Directional image representations using nonseparable lifting

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 into blocks of consistent directional bias. To allow sufficient adaptivity while reducing overhead, this segmentation must allow for multiple sizes of blocks dependent on the image data. We solve this problem by extending a classic tree pruning algorithm used in classification for adaptive block-based transforms. Furthermore, as images do not directly include directional information, we propose a weighted estimation method using the techniques of directional statistics to determine the dominant direction of an image block. Within a compression framework, we see that the directional estimation and adaptive segmentation algorithms robustly and accurately determine the dominant direction of variably sized blocks; however, because of limitations caused by the discrete nature of the data and dimensional degeneracy of polynomial interpolation over various point sets, our directional image representation was not able to provide a coding gain over traditional methods.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Blackburn, Joshua P.

Contributors dc:contributor

• Do, Minh N.

• image processing
• lifting transforms
• adaptive segmentation
• direction estimation

Statement dc:rights

• Copyright 2010 Joshua P. Blackburn

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16843

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16843