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IMAGE COMPRESSION
TECHNIQUES
S.Esakkirajan
Assistant Professor
I&CE DepartmentPSG College of Technology
Coimbatore
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Topics of Presentation
Need for image compression
Transform based image compression
Vector Quantization
Image Compression Standards
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What is Compression?
Compact representation.
Representing the data with minimum
number of bits.
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Need for Compression
To minimize the storage space
To enable higher rate of data transfer
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Philosophy of Compression
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DATA
INFORMATION
DATA=USEFULDATA + UNWANTED DATA
Unwanteddata
RedundantData
Irrelevant data
Useful information = Data[Redundant + Irrelavant data]
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Philosophy of Compression(Cont.,)
H2OH2O
http://www.google.co.in/imgres?imgurl=http://www.hort.purdue.edu/ext/senior/fruits/images/large/orange3.jpg&imgrefurl=http://www.hort.purdue.edu/ext/senior/fruits/orange1.htm&usg=__0w_U6Cnc7z8xBef1TvusLzCDhtk=&h=480&w=640&sz=53&hl=en&start=33&itbs=1&tbnid=aMhGF8c-jF9kvM:&tbnh=103&tbnw=137&prev=/images%3Fq%3Dbunch%2Bof%2Borange%2Bfruits%26start%3D18%26hl%3Den%26sa%3DN%26gbv%3D2%26ndsp%3D18%26tbs%3Disch:17/31/2019 Data Compression(2)
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Classification of Redundancy
Redundancy in Image
SpatialRedundancy
PsychoVisualRedundancy
CodingRedundancy
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Classification of Compression
Techniques
Original DataCompressedData
Lossless
Original Data
Approximated
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Transform Coding
Transform QuantizationEntropyCoding
InputImage
Compressedbitstream
InverseTransform
InverseQuantization
EntropyDeCoding
ReconstructedImage
Compressedbitstream
Image Encoding
Image Decoding
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Transform
Compact energy into a few coefficients.
Decorrelate (reduce linear dependence)among coefficients.
KL transform, DCT, Wavelet.
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KL transform
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Input Image
Partition of the imageinto blocks
Compute the Mean
Compute the
Covariance Matrix
Eigen Vector of theCovariance Matrix
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Discrete Cosine Transform
Fourier basis: Complex exponential (ejt )
cos(t)= 0.5[ejt +e-jt ]
Symmetrical extension of DFT
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DCT (Cont.,)
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n
xe[n]
n
x[n]
xe[n]
n
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DCT (Cont.,)
14
otherwise
Nk
Nk
N
kn
N
knnnx
kkC
N
n
N
nx
,0
10
10,
2
12cos
2
12cos],[4
],[22
11
2
22
1
11
21
1
0
1
021
1
1
2
2
otherwise
Nk
Nk
N
kn
N
knkkCkwkw
NNnnx
N
k
N
k
x
,0
10
10,
2
12cos
2
12cos],[][][
1
],[22
11
2
22
1
11
21
1
0
1
0
2211
2121
1
1
2
2
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Wavelet Transform
Oscillatory function of finite duration.
