mahmoud el-sakka, 1999 - pami.uwaterloo.capami.uwaterloo.ca/mkamel/sd776/notes/compression.pdf · 7...
TRANSCRIPT
Mahmoud El-Sakka, 1999
Adaptive Block-Based Image Compression:
Is it Worth it?
Mahmoud El-Sakka
Pattern Analysis and Machine Intelligence group
Systems Design department
University of Waterloo
Waterloo, Ontario, Canada
Summer 1999
Mahmoud El-Sakka, 1999
Outline
� Introduction
� Image Compression Techniques
� JPEG: The Current Still Image Compression Standard
� ABC-SC: A New Adaptive Compression Scheme
� Objectives
� Methodology
� Scheme Description
� Experimental results
� JPEG2000: The New Still Image Compression Standard
� Conclusions
#
Mahmoud El-Sakka, 1999
Introduction to Image Compression
� Image:
� Is a representation of the visual information of a
given object
� Can be:
� Single frame (Still image)
� Sequence of frames (Moving sequence)
#
Mahmoud El-Sakka, 1999Image Information
� Types:
� Redundant (e.g., background)
� Irrelevant (e.g., enormous details)
� Useful (e.g., edges)
The Lena image
#
Mahmoud El-Sakka, 1999
Introduction to Image Compression
� Compression is a process intended to yield a
compact representation of a given object
� Do we need image compression?
� Storage (Memory)
� Transmission (Communication channels)
#
Mahmoud El-Sakka, 1999
De�nitions
� MEANfXg = EXPECTEDfXg
= EfXg
= �x
� VARIANCEfXg = VARfXg
= Ef(X-�x)2g
= EfX2g - �2x
= �2
x
� STANDARD DEVIATIONfXg = �x
� COVARIANCEfX,Yg = COVfX,Yg
= Ef(X-�x) � (Y-�y)g
= EfX � Yg - �x � �y
= �x;y
� COVfX,Xg = �x;x
= �2
x
#
Mahmoud El-Sakka, 1999
De�nitions
� SIMPLE CORRELATION FACTOR= �x;y
=
COV fX;Y gpV ARfXg�V ARfY g
=
�x;y
�x��y
� Note that:
� �1 � �x;y � 1
� �x;x = 1
� �x;�x = �1
� �x;y 2 f1;�1g =) these two variables can be repre-
sented by only one variable.
� �x;y = 1 =) both values are exactly the same.
� �x;y = �1 =) both values are exactly the same but
just with opposite sign.
� �x;y = 0 =) both values are un-correlated.#
Mahmoud El-Sakka, 1999
De�nitions
COVARIANCE MATRIX = � =
26666666664�11 �12 � � � �1j � � � �1n
�21 �22 � � � �2j � � � �2n
...
...
. . .
...
...
�i1 �i2 � � � �ij � � � �in
...
...
...
. . .
...
�n1 �n2 � � � �nj � � � �nn3
7777777775
CORRELATION MATRIX = � =
26666666664�11 �12 � � � �1j � � � �1n
�21 �22 � � � �2j � � � �2n
...
...
. . .
...
...
�i1 �i2 � � � �ii � � � �in
...
...
...
. . .
...
�n1 �n2 � � � �nj � � � �nn3
7777777775
=
266666666641 �12 � � � �1j � � � �1n
�21 1 � � � �2j � � � �2n
...
...
. . .
...
...
�i1 �i2 � � � 1 � � � �in
...
...
...
. . .
...
�n1 �n2 � � � �nj � � � 1
37777777775
� If data values are de-correlated, then the correla-
tion matrix will equal unity.
� If data values are totally correlated (totally depen-
dent), then the correlation matrix elements will be
2 f�1; 1g and the whole vector can be represented
by a scaler value.
#
Mahmoud El-Sakka, 1999
� Example 1:
Y
X1 2 4 6
1
2
4
6
� data = f (1, 1), (2, 2), (4, 4), (6, 6) g
� � = (3:25; 3:25)
� � =2
4 3:6875 3:6875
3:6875 3:68753
5
� CORRELATION MATRIX =2
4 1 11 1
35
� These data are totally correlated, i.e., totally
dependent.
#
Mahmoud El-Sakka, 1999
Example 2
� The relationship between neighboring pixels (to the left)
0
32
64
96
128
160
192
224
0 32 64 96 128 160 192 224
Pre
viou
s P
ixel
Val
ue
Pixel Value
0
32
64
96
128
160
192
224
0 32 64 96 128 160 192 224
Pre
viou
s P
ixel
Val
ue
Pixel Value
#
Mahmoud El-Sakka, 1999
Example 2
� The relationship between neighboring pixels (to the left)
before noise
0
32
64
96
128
160
192
224
0 32 64 96 128 160 192 224
Pre
viou
s P
ixel
Val
ue
Pixel Value
Gaussian noise
� = 40
#
Mahmoud El-Sakka, 1999
How Can Compression Be Achieved?
