Directional image representations using nonseparable lifting
Joshua Blackburn · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · 2010
Sparse representations of visual information are essential for many image processing tasks. Because of the nonstationary geometric structure of natural images, representations derived from one-dimensional tensor products or compact frequency support will be suboptimal. Therefore, there is strong motivation to search for more powerful methods to efficiently represent the geometric structure of visual information. This thesis demonstrates a method to create a directional image representation with compact spatial support which is not limited to a single dimension. Within the lifting framework of perfect reconstruction filter banks, sparse representation requires prediction filters able to adapt to the local structure of the signal. As most images are locally regular except at edges, this adaptation adjusts the support of the prediction filters in order that a larger percentage of the output is predicted from pixels which do not come from both sides of an edge. To allow for the adaptation of filter support, the image must be segmented