12/12/2003 EZW Image Coding Duarte and Haupt

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Examining The Embedded Zerotree Wavelet (EZW) Image Coding Method

Marco Duarte and Jarvis Haupt

ECE 533

December 12, 2003

12/12/2003 EZW Image Coding Duarte and Haupt

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Overview

Statement of the Problem Our Approach Results Analysis Conclusions

12/12/2003 EZW Image Coding Duarte and Haupt

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The Desire

The EZW Algorithm addresses a twofold goal: Optimal image quality for a given compression

rate Incremental quality levels achieved by simple

bitstream truncation

12/12/2003 EZW Image Coding Duarte and Haupt

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How does EZW Succeed?

While no claims of optimality are made, the nature of multiresolution analysis gives substantial quality for compressed images

Embedding is accomplished via a series of decisions that distinguish the reconstructed image from the null image

Using more of the symbol stream refines the image

12/12/2003 EZW Image Coding Duarte and Haupt

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Our Approach

The EZW Algorithm was implemented in Matlab using the Haar Wavelet Decomposition

Reconstruction Approximations were generated and compared to the original images

Error was qualified visually and quantified using the PSNR (Peak Signal to Noise Ratio)

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Results - Lena

Compare the original Lena image (left) to its reconstruction using 10% of the EZW-generated symbols

Notice the blurred edges, loss of detail, and blocking

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Lena

Now, the original Lena (left) is compared to the reconstruction using 30% of the symbol stream

Compression artifacts are almost invisible!

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Marco

Now, we compare the original Marco image (left) to its 10% reconstruction

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Marco

And again, compare the original (left) to the 30% reconstruction Notice the fine detail in the hair in the reconstructed image!

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Jarvis

Finally, compare the original Jarvis image (left) to the 10% reconstruction. Blocking artifacts can be seen in skin color.

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Jarvis

And to the 30% reconstruction. No noticeable artifacts!

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PSNR

PSNR calculations were performed for each image using a variety of bits per pixel compressions

For each test image, PSNR data is shown for three cases No Compression Huffman Encoding Arithmetic Coding

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PSNR vs. Compression RateLena Image

As expected, PSNR is higher for the encoded streams for a given compression rate

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PSNR vs. Compression RateMarco Image

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PSNR vs. Compression RateJarvis Image

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Algorithmic Performance

The next figure illustrates how efficiently the EZW Algorithm encodes position information

The best case would be a one-to-one correspondence between percent of symbols and percent of nonzero coefficients (no position information)

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Close to Theoretical Bound

Note how close the correspondence for each image is to the one-to-one limit

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Conclusions

The EZW Algorithm encodes significance information very compactly

Coupled with the power of multiresolution analysis, the EZW Algorithm yields significant compression with little quality loss

Image quality improves progressively as more symbols are used in decoding

Modest extensions of the EZW Algorithm have been proposed and were examined but not implemented