paper information and status

A. Chebira, M. C. Fickus and J. Kovačević. Classifying compact sets with frames. Appl. Comput. Harmon. Anal., 27(1):73-86, July 2009.

[ pdf | @ @ ScienceDirect | bibtex]


Classification is a fundamental image processing task. Recent empirical evidence suggests that classification algorithms which make use of redundant linear transforms will regularly outperform their nonredundant counterparts. We provide a rigorous explanation of this phenomenon in the single-class case. We begin by developing a measure-theoretic analysis of the set of points at which a given decision rule will have an intolerable chance of making a classification error. We then apply this general theory to the special case where the class is compact and convex, showing that such a class may be arbitrarily well-approximated by frame sets, namely, preimages of hyperrectangles under frame analysis operators. This leads to a frame-based classification scheme in which frame coefficients are regarded as features. We show that, indeed, the accuracy of such a classification scheme approaches perfect accuracy as the redundancy of the frame grows large.



The zipped archive contains the code to generate the figures in the paper.



All necessary proofs are included in the paper.

list of tested configurations

MATLAB 7.0.1 on Windows XP Professional


For more information or to report bugs contact jelenak at cmu dot edu.