Adaptive Linear Prediction Lossless Image Coding

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Adaptive Linear Prediction Lossless Image Coding
DCC 99 - Adaptive 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_at_cs.brandeis.edu
Bruno Carpentieri Universita' di Salerno Dip. di
Informatica ed Applicazioni "R.M.
Capocelli I-84081 Baronissi (SA),
Italy bc_at_dia.unisa.it
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Problem
Graylevel lossless image compression addressed
from the point of view of the achievable
compression ratio
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Outline

• Motivations
• Main Idea
• Algorithm
• Predictor Assessment
• Entropy Coding
• Final Experimental Results
• Conclusion

DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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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
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Past Results / Related Works

• In spite of the its high computational
  complexity, TMWs 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
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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
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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
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Prediction Window
2Rp1
Rp1
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
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Prediction Context

• 6 pixels
• fixed shape
• weights w0,,w5 change to
• minimize error energy inside Wx,y(Rp)

w0
w1
w2
w3
-1
w5
w4
Prediction I(x,y) int(w0 I(x,y-2) w1
I(x-1,y-1) w2 I(x,y-1) w3
I(x1,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
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Predictor Refinement
2Rp1
Rp1
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
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Algorithm
for every 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 Piw0, .., 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
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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
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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
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Outline

• Motivations
• Main Idea
• Algorithm
• Predictor Assessment
• Entropy Coding
• Final Experimental Results
• Conclusion

DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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File Size vs. Number of Predictors. (Rp6) Using
an adaptive AC
of predictors 1 2 4 6
8 Balloon 154275 150407 150625 150221 150298 B
arb 227631 223936 224767 225219 225912 Barb2 25
0222 250674 254582 256896 258557 Board 193059 19
0022 190504 190244 190597 Boats 210229 208018 20
9408 209536 210549 Girl 204001 202004 202326 202
390 202605 Gold 235682 237375 238728 239413 2403
52 Hotel 236037 236916 239224 240000 240733 Zel
da 195052 193828 194535 195172 195503 Total
(bytes) 1906188 1893180 1904699 1909091
1915106
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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File Size vs. window radius RP ( pred.2) Using
an adaptive AC
Rp 6 8 10 12
14 Balloon 150407 149923 149858 150019 150277
Barb 223936 223507 224552 225373 226136 Barb2 2
50674 249361 246147 247031 246265 Board 190022 1
90319 190911 191709 192509 Boats 208018 206630 2
06147 206214 206481 Girl 202004 201189 201085 20
1410 201728 Gold 237375 235329 234229 234048 234
034 Hotel 236916 235562 235856 236182 236559 Ze
lda 193828 193041 192840 192911 193111 Total
(bytes) 1893180 1884861 1881625 1884897
1887100
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Prediction Error
5.50
5.00
4.50
4.00
3.50
LOCO-I (Error Entropy after Context Modeling)
3.00
LOCO-I (Entropy of the Prediction Error)
2 Predictors, Rp10, Single Adaptive AC
2.50
baloon
barb
barb2
board
boats
girl
gold
hotel
zelda
Image
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Prediction Error
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Prediction Error (histogram)
Test image Hotel
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Prediction Error (magnitude and sign)
Test image Hotel
Sign
Magnitude
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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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
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Outline

• Motivations
• Main Idea
• Algorithm
• Predictor Assessment
• Entropy Coding
• Final Experimental Results
• Conclusion

DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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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
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Compressed File Size vs. error window radius Re
( of predictors 2 and Rp10)
Re 8 10 12
14 16
18 balloon 147227 147235
147341 147479 147620
147780 barb 216678 216082
215906 215961 216135
216370 barb2 234714 233303
232696 232455 232399
232473 board 186351 186171
186187 186303 186467
186646 boats 202168 201585
201446 201504 201623
201775 girl 197243 197013
197040 197143 197245
197356 gold 230619 229706
229284 229111 229026
229012 hotel 229259 228623
228441 228491 228627
228785 zelda 189246 188798
188576 188489 188461
188469 Total (bytes) 1833505 1828516
1826917 1826936 1827603 1828666
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Outline

• Motivations
• Main Idea
• Algorithm
• Predictor Assessment
• Entropy Coding
• Final Experimental Results
• Conclusion

DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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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
3.79 4.08 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, Rp10)
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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Comparisons
DCC 99 - Adaptive Linear Prediction Lossless
Image Coding
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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
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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
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DCC 99 - Adaptive Prediction Lossless Image
Coding