� Correlation
redundant information reduction, lossless
� Prediction
� Transformation
� Quantization, lossy
resolution reduction
dimensionality reduction
� Modeling
approximation, lossy
� Omitting, or at least reducing, irrelevant details
approximation, lossy
� E�cient encoding
#
Mahmoud El-Sakka, 1999
Image Compression Techniques
� Can be classi�ed based on:
� Reversibility
� Reversible (lossless): exactly the same as the original image
� Irreversible (lossy): close to the original image
� Adaptivity
� Adaptive: adjusts itself according to the input
� Static: treats all the inputs similarly, regardless of their con-
tent
� The compression domain
� Spatial-domain (waveform techniques)
� Transform-domain (transform techniques)
� Feature-domain (model-based techniques)
� Basic compression element
� Pixel-based: (e.g., PCM, DPCM)
� Block-based: (e.g., DCT, KLT, BTC, VQ, Fractal)
� Image-based: (e.g., Wavelet, Multi-resolution Pyramids)
#
Mahmoud El-Sakka, 1999
Patent and Compression
� Patent: To secure the exclusive right/privilege
of inventors for a term of years to make,
use, or sell their inventions, i.e., a granted
monopoly
� Example 1: The LZW algorithm is patented by
Unisys
� GIF issue
� Example 2: The Q-coder implementation of the
arithmetic coding is patented by IBM
� JPEG issue
#
Mahmoud El-Sakka, 1999
The Current Still Image Compression Standard
Joint Photographic Experts Group (JPEG)
� Objectives:
� Capability to do:
� sequential encoding
� progressive encoding
� lossy encoding
� lossless encoding
� feasibility for hardware implementation at 64 Kbits/sec
� March, 1987: 12 proposals were registered
� June, 1987: The selection �eld was narrowed
to 3 approaches
� January 1988: The DCT-based and DPCM-
based approachs were selected
� 1992: JPEG became the ISO/CCITT still
image compression standard
Note that: Wavelet was not a part of the
JPEG, although it exists in the literature
decades ago
#
Mahmoud El-Sakka, 1999
JPEG
� Basic Idea
SourceImageData
ReconstructedImageData
Run-lengthDecoding IDCT
EntropyDecoding
Compressed
Image Data reorderingZigzag Dequantizer
Run-lengthEncoding
EntropyEncoding
Compressed
Image DataFDCT QuantizerOrdering
Zigzag
JPEG Encoder
8x8 blocks
JPEG Decoder
#
Mahmoud El-Sakka, 1999
The ABC-SC Compression Algorithm �
� An Adaptive Block Compression method based
on Segmentation and Classi�cation (ABC-SC)
� Objectives:
� Exceed the compression performance of the current
image compression standard
� Provide a state-of-the-art block-based compression
technique
� Give users the ability to trade o� between desired
compression and image quality
� Have modest computational complexity
� Be amenable to hardware implementation
� Mahmoud R. El-Sakka, \Adaptive Digital Image Compression
Based on Segmentation and Block Classi�cation", Ph.D. Disserta-
tion, Systems Design Engineering, University of Waterloo, Water-
loo, Ontario, Canada, 1997.
#
Mahmoud El-Sakka, 1999
Methodology
� Focus on the useful information
� Reduce the redundant information
� Inter-pixel (Transformation, Reordering, � � � etc)
� Encoding (Prediction, Variable-length Encoding, � � � etc)
� Omit, or at least reduce, the irrelevant information
� Psycho-visual (Image Understanding, Quantization, � � � etc)
#
Mahmoud El-Sakka, 1999
ABC-SC Block Diagram
decompressor
Side information
InformationSide
Smooth regions
decompressor
DecompressedSmooth Regions
DecompressedEdgeRegions
decompressor
Edge regions
decompressor
DecompressedTexturalRegions
Textural regions
Quad-tree reconstructor
Smooth regions
compressor
RegionsSmooth Edge
Regions
compressor
Edge regions
Regions
Quad-tree generator
SmoothRegions Regions
Regions
Blocking suppressor
compressor
Side information
InformationSide
Compressed Image
Dec
oder
Enc
oder
Input Image
Reconstructed Image
Image divider
Textural
Textural
Image reconstructor
compressor
Textural regions
Edge
Side
Information
#
Mahmoud El-Sakka, 1999
Quad-tree Representation
non-homo
homo
homo
non-homo
non-homo
homo
homohomo
homo
non-homo
homonon-homo
homo
homo
homo
homohomo
homo
non-homo
non-homo
non-homo
homoNon-leaf node,
Non-homogeneous leaf,
or Homogeneous leaf.
