{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/17376"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/17376","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"A hierarchical wavelet-based framework for pattern analysis and synthesis","abstract":"Despite their success in other areas of statistical signal processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations inherent in most pattern observations. In this thesis we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. This framework takes advantage of the efficient image representations afforded 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, 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. If we are given several trained models for different patterns, our framework provides a low-dimensional subspace classifier that is invariant to unknown pattern transformations as well as background clutter.","abstract_html":"Despite their success in other areas of statistical signal processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations inherent in most pattern observations. In this thesis we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. 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