model from training data, we introduce Template Learning from Atomic Representations (TEMPLAR): a novel template learning algorithm. The problem solved by TEMPLAR is the recovery of a pattern template from a collection of noisy, randomly translated, and rotated observations of the pattern. 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 classification, and image registration.