1. A New Image Compression Scheme Based on Locally Adaptive Coding
Chair Professor Chin-Chen Chang
Feng Chia University

2. Introduction Image compression technique w h Image Index table
Vector Quantization Encoder

3. Introduction (Cont.) Image compression technique w h Image Index table
Vector Quantization Decoder

4. Introduction (Cont.) Histogram VQ Index table Image 207 246 : 218 223… VQ
Histogram
Index table
Image

5. Introduction (Cont.) Locally adaptive scheme
Ex: a a b b c a c a b d c c e f b a
List
List a b a
0 1
List
List
List
List … c b a a c b c a b a c b
0 a b c …
0: the symbol does not exist in list
1: index existed in list
Concept: Moving the Recently Used to the Front

6. The Proposed Method Image I Divide the temporary codebook into two
Parts (frequently-used
and infrequently-used)
Refine the
frequently-used
part of temporary
codebook
Divide image into
non-overlapping
blocks
Generate
temporary
codebook
Image I
Refine the
infrequently-used
part of temporary
codebook
generated
codebook
Output
Compress I
by referencing
the generated
codebook
Compression code

7. The Proposed Method (Cont.)
The proposed method includes two phases for codebook generation
Temporary codebook generation
Codebook refining

8. Temporary Codebook Generation
The codebook generation is based on the concept of locally adaptive coding
Temporary Codebook w
Bi = {84, 170, 166, 167, 83, …, 168}
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}} h
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
∵ d(Bi , g2,1) = 2.24 TH = 25
∴ add Bi into G2 and move
G2 to be the first one
Image
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
*d(•): Euclidean distance function

9. Temporary Codebook Generation (Cont.)
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}

10. Temporary Codebook Generation (Cont.)w
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
Bj = {220, 212, 182, 179, 240, …, 246} h
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
Image
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
∵ No any block satisfies
d(Bj, gk) TH = 25
∴ Create a new group Gn+1,
add Bj into Gn+1, and move
Gn+1 to be the first one

11. Temporary Codebook Generation (Cont.)
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
Gn+1 = { gn+1,1={220, 212, 182, 179, 240, …, 246}}
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
Gn+1 = { gn+1,1={220, 212, 182, 179, 240, …, 246}}

12. Codebook Refining ||Gn+1|| =1 Frequently-used ||G2|| =3 Gn ||G1|| =3
IF ||Gi|| > THF = 3 Then
Add Gi into Frequently-used part
Else add Gi into Infrequently-used part
Temporary Codebook
Gn+1 = { gn+1,1={220, 212, 182, 179, 240, …, 246}}
||Gn+1|| =1
G2 = { g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
Frequently-used
||G2|| =3
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}} Gn
||G1|| =3 G3
G3 = { g3,1={184, 83, 194, 170, 166, …, 110},
g3,2={180, 80, 194, 166, 168, …, 114},
g3,3={185, 85, 190, 172, 160, …, 120},
g3,4={191, 88, 197, 170, 162, …, 107}}
||G3|| =4
Infrequently-used
Gn+1
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}} G2
||Gn|| =4 G1

13. Codebook Refining (Cont.)
For frequently-used part
c3={185, 84, 194, 170, 164, …, 113}
Compute Gi’s centroid
cn={243, 85, 176, 211, 164, …, 127}
G3 = { g3,1={84, 83, 94, 170, 166, …, 210},
g3,2={80, 80, 94, 166, 168, …, 214},
g3,3={85, 85, 90, 172, 160, …, 220},
g3,4={91, 88, 97, 170, 162, …, 207}} :
∵ d(c3, cn) = 32 THH = 35
∴ Combine c3 and cn by
c3’ = (c3 + cn)/2
Use the centroids to
represent the codewords
c3={185, 84, 194, 170, 164, …, 113}
Gn = { gn,1={244, 83, 174, 210, 166, …, 127},
gn,2={243, 80, 175, 213, 168, …, 128},
gn,3={240, 85, 176, 209, 160, …, 126},
gn,4={244, 88, 178, 213, 162, …, 127}}
cn={243, 85, 176, 211, 164, …, 127}
c3’={214, 85, 185, 191, 164, …, 120} :
Centroid of Gn

