A unified projection method for fast search of vector quantization

1
A unified projection method for fast search of
vector quantization

• Source IEEE Signal Processing Letters, vol. 11,
  issue 7, July 2004, pp. 637 - 640.
• Author Zhibin Pan Kotani, K. Ohmi, T.
• Speaker Chang-Chu Chen
• Date 04/28/2005

2
Outline

• Vector Quantization
• Projection Method
• Two Estimations
• Experimental Result
• Conclusions

3
Vector Quantization (VQ)
Image compression technique
Codebook








51 46 6 84 41 52 74 3
2






0







1
2
(20,45,,76)
253
254
Original image
Index table
255
Vector Quantization Encoder
4
Vector Quantization (VQ)
Image compression technique
Codebook








51 46 6 84 41 52 74 3
2






0







1
2
(20,45,,76)
253
254
Original image
Index table
255
Vector Quantization Decoder
5
Codebook search

• Find closest code vector

Codebook







Image vector
(20,45,,76)
Index
(21,44,,78)
2
6
Euclidean Distance

• The dimensionality of vector kAn input vector
  I (I1, I2, , Ik)A code vector Ci (Ci,1,
  Ci,2, , Ci,k)
• The Euclidean distance between I and Ci
• Full Search (FS)To find closest Cw , where
  codebook C of size Nc

7
Projection Method
I (I1, I2, , Ik)
(IP , IP,?)
Rk
R2
8
Two Estimations
addition1subtraction2multiplication1
1
subtraction1multiplication1
2
DiI-Ci
I
Ci
IP,?
(Ci)P,?
P
(Ci)P
IP
9
Search flowchart

• Step 1(off-line)

• Step 2(on-line)

Set up P
Compute and of all code vector Ci
yes
no
yes
no
yes
no
10
Experimental Result
Eq.4
S1 P1(1,1,1,1,,1,1,1,1)
Eq.5
S2 P2(1,1,-1,-1,,1,1,-1,-1)
11
Conclusions

• A unified projection method is proven
  mathematically.
• Two criteria on how to select an optimal P
• P parallels to Di.
• P lies in the plane determined by I and Ci.
• How to really select an optimal projection axis
  is out of the scope of this paper and is
  impractical.

12
Law of Cosines
13
Estimation 1
by
,
,
,