CWT and DWT
Multi-resolution Analysis
Wide variety of basis function
15
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DWT - Implementation
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LPF
HPF
2
2
LPF 2
HPF 2
LPF 2
HPF 2
InputImage
Column
processing
Rowprocessing
LL
LH
HL
HH
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SUBBAND DECOMPOSITION
0
0
0
0 0
0
0 0
0
00
0
0
0
0
0
0 0 0
0
0 0
0
0
0 0
0
0
0 1
1
0
1
11
11
1
1
1
0 0
1
0
1
1
1
1
1
0 0 00 0 0 0
0
0
0
0
0
0
0
0
Low pass filter is ,
INPUT IMAGE
RESULTANT IMAGE
AFTER ROW
PROCESSING
0 0 0
0 0
0
0
0
0
0
0
0
0
0
0
0 0
0
0
0
00
0 0
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Step 1b :COLUMN PROCESSING OF THERESULTANT
0
0
00 0
0 0
0
0
0 0
0
0
000
0
0
0
0
0
0
0
0
LOW PASS FILTERED IMAGE
LL SUBBAND
0 0 0
0
0
0 0 0
0
0
0
0
2 2
2 2
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STEP 2:TO FIND THE SUBBAND LH
0
0
00 0
0 0
0
0
0 0
0
0
000
0
0
0
0
0
0
0
0
LOW PASS FILTERED IMAGE ALONG ROW
THE LH SUBBAND
0 0 00
0
0
0
0 0
0
00
0
0
0
0
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STEP 3:TO FIND HL SUBBANDSTEP 3a :HIGH PASS FILTERING ALONG ROW
0
0
0
0 0
0
0 0
0
00
0
0
0
0
0
0 0 0
0
0 0
0
0
0 0
0
0
0 1
1
0
1
11
11
1
1
1
0 0
1
0
1
1
1
1
1
0 0 00 0 0 0
0
0
0
0
0
0
0
0
IMPUT IMAGE HIGH PASS FILTERED
IMAGE
0 00 0
0
0
0
0
0
0
0
0
0
0
0
0000
0
0
00
0
0
0
0
00
00
0
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STEP 3B: LOW PASS FILTERING OFRESULTANT IMAGE ALONG COLUMN
0 00 0
0
0
0
0
0
0
0
0
0
0
0
0000
0
0
00
0
0
0
0
00
00
0
HIGH PASS FILTERED IMAGE
OBTAINED IN STEP 3a
HL SUBBAND
0 0 00
0
0
0
0 0
0
00
0
0
0
0
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STEP 4 :TO FIND HH SUBBAND (HIGH PASS FILTERING
ALONG ROW & THEN HIGH PASS FILTERING ALONGCOLUMN)
0 00 0
0
0
0
0
0
0
0
0
0
0
0
0000
0
0
00
0
0
0
0
00
00
0
HIGH PASS FILTERED IMAGEHH SUBBAND
0 0 00
0
0
0
0 0
0
00
0
0
0
0
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STEP 5:DECOMPOSITION OF INPUT IMAGE INTOFOUR SUBBANDS LL,LH,HL,HH
0
0
0
0 0
0
0 0
0
00
0
0
0
0
0
0 0 0
0
0 0
0
0
0 0
0
0
0 1
1
0
1
11
11
1
1
1
0 0
1
0
1
1
1
1
1
0 0 00 0 0 0
0
0
0
0
0
0
0
0
INPUT IMAGE
FIRST LEVEL
WAVELET
DECOMPOSITION
00 00
0
0
0
2 2
0
2 2
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
LL LH
HL HH
00 00
0
0
0
2 2
0
2 2
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
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SECOND LEVEL DECOMPOSITION
00 00
0
0
0
2 2
0
2 2
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
00 00
0
0
0
0 0
0
0 0
0
0
0
0
SECOND LEVEL
WAVELET
DECOMPOSITION
01 01
1
0
0
1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
LL
HL HH
LH
01 01
1
0
0
1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
0-1 0-1
-1
0
0
-1 0
0
0 0
0
0
0
0
FIRST LEVEL DECOMPOSED IMAGE
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Properties of Wavelet Filters
Compact support
Symmetric
Vanishing Moment
Regularity
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Quantization
26
Approximation.
Mapping large set of values to small set of
values.
It is a non-linear and irreversible process
Range of Marks Grade
0 to 49 F
50-54 E
55-59 D
60-69 C
70-79 B
80-89 A
90-100 S
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Quantization Techniques - Classification
Quantization
VectorQuantization
EmbeddedQuantization
ScalarQuantization
Uniform
Non-
Uniform
Mid-tread Mid-rise
EZW SPIHT SPECK
TSVQ MSVQ HVQ
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Vector Quantization
Search
Engine
..
..
..
Codebook Indices
The Encoder
Output
Vector
..
..
..
