### Drawbacks of VQ

```Date: 2011.11.23
Reporter: Hsin-Hui Chen
 Vector
Quantization(VQ)-Based Image
Coding
 Block Truncation Coding(BTC)
 Wavelet-Based Image Coding
Scalar
Quantization (SQ)
• A real number
Vector
Quantization (VQ)
• A set of real numbers
 Vector
Quantization (VQ)
 Side-Match Vector Quantization (SMVQ)
 Classified Vector Quantization (CVQ)
 Tree Structured Vector Quantization (TSVQ)
 Drawbacks of VQ
 Block Effect
 Time Complexity for LBG algorithm
 Block Effect
 SMVQ
 Derailment
 CSMVQ
 Time Complexity
 CVQ
 TSVQ
 PCA
Encoder
Codebook
Find the closest codeword
…
w
…
codeword
i
i
k
…
…
Index Table
Original Image
k=wxh
Output: i
Codebook
codeword
i
Decoder
Codebook
Look-up Table
codeword
w
h
k
i
Similar block
Index Table
k=wxh
Reconstructed
Image
LBG
 Splitting

Block Effect
…
…
…
…
Original Image
Seed blocks
=>VQ
Residual blocks
=>SMVQ
State Codebook
Generate
Super Codebook
Codebook)
codeword
Super Codebook
codeword
167 150 122 101
133 150 150 122 101
129 129
118 118
123 123
Find N Closest Codewords from Super Codebook
Derailment
State Codebook
codeword
Error <= TH
Super Codebook
codeword
Error > TH
Block indicator:
Bit “1” => VQ
Bit “0”=> SMVQ
Compared to SMVQ:
• More Robust to derailment
• But less coding efficiency
Two Thresholds:
THc
THD
Size
State Codebook
Choose one
Super Codebook
State Codebook Size Decision
If Var(U)<=THc and Var(V)<=THc :
Class(X)=1
If (Var(U)<=THc and Var(V)>THc ) or
(Var(U)>THc and Var(V)<=THc ):
Class(X)=2
If Var(U)>THc and Var(V)>THc:
Class(X)=3
Three State Codebooks:
Class(X)=1
Class(X)=2
Class(X)=3
N
2N
4N
min(X,CWi)<=THD
State Codebook
CWi
min(X, CWi)>THD
Super Codebook
Spent much time to full search
Full Search
Codebook
Find the closest codeword
…
w
…
codeword
i
i
k
…
…
Index Table
Original Image
k=wxh



Classified Vector Quantization (CVQ)
Tree Structured Vector Quantization (TSVQ)
Principal Component Analysis (PCA)
Comparable image quality to VQ
 Less computational time

Encoder
…
w
Output
index
CVQ Encoder
…
…
…
Block
Classifier
Original Image
……
Codebook1
Codebook2
Codebook N
VQ Codebook
Tree Structured
VQ Codebook
Codebook
codeword
i
Covariance Matrix
K
C
KxK
MxK
Covariance Matrix
CV=VD
C
V
KxK
KxK
D
V: Eigenvectors matrix
D: Eigenvalues matrix
KxK
sort
V
Find the eigenvector with
the largest eigenvalue
KxK
Projection coordinate
D
V: Eigenvectors matrix
D: Eigenvalues matrix
KxK
Codebook
codeword
i
K
Projection coordinate
MxK
Codebook Projection
Values
Codebook
codeword
i
Codebook Projection
Values
K
MxK
…
Projection coordinate
…
Find the closest codebook
projection value
Projection value
Codebook
…
…
codeword
K
Original Image
i
i
Search Range
Codebook Projection Values
…
…
…
…
Original Image
BTC
Bit map
a
b

An Example:
Bit map
a
b
Original Block
Average Value
Reconstructed Block



Embedded Zero Wavelet (EZW)
Set Partitioning in Hierarchical Tree(SPIHT)
JPEG2000

Parent-Descendant Relationship

Scan Order
Thresholds
Bitstream
101001110….
Q&A
Q&A
```