Lossless Compression Schemes of Vector Quantization Indices Using

Lossless Compression Schemes of Vector Quantization Indices Using State Codebook Chair Professor Chin-Chen Chang Feng Chia University National Chung Cheng University National Tsing Hua University http: //msn. iecs. fcu. edu. tw/~ccc

Outline u Introduction l VQ l PCA l SOC u Proposed schemes l Scheme 1 l Scheme 2 u Experimental results u Conclusions 2

Alan Chang 3

Vector Quantization (VQ) Concept Encoding and Decoding 4

Introduction (VQ) Image compression technique h w Image Index table Vector Quantization Encoder 5

Introduction (VQ) (Cont. ) 6

Introduction (VQ) (Cont. ) u Training phase Codebook ………………. …. divided into blocks with pixels Codebook size ex : 128, 256, 512 or 1024 ………………. 16 -dimension 7

Introduction (VQ) (Cont. ) 0 1. . . Index sets (1, 2, 5, 9, 45, …) (101, 179, 201, …) (8, 27, 38, 19, 200, …) 0 1. . . 254 255 N-1 Training set (23, 0, 67, 198, 224, …) Codebook Ci Compute mean values Replace the old vectors 0 1. . 254. 255 New Codebook Ci+1 Training using iteration algorithm 8

Introduction (VQ) (Cont. ) u LBG Algorithm u 一次訓練 256 個 codewords u 做了100次 u 連續兩次 MSE 之差別已經夠小 9

• Ex: Codebook To encode an input vector, for example, v = (150, 145, 121, 130) (1) Compute the distance between v with all vectors in codebook d(v, cw 1) = 114. 2 d(v, cw 2) = 188. 3 d(v, cw 3) = 112. 3 d(v, cw 4) = 124. 6 d(v, cw 5) = 122. 3 d(v, cw 6) = 235. 1 d(v, cw 7) = 152. 5 d(v, cw 8) = 63. 2 (2) So, we choose cw 8 to replace the input vector v. 10

Introduction (VQ) (Cont. ) u Encoding Codebook 123456 index table encoding Original image Nc-1 Nc 11

Introduction (VQ) (Cont. ) u Decoding look-up procedure 123456 index table Codebook decoding Nc-1 Nc 12

Introduction (PCA) u Principal component analysis (PCA) u Ex: 2 -dimension X 2 D 2 . . . D 1. . X 1 13

Introduction (SOC) u. Search-order coding (SOC) u. Ex: 14

Introduction (SOC) (Cont. ) Searched point Non-searched point 15

Introduction (SOC) (Cont. ) Indicator The compressing steps 207 211 31 207 8 207 31 211 8 7 31 8 7 P 3 = 0 00 P 6 = 0 01 … 35 P 2 = 1 11001111 … 31 P 1 = 1 00011111 Compression codes = 100011111 111001111 000 … 16

The proposed scheme start PCA run SOC yes SOC end no our scheme no yes end our scheme original index value end 17

The proposed scheme (Cont. ) u Indicator l SOC “ 0” l Our scheme “ 10” l Original index value “ 11” 18

The proposed scheme (Cont. ) u State codebook is generated in real-time u Three cases l CASE 1 One-bit indicator (0)+ SOC l CASE 2 Two-bits indicator (10)+ index value l CASE 3 Two-bits indicator (11)+ VQ index value 19

The proposed scheme (Cont. ) Example 1: 61 54 SOC: CASE 1 u. One-bit indicator (0)+ SOC u. Compression result of (3, 3) is “ 0001” (101) 61 (001) (010) 54 (100) (000) 20

Scheme 1 Example: 2 61 CASE 2 • Two-bits indicator (10)+ index value • Compression result of (3, 3) is “ 101110” 21

Scheme 1 (Cont. ) Example 3: 61 60 CASE 3 No match found in Cases 1 and 2 • Two-bits indicator (11) + VQ index “ 1110” 47 22

Scheme 2 • Also called “The Optimized State Codebook Scheme” • The exclusion of repetition indices • Four state codebooks • Codebook 1 61 23

Scheme 2 (Cont. ) • Codebook 2 ? • Check if {53, 54, 56, 57} ∩{52, 53, 55, 56} = ø Yes: 61 The similar neighboring index (2, 2), which equals to “ 54” The index of the state codebook The indices of the closest codewords of “ 54” in the codebook “ 0100” “ 0101” “ 0110” “ 0111 52 53 55 56 NO: The similar neighboring index (2, 2), which equals to “ 54” The index of the state codebook The indices of the closest codewords of “ 54” in the codebook “ 0100” “ 0101” “ 0110” “ 0111 51 52 58 59 52 53 55 56 53 54 56 57 24

Scheme 2 (Cont. ) • Codebook 3 ? • Check if ({53, 54, 56, 57} ∪ {51, 52, 58, 59}) ∩ {50, 51, 53, 54} = ø Yes: The similar neighboring index (2, 4), which equals to “ 52” The index of the state codebook The indices of the closest codewords of “ 52” in the codebook “ 1000” “ 1001” “ 1010” “ 1011” 50 51 53 54 61 NO: The similar neighboring index (2, 4), which equals to “ 52” The index of the state codebook The indices of the closest codewords of “ 52” in the codebook “ 1000” “ 1001” “ 1010” “ 1011” 49 50 60 61 50 51 53 54 51 52. . . 58 59 25

Scheme 2 (Cont. ) • Codebook 3 The similar neighboring index (2, 4), which equals to “ 52” 61 The index of the state codebook The indices of the closest codewords of “ 52” in the codebook “ 1000” “ 1001” “ 1010” “ 1011” 49 50 60 61 CASE 2 • Two-bits indicator (10)+ index value • Compression results of (3, 3)= “ 10 1010” 26

Scheme 2 (Cont. ) • Codebook 4 ? • Check if ({53, 54, 56, 57} ∪ {51, 52, 58, 59} ∪ {49, 50, 61, 62}) ∩ {44, 45, 47, 48} = ø Yes: The similar neighboring index (3, 1), which equals to “ 46” The index of the state codebook The indices of the closest codewords of “ 46” in the codebook “ 1100” “ 1101” “ 1110” “ 1111” 44 45 47 48 61 27

Experimental results (1/4) • The codebook is designed by using LBG algorithm 28

Experimental results (2/4) 1 29

Experimental results (3/4) 2 30

Experimental results (4/4) 3 31

Conclusions • Two new schemes for VQ index table • Scheme 2 excludes the repetitive indices • Scheme 2 presents better performance than SOC and Scheme 1 • Both schemes achieve the goal of reducing bit rate 32