Indices Codebook
The Decoder
Channel
Input
Vector
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2 4 6 8
10 11 16 15
9 3 1 7
12 14 13 5
Consider an input image
of size 4 by 4
Choose the dimension
as two
16
1
Here Maximum value=16
Minimum value =1
Dynamic range=Maximum-Minimum
=16-1=15
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4 8 12 160
4
8
12
16
*
*
*
*
*
*
*
*
* *
* *
*
*
*
*
C12
C8
C4
C0
C13
C9
C14 C15
C10 C11
C5 C6 C7
C1 C2 C3
(2,2)
(2,6)
(2,10)
(2,14)
(6,2)
(6,6)
(10,6)
(14,6)
(10,2)
(10,6)
(10,10)
(14,2)
(14,6)
(14,10)
(14,14)(14,10)
In this example,
rate(R)=2,dimension(L)=2
Number of code
vectors=2^(R*L)=16
Code vectors are
C0 to C15
Fixing the interval
LR
geDynamicRanInterval
In our case
interval=4
C0 to C15 is
obtained using
Centroid Method
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2 4 6 8
10 11 16 15
9 3 1 7
12 14 13 5
0 4 8 16
4
8
12
16
12
*
*
* * *
*
*
*
* * *
*
*
*
* *
.
.
..
.
.
.
.
Mapping of Input Image Vector to Code Vector
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0 4 8 16
4
8
12
16
12
*
*
* * *
*
*
*
* * *
*
*
*
* *
(1,7)
(6,8)
(2,4)
(10,11)
(12,14) (16,15)
(9,3) (13,5)(2,6) (6,6)
(2,2)
(10,10)
(14,14)(14,14)
(10,2)
(14,6)
Adjust the Input Vectors to fall into one of the
Code Vectors
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12(2,4)
Input Image
Vectors
Transmitted
Indices
(6,8)
(10,11)
(9,3)
(1,7)
(16,15)
(12,14)(13,5)
9
6
3
11
3
8
14
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2 2 6 6
10 10 14 14
10 2 2 6
14 14 14 6
Original image Reconstructed image
2 4 6 8
10 11 16 15
9 3 1 7
12 14 13 5
12 9 6 3 14 8 113
Si l C ffi i tTransform
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Detachment from Attachment
Attachment
Signal CoefficientTransform
Decorrelation
Coefficients are correlated
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Embedded Quantization
Progressive Quantization
(a) EZW (b) SPIHT (c) SPECK etc
Starting point Wavelet Coefficients
Parent-child relationship in waveletdomain
36
T i l i i EZW
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Terminologies in EZW
Root node/ Parent node
Child node
(a) Significant Positive (SP)
(b) Significant Negative (SN)
(c) Zero-tree Root (ZR)
(d) Isolated Zero (IZ)
Dominant Pass and Refinement pass
37
T i l i i EZW (C t )
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Terminologies in EZW (Cont.,)
38
R C1
C3C2
X X
X X
X X
X X
X X
X X
Maximum Coefficient Value Cmax= R
T0
= 2floor(log2(Cmax))Magnitude of the coefficient > Magnitude of Threshold = SPMagnitude of the coefficient > Magnitude of Threshold = SNMagnitude of the coefficient < Magnitude of Threshold &
ALL Descendents magnitude Threshold = IZ
Computation ofThreshold
EZW Ill t ti
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EZW - Illustration
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34 0
00
1 -1
1-1
4
-4
-4
4
10 -6
6 -10
T0 = 2floor(log2(34)) = 25 = 32
Dominant Pass
34>32 = SP ZR ZR ZR Ls = {34}
Data transmitted: Threshold, SP, ZR,ZR,ZR
48 0
00
0 0
00
0
0
0
0
0 0
0 0
Reconstructed value: (3/2)T0 =48
Refinement Pass
Ls Reconstructed value = -14
Correction term sign:
Correction term = (T0/4) = (32/4) = 8Corrected value= 48-8 = 40
40
EZW Illustration
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EZW - Illustration
40
40 0
00
0 0
00
0
0
0
0
0 0
0 0
X
Dominant Pass
Threshold value T1 = (T0/2) =16
zr zr zr Ls = {34}
0
00
0 0
00
0
0
0
0
0 0
0 0
40
Refinement Pass
Correction term sign:
Ls Reconstructed value =- 6
Correction term = (T1/4) = (16/4) = 4
36
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Runlength Coding
0(12)
0(12)
0(12)
0(12)
0(12)0(5)1(2)0(5)
0(5)1(2)0(5)
0(12)
0(12)
0(12)0(12)
0(12)
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Runlength Coding
0(12)
0(12)
0(12)
0(12)
0(12)0(5)1(2)0(5)
0(5)1(2)0(5)
0(12)
0(12)
0(12)0(12)
0(12)
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Runlength limitation
HUFFMAN CODE
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HUFFMAN CODE
Based on probability and entropy
Basic philosophy of Huffman code
Variable length code
Prefix code
H ff d E l
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Huffman code - Example
Symbol Probability
1/2
1/4
1/8
1/8
Spade
HeartDiamond
Club
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Huffman code Example (Cont.,)
Code Symbol Probability Step 1 Step 2
1/2
1/4
1/8
1/8
1/4
1/4
1/2
1/2
1/2 (0)
(1)
(0)
(1)
(0)
(1)
0
10
110
111
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LOSSLESS DPCM
Signal to be Transmitted
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Predictor
EntropyEncoder
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EntropyDecoder
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Channel
Channel
Received Signal
Signal to be Transmitted
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EntropyEncoder
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EntropyDecoder
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Signal to be Transmitted
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EntropyDecoder
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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EntropyEncoder
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EntropyDecoder
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Signal to be Transmitted
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EntropyEncoder
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Signal to be Transmitted
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Predictor
EntropyEncoder
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Signal to be Transmitted
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Predictor
