Examining The Embedded Zerotree Wavelet (EZW) Image Coding Method

1. Examining The Embedded Zerotree Wavelet (EZW) Image Coding Method Marco Duarte and Jarvis Haupt ECE 533 December 12, 2003 EZW Image Coding Duarte and Haupt

2. Overview • Statement of the Problem • Our Approach • Results • Analysis • Conclusions EZW Image Coding Duarte and Haupt

3. 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 EZW Image Coding Duarte and Haupt

4. 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 EZW Image Coding Duarte and Haupt

5. 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) EZW Image Coding Duarte and Haupt

6. 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 EZW Image Coding Duarte and Haupt

7. Lena • Now, the original Lena (left) is compared to the reconstruction using 30% of the symbol stream • Compression artifacts are almost invisible! EZW Image Coding Duarte and Haupt

8. Marco • Now, we compare the original Marco image (left) to its 10% reconstruction EZW Image Coding Duarte and Haupt

9. Marco • And again, compare the original (left) to the 30% reconstruction • Notice the fine detail in the hair in the reconstructed image! EZW Image Coding Duarte and Haupt

10. Jarvis • Finally, compare the original Jarvis image (left) to the 10% reconstruction. Blocking artifacts can be seen in skin color. EZW Image Coding Duarte and Haupt

11. Jarvis • And to the 30% reconstruction. No noticeable artifacts! EZW Image Coding Duarte and Haupt

12. 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 EZW Image Coding Duarte and Haupt

13. PSNR vs. Compression RateLena Image As expected, PSNR is higher for the encoded streams for a given compression rate EZW Image Coding Duarte and Haupt

14. PSNR vs. Compression RateMarco Image EZW Image Coding Duarte and Haupt

15. PSNR vs. Compression RateJarvis Image EZW Image Coding Duarte and Haupt

16. 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) EZW Image Coding Duarte and Haupt

17. Close to Theoretical Bound • Note how close the correspondence for each image is to the one-to-one limit EZW Image Coding Duarte and Haupt

18. 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 EZW Image Coding Duarte and Haupt