Template Learning from Atomic Representations:
A Wavelet Based Approach to Pattern Analysis
Clayton Scott and Robert Nowak
Rice University
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 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 (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 classification, and
image registration.