EntropyEncoder
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EntropyDecoder
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Signal to be Transmitted
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Predictor
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EntropyDecoder
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Signal to be Transmitted
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Signal to be Transmitted
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Signal to be Transmitted
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EntropyEncoder
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EntropyDecoder
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Signal to be Transmitted
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Predictor
EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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94
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94
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-3
91
Signal to be Transmitted
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Predictor
EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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94
94
94
91
-3
91
Signal to be Transmitted
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Predictor
EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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94
91
91
Signal to be Transmitted
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Predictor
EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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94
91
91
91
Signal to be Transmitted
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97Predictor
EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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91
91
91
91
Signal to be Transmitted
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EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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91
91
91
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Signal to be Transmitted
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EntropyEncoder
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Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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91
91
91
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Signal to be Transmitted
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EntropyEncoder
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Predictor
EntropyDecoder
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Channel
Channel
Received Signal
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91
91
91
91
6
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Signal to be Transmitted
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EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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91
91
91
6
Signal to be Transmitted
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EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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91
9191
91
6
Signal to be Transmitted
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EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
92 94
91
9191
91
697
Signal to be Transmitted
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EntropyEncoder
-
Predictor
EntropyDecoder
+
Channel
Channel
Received Signal
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9191
91
697
97
P f I di
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Performance Indices
Compression Ratio (CR)
Bitrate
PSNR
82
filecompressedtheofsize
fileoriginaltheofsizeCR
imagetheinpixels
filecompressedtheofsizebpp
MSE
1PSNRb 2
10
12log0
JPEG
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JPEG
JPEG CODEC
InputImage
FDCT Quantizer EntropyEncoder
Channel
IDCT DequantizerEntropy
Decoder
DCT based Decoder
DCT based Encoder8 X 8 blocks
zigzag
Reverse
zigzag
JPEG MODES
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JPEG MODES
Sequential Mode
Progressive Mode
Hierarchical Mode
Lossless Mode
D b k f JPEG
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Drawback of JPEG
Artifact
Blocking artifact Ringing artifact
Due to block processing Sharp oscillation or
ghost shadows
Bl ki tif t
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Blocking artifact
JPEG 2000
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JPEG 2000
Wavelet Trasform.
Compress once and decode many times
Supports different scalability
Supports Region of Interest Coding
Error Resilience
JPEG 2000
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J G 000
2D FDWTScalar
Quantization
Block based
Arithmetic
coding
2D IDWTInverse
Quantization
Block based
Arithmetic
decoding
Bitstream j2k3HH
3HL
3LH
2HL
2LH
1HL
2HH
1LH 1HH
0LL
Rate-distortion
Allocation
optimisation
Progressive Transmission by
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g y
resolutionCompressed Image bitstream
Progressive Transmission by
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Compressed Image bitstream
g y
position
Progressive Transmission by
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Compressed Image bitstream
g y
components
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Image Segmentation
Subdivide the image into its componentregions
92
Segmentation Algorithms
Discontinuity Similarity
Robert Prewitt Sobel Region
growing
Region
Splitting
Split and
Merge
Image Segmentation Example
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Image Segmentation - Example
93
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