An efficient histogrambased index mapping mechanism for reversible

An efficient histogram-based index mapping mechanism for reversible data hiding in VQ-compressed images u. Source : Information Sciences, vol. 435, pp. 224 -239, 2018 u. Authors : Peyman. Rahmani and Gholamhossein. Dastghaibyfard u. Speaker : Chia-Shuo Shih u. Date : 2018/02/22 1

Outline �Introduction ① Vector-quantization (VQ) ② Side-match vector quantization (SMVQ) ③ Locally adaptive data compression scheme (LAS) �Proposed method �Experimental results �Conclusions 2

Introduction --- Vector Quantization (VQ) �VQ is a lossy image coding technique. �VQ consists of three procedures: ① Codebook design �Generate a set of representative codewords. �The LBG algorithm is the most commonly used method. ