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Adaptive Linear Prediction Lossless Image Coding

DCC ‘99 - Adaptive Prediction Lossless Image Coding. Adaptive Linear Prediction Lossless Image Coding. Giovanni Motta , James A. Storer Brandeis University Volen Center for Complex Systems Computer Science Department Waltham MA-02454, US {gim, storer}@cs.brandeis.edu. Bruno Carpentieri

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Adaptive Linear Prediction Lossless Image Coding

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  1. DCC ‘99 - Adaptive Prediction Lossless Image Coding Adaptive Linear Prediction Lossless Image Coding Giovanni Motta, James A. Storer Brandeis University Volen Center for Complex Systems Computer Science Department Waltham MA-02454, US {gim, storer}@cs.brandeis.edu Bruno Carpentieri Universita' di Salerno Dip. di Informatica ed Applicazioni "R.M. Capocelli” I-84081 Baronissi (SA), Italy bc@dia.unisa.it DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  2. Problem Graylevel lossless image compression addressed from the point of view of the achievable compression ratio DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  3. Outline • Motivations • Main Idea • Algorithm • Predictor Assessment • Entropy Coding • Final Experimental Results • Conclusion DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  4. Past Results / Related Works Until TMW, the best existing lossless digital image compressors (CALIC, LOCO-I, etc..) seemed unable to improve compression by using image-by-image optimization techniques or more sophisticate and complex algorithms A year ago, B. Meyer and P. Tischer were able, with their TMW, to improve some current best results by using global optimization techniques and multiple blended linear predictors. DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  5. Past Results / Related Works • In spite of the its high computational complexity, TMW’s results are in any case surprising because: • Linear predictors are not effective in capturing image edginess; • Global optimization seemed to be ineffective; • CALIC was thought to achieve a data rate close to the entropy of the image. DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  6. Motivations Investigation on an algorithm that uses: Multiple Adaptive Linear Predictors Pixel-by-pixel optimization Local image statistics DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  7. Main Idea • Explicit use of local statistics to: • Classify the context of the current pixel; • Select a Linear • Predictor; • Refine it. DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  8. Prediction Window 2Rp+1 Rp+1 Encoded Pixels Window Wx,y(Rp) Current Context Current Pixel I(x,y) Statistics are collected inside the window Wx,y(Rp) Not all the samples in Wx,y(Rp) are used to refine the predictor DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  9. Prediction Context • 6 pixels • fixed shape • weights w0,…,w5 change to • minimize error energy inside Wx,y(Rp) w0 w1 w2 w3 w4 w5 -1 Prediction: I’(x,y) = int(w0 * I(x,y-2) + w1 * I(x-1,y-1) + w2 * I(x,y-1) + w3 * I(x+1,y-1) + w4 * I(x-2,y) + w5 * I(x-1,y)) Error: Err(x,y) = I’(x,y) - I(x,y) DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  10. Predictor Refinement 2Rp+1 Rp+1 Gradient descent is used to refine the predictor Encoded Pixels Window Wx,y(Rp) Current Context Current Pixel I(x,y) DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  11. Algorithm forevery pixel I(x,y)do begin /* Classification */ Collect samples Wx,y(Rp) Classify the samples in n clusters (LBG on the contexts) Classify the context of the current pixel I(x,y) Let Pi={w0, .., w5} be the predictor that achieves the smallest error on the current cluster Ck /* Prediction */ Refine the predictor Pi on the cluster Ck Encode and send the prediction error ERR(x,y) end DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  12. Results Summary • Compression is better when structures and textures are present • Compression is worse on high contrast zones • Local Adaptive LP seems to capture features not exploited by existing systems DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  13. Test Images 9 “pgm” images,720x576 pixels, 256 greylevels (8 bits) Balloon Barb Barb2 Board Boats Girl Gold Hotel Zelda downloaded from the ftp site of X. Wu: ”ftp:\\ftp.csd.uwo.ca/pub/from_wu/images” DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  14. Outline • Motivations • Main Idea • Algorithm • Predictor Assessment • Entropy Coding • Final Experimental Results • Conclusion DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  15. File Size vs. Number of Predictors. (Rp=6) Using an adaptive AC # of predictors 1 2 4 6 8 Balloon154275 150407 150625 150221 150298 Barb227631 223936 224767 225219 225912 Barb2 250222 250674 254582 256896 258557 Board193059 190022 190504 190244 190597 Boats210229 208018 209408 209536 210549 Girl204001 202004 202326 202390 202605 Gold 235682 237375 238728 239413 240352 Hotel 236037 236916 239224 240000 240733 Zelda195052 193828 194535 195172 195503 Total (bytes)1906188 1893180 1904699 1909091 1915106 DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  16. File Size vs. window radius RP (# pred.=2) Using an adaptive AC Rp 6 8 10 12 14 Balloon150407 149923 149858 150019 150277 Barb223936 223507 224552 225373 226136 Barb2250674 249361 246147 247031 246265 Board 190022 190319 190911 191709 192509 Boats208018 206630 206147 206214 206481 Girl202004 201189 201085 201410 201728 Gold237375 235329 234229 234048 234034 Hotel236916 235562 235856 236182 236559 Zelda193828 193041 192840 192911 193111 Total (bytes)1893180 1884861 1881625 1884897 1887100 DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  17. Prediction Error 5.50 5.00 4.50 4.00 3.50 LOCO-I (Error Entropy after Context Modeling) LOCO-I (Entropy of the Prediction Error) 3.00 2 Predictors, Rp=10, Single Adaptive AC 2.50 baloon barb barb2 board boats girl gold hotel zelda Image DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  18. Prediction Error DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  19. Prediction Error (histogram) Test image “Hotel” DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  20. Prediction Error (magnitude and sign) Test image “Hotel” Magnitude Sign DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  21. Prediction Error (magnitude and sign) Test image “Board” Magnitude Sign DCC ‘99 - Adaptive Prediction Lossless Image Coding DCC ‘99 - Adaptive Linear Prediction Losless Image Coding

