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Proceedings Paper

Self-quantized wavelet subtrees: wavelet-based theory of fractal image compression
Author(s): Geoffrey M. Davis
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Paper Abstract

We describe a novel adaptive wavelet-based compression scheme for images which takes advantage of image redundancy across scales. As with standard wavelet transform coders, our compressed image representation consists of a set of quantized wavelet coefficients and quantized wavelet subtrees. Instead of having a fixed subtree codebook, however, we construct a codebook from the image being compressed. Subtrees are quantized to contracted isometries of coarser scale subtrees. This codebook drawn from the image is effective for quantizing locally smooth regions and locally straight edges. We prove that this self- quantization enables us to recover the fine scale wavelet coefficients of an image given its coarse scale coefficients. We show that this self-quantization algorithm is equivalent to a fractal image compression scheme when the wavelet basis is the Haar basis. The wavelet framework greatly simplifies the analysis of fractal compression schemes and places fractal compression in the context of existing wavelet subtree coding schemes. We obtain a simple convergence proof which strengthens existing fractal compression results, we describe a new reconstruction algorithm which requires O(N) operations for an N pixel image, and we derive an improved means of estimating the error incurred in decoding fractal compressed images. We show the effect of self-quantization for a test image.

Paper Details

Date Published: 6 April 1995
PDF: 12 pages
Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205381
Show Author Affiliations
Geoffrey M. Davis, Dartmouth College (United States)

Published in SPIE Proceedings Vol. 2491:
Wavelet Applications II
Harold H. Szu, Editor(s)

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