Burrows Wheeler Transform In Image Compression Markus Grtner

Burrows Wheeler Transform In Image Compression Markus Gärtner David Havelin Classroom Presentation 1 st December 2000 Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000

Overview Project Goals Burrows Wheeler Transform (BWT) Application of the BWT: Lossless Compression Lossy Compression Performance Conclusion Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 2

Project Goals Implementation of an efficient Burrows. Wheeler Transform (BWT) algorithm Implementation of coding scheme for transformed data Analysis of lossless compression performance Possible combinations of BWT with Subband Coding schemes Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 3

Burrows-Wheeler Transform Lossless Reversible Block-Sorting Algorithm Input: ABDACA 1 A A B D A C 2 A B D A C A 3 A C A A B D 4 B D A C A A 5 C A A B D A 6 D A C A A B Output: CADAAB I=2 Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 4

Lossless Compression BWT Move-to Front Entropy 1 D Image Original MTF/BWT JPEG-LS Peppers 7. 5925 6. 9449 5. 5727 4. 513 Lena 7. 4451 6. 6973 5. 4819 4. 237 Bridge 5. 7056 5. 1756 4. 7974 5. 500 Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 5

Subband Coding Wavelet Transform Runlength Q BWT MTF Entropy Wavelet-BWT 1 D DCT Q Runlength DCT-BWT Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 6

Subband Coding - DCT PSNR vs. Rate for image “peppers. tif” JPEG quantization Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 7

Subband Coding - Wavelets PSNR vs. Rate for image “peppers. tif” Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 8

Conclusions Image compression with BWT possible Limitations Lack of scalability Performance of Said-Pearlman hard to reach Possibilities for improvement Sophisticated scanning techniques (Peano) Run-length Encoder Optimized Quantization Markus Gärtner, David Havelin: Burrows Wheeler Transform Stanford University, 1 st December 2000 9