14. Codebook Refining (Cont.)
For infrequently-used part
c1={200, 96, 85, 167, 83, …, 131}
c2={85, 170, 166, 169, 86, …, 168}
Compute Gi’s centroid
cn+1={220, 212, 182, 179, 240, …, 246}
Gn+1 = {gn+1,1={220, 212, 182, 179, 240, …, 246}}
cn+1={220, 212, 182, 179, 240, …, 246}
Use the centroids to
represent the codewords
G2 = {g2,1={84, 170, 166, 167, 84, …, 170},
g2,2={86, 168, 165, 170, 90, …, 165},
g2,3={84, 170, 166, 167, 83, …, 168}}
c2={85, 170, 166, 169, 86, …, 168}
G1 = { g1,1={199, 96, 84, 167, 83, …, 130},
g1,2={201, 97, 90, 167, 85, …, 132},
g1,3={200, 95, 82, 167, 81, …, 131}}
c1={200, 966, 85, 167, 83, …, 131}

15. Codebook Refining (Cont.)
Frequently-used part
C3’={214, 85, 185, 191, 164, …, 120} :
∵ d(c3’, c1) = THL = 135
∴ Delete c1 from Infrequently-used part
Infrequently-used part
c1={200, 96, 85, 167, 83, …, 131}
c1={200, 96, 85, 167, 83, …, 131}
c2={85, 170, 166, 169, 86, …, 168}
c2={85, 170, 166, 169, 86, …, 168}
cn+1={220, 212, 182, 179, 240, …, 246}
cn+1={220, 212, 182, 179, 240, …, 246}

16. Codebook Refining (Cont.)
Frequently-used part
C3’={214, 85, 185, 191, 164, …, 120}
C3’={214, 85, 185, 191, 164, …, 120}
c2={85, 170, 166, 169, 86, …, 168} : :
Infrequently-used part
c2={85, 170, 166, 169, 86, …, 168}
∵ No any codeword cj from frequently-used
part satisfies d(c2, cj) THL = 135
∴ Add c2 into frequently-used part
and delete c2 from infrequently-used part
cn+1={220, 212, 182, 179, 240, …, 246}

17. Codebook Refining (Cont.)
Frequently-used part
C3’={214, 85, 185, 191, 164, …, 120}
C3’={214, 85, 185, 191, 164, …, 120}
c2={85, 170, 166, 169, 86, …, 168}
c2={85, 170, 166, 169, 86, …, 168}
cn+1={220, 212, 182, 179, 240, …, 246} : :
Generated codebook
Infrequently-used part
cn+1={220, 212, 182, 179, 240, …, 246}
∵ No any codeword cj from frequently-used
part satisfies d(cn+1, cj) THL = 135
∴ Add cn+1 into frequently-used part
and delete cn+1 from infrequently-used part
Empty

18. Image Compression Generated codebook : Index table Image 1w h 1
C0={214, 85, 185, 191, 164, …, 120}
c1={85, 170, 166, 169, 86, …, 168} :
cn={220, 212, 182, 179, 240, …, 246}
Index table
Image

19. Experimental Results
(a) Alan
(b) Goldhill
(c) Lena
(d) Tiffany

20. Experimental Results (Cont.)
(a) Codebook size comparison

21. Experimental Results (Cont.)
(b) PSNR comparison with different THs

22. Experimental Results (Cont.)
Methods
Images
Proposed method
(TH = 25, THH =30, THL = 115) VQ
PSNR CR
number of codewords
Alan
31.82
0.0547 77
31.75
0.0625
256
Boat
28.68
229
28.85
Goldhill
28.96
180
29.55
Jet
29.47
178
29.81
Lena
30.27
170
31.15
Pepper
30.56
177
30.94
Tiffany
30.87
107
30.92
Toys
30.53
233
29.10
Zelda
33.320
136
34.29
Average
30.50
0.0608
30.71

23. Conclusions
The proposed method significantly reduces the size of codebook and maintains a good image quality of the compressed images.