  22. Outline • Motivations • Main Idea • Algorithm • Predictor Assessment • Entropy Coding • Final Experimental Results • Conclusion DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  23. Entropy Coding • AC model determined in a window Wx,y(Re) • Two different ACs for typical and non typical symbols • (for practical reasons) • Global determination of the cutting point DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  24. Compressed File Size vs. error window radius Re (# of predictors = 2 and Rp=10) Re 8 10 12 14 16 18 balloon 147227 147235 147341 147479 147620 147780 barb216678 216082 215906 215961 216135 216370 barb2234714 233303 232696 232455 232399 232473 board186351 186171 186187 186303 186467 186646 boats202168 201585 201446 201504 201623 201775 girl197243 197013 197040 197143 197245 197356 gold230619 229706 229284 229111 229026 229012 hotel229259 228623 228441 228491 228627 228785 zelda189246 188798 188576 188489 188461 188469 Total (bytes)1833505 1828516 1826917 1826936 1827603 1828666 DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  25. Outline • Motivations • Main Idea • Algorithm • Predictor Assessment • Entropy Coding • Final Experimental Results • Conclusion DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  26. Comparisons balloon barb barb2 board boats girl gold hotel zelda Avg. SUNSET 2.89 4.64 4.71 3.72 3.99 3.90 4.60 4.48 3.794.08 LOCO-I 2.90 4.65 4.66 3.64 3.92 3.90 4.47 4.35 3.87 4.04 UCM 2.81 4.44 4.57 3.57 3.85 3.81 4.45 4.28 3.80 3.95 Our 2.84 4.16 4.48 3.59 3.89 3.80 4.42 4.41 3.64 3.91 CALIC 2.78 4.31 4.46 3.51 3.78 3.72 4.35 4.18 3.69 3.86 TMW 2.65 4.08 4.38 3.61 4.28 3.80 Compression rate in bit per pixel. (# of predictors = 2, Rp=10) DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  27. Comparisons DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  28. Conclusion • Compression is better when structures and textures are present • Compression is worse on high contrast zones • Local Adaptive LP seems to capture features not exploited by existing systems DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  29. Future Research • Compression • Better context classification (to improve on high contrast zones) • Adaptive windows • MAE minimization (instead of MSE min.) • Complexity • Gradient Descent • More efficient entropy coding • Additional experiments • On different test sets DCC ‘99 - Adaptive Linear Prediction Lossless Image Coding

  30. DCC ‘99 - Adaptive Prediction Lossless Image Coding

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