#
Mahmoud El-Sakka, 1999
A Segmentation Example
the original Lena image smooth segment image
textural segment image edge segment image
#
Mahmoud El-Sakka, 1999ADPCM Predictor
� Utilizes di�erent linear prediction rules, including
2nd and 3rd order two-dimensional prediction rules
� Applies only one rule per prediction
� The choice between these rules is based on the dif-
ferences between the neighboring encoded block av-
erages
C
A
being predictedBlock-average
B L1
L2 L3
#
Mahmoud El-Sakka, 1999
Performance Metrics
� Compression ratio (CR)
� From actual runs, not an entropy estimate
CR =image width� image height
actual compressed �le size
� Objective evaluation
� Root Mean Squared Error (RMSE)
RMSE =vuuut 1
MN
M�1Xx=0
N�1Xy=0
�^f(x; y)� f(x; y)�2
� Peak Signal-to-Noise-Ratio (PSNR)
PSNR = 10 log10
255
RMSE!2
dB
#
Mahmoud El-Sakka, 1999Experimental Results
� Results are presented for the Lena image
� We do compress other images:
for example, the Woman, Tulips, Bridge,
Man, Monarch, Boats, Rocks, Barbara, Zelda,
Peppers, Goldhill, and F16
� Results categories:
� ABC-SC vs JPEG/IJPEG
� ABC-SC vs other segmentation-based techniques
� ABC-SC vs SPIHT-A/SPIHT-B
� Three-class case
� Adaptive prediction e�ect
� Post-processing e�ect
� Execution time
#
Mahmoud El-Sakka, 1999
ABC-SC vs JPEG/IJPEG
ABC-SC, QF = 147 IJPEG, QF = 6
CR = 62:47, RMSE = 8:43 CR = 59:89, RMSE = 9:86JPEG IJPEG
0
4
8
12
16
20
24
28
32
0 50 100 150 200 250 300 350
R.M
.S. e
rror
Compression ratio
ABC-SC
JPEG, QF = 2 rate-distortion relation
CR = 62:22, RMSE = 20:42
#
Mahmoud El-Sakka, 1999ABC-SC vs IJPEG
ABC-SC, QF = 184 IJPEG, QF = 11
CR = 36:81, RMSE = 6:50 CR = 36:69, RMSE = 7:39
ABC-SC, QF = 89 IJPEG, QF = 1
CR = 177:01, RMSE = 12:66 CR = 176:05, RMSE = 32:27
#
Mahmoud El-Sakka, 1999
ABC-SC vs Other Segmentation-based
Techniques
[Vaisey’92][Lee’94][Ran’95]
[Chen’89][Nasiopoulos’91]
[Radha’96]
0
2
4
6
8
10
12
14
16
0 25 50 75 100 125
Compression ratio
R.M
.S. e
rror
IJPEG
JPEG
ABC-SC
#
Mahmoud El-Sakka, 1999
ABC-SC vs Other Segmentation-based
Techniques
[Chen'89 ] C. Chen, \Adaptive Transform Coding Via Quadtree-
Based Variable Blocksize DCT", IEEE International Conference
on Acoustics, Speech and Signal Processing (ICASSP'89), Vol. 3,
pp. 1854-1857, May 1989.
[Nasiopoulos'91 ] P. Nasiopoulos, R.Ward, and D. Morse, \Adap-
tive Compression Coding", IEEE Transactions on Communica-
tions, Vol. 39, No. 8, pp. 1245-1254, August, 1991.
[Vaisey'92 ] J. Vaisey and A. Gersho, \Image Compression with
Variable Block Size Segmentation", IEEE Transactions on Sig-
nal Processing, Vol. 40, No. 8, pp. 2040-2060, August 1992.
[Lee'94 ] M. Lee and G. Crebbin, \Classi�ed Vector Quantisation
With Variable Block-Size DCT models", IEE proceedings: Vi-
sion, Image and Signal Processing, Vol. 141, No. 1, pp. 39-48,
February 1994.
[Ran'95 ] X. Ran and N. Farvardin, \A Perceptually Motivated
Three-Component Image Model - Part II: Applications to
Image Compression", IEEE Transactions on Image Processing,
Vol. 4, No. 4, pp. 430-447, April 1995.
[Radha'96 ] H. Radha, M. Vetterli, and R. Leonardi, \Image
Compression Using Binary Space Partitioning Trees", IEEE
Transactions on Image Processing, Vol. 5, No. 12, pp. 1610-
1624, December 1996.
#
Mahmoud El-Sakka, 1999
ABC-SC vs SPIHT-A/SPIHT-B
ABC-SC, QF = 32 SPIHT-A
CR = 235:11, RMSE = 13:97 CR = 235:11, RMSE = 12:29
0
4
8
12
16
0 50 100 150 200 250 300 350
Compression ratio
SPIHT-B
SPIHT-A
R.M
.S. e
rror
2
6
10
14ABC-SC
SPIHT-B rate-distortion relation
CR = 235:11, RMSE = 12:95
#
Mahmoud El-Sakka, 1999
ABC-SC vs SPIHT-A/SPIHT-B
ABC-SC, QF = 1
CR = 374:49, RMSE = 16:34
SPIHT-A SPIHT-B
CR = 374:49, RMSE = 14:70 CR = 374:49, RMSE = 15:12
#
Mahmoud El-Sakka, 1999
Three-class Case
ABC-SC, QF = 200, TQR = 1:0 ABC-SC, QF = 200, TQR = 0:3
CR = 32:05, RMSE = 6:11 CR = 38:14, RMSE = 7:38
the absolute error the absolute error
in the above image in the above image
#
Mahmoud El-Sakka, 1999
Adaptive Prediction E�ect
block average predictionusing no
ABC-SC
block average prediction
ABC-SCusing JPEG
ABC-SC
block average predictionusing ADPCM
0
2
4
6
8
10
14
16
0 50 100 150 200 250 300 350
12
R.M
.S. e
rror
Compression ratio
#
Mahmoud El-Sakka, 1999
Execution Time
Average Average Average
Encoding compression decompression enhancement
scheme time time time
ABC-SC,
TQR = 1:0 0.919 0.846 0.414
ABC-SC,
TQR = 0:3 1.070 0.815 0.414
SPIHT-A 1.253 1.051
SPIHT-B 0.763 0.532
JPEG 0.109 0.084
IJPEG 0.122 0.081
� Execution time in seconds,
based on runs on a SUN Ultra 1 computer
#
Mahmoud El-Sakka, 1999
Summary of ABC-SC Results
� Experimental results have demonstrated the
following characteristics of the ABC-SC tech-
nique:
� Excellent reconstructed image quality (visual)
� Excellent reconstructed rate-distortion performance
� Outperforms and surpasses JPEG/IJPEG
� Moves block-based compression beyond the limits
of JPEG/IJPEG
� Comparable to the wavelet-based compression tech-
niques (SPIHT-A/SPIHT-B)
� A good alternative to the wavelet-based compres-
sion techniques, especially when adaptability to im-
age content is of interest
� Fast execution time
� Potential for even faster execution time
#
Mahmoud El-Sakka, 1999
JPEG2000
The New Still Image Compression Standard
� Objective: To improve in areas where cur-
rent standard fails to produce the best qual-
ity, including:
� low bit-rate compression
� compound documents compression
� �xed-rate (�xed-size) compression
� protective image security
� March, 1997: A call for contributions is
issued (24 algorithms has been submitted)
� November, 1997: TheWavelet Trellis Coded
Quantization (WTCQ) approach has been
selected
� 200x: JPEG2000 is expected to become the
new ISO/CCITT still image compression stan-
dard
#
Mahmoud El-Sakka, 1999
JPEG2000
� Basic Idea
Compressed
Image Data
ReconstructedImageData
QuantizerInverse Inverse
ScannerEntropy
Decoding
JPEG2000 Decoder
InverseDWT
Compressed
Image Data
SourceImageData
EntropyEncodingDWT Scanner
Classifier
SequencesQuantizer
TCQ
Indices
JPEG2000 Encoder
RateAllocator
... ......
to 8x8 blocks
HL(1)
Map 2 appliedto 8x8 blocks
HH(1)
Map 3 applied
to 8x8 blocks
LH(1)
Map 1 appliedMap 2appliedto 4x4blocks
Map 3appliedto 4x4blocks
Map 1appliedto 4x4blocks
* Calculate variance of 8x8 blocks in level 1* K-means cluster the variances* Label each 8x8 block as belonging to one K classes* Propagate labels up through tree* Include entropy encoded class maps in code stream header
#
Mahmoud El-Sakka, 1999
Conclusions
� Image compression standards are outlined
� A new adaptive block-based compression
scheme (ABC-SC) is introduced
� This new compression scheme outperforms
and surpasses the current image compres-
sion standard
� Its performance is comparable to the per-
formance of the wavelet compression tech-
niques
#
Mahmoud El-Sakka, 1999
Adaptive Block-Based Image Compression
Is it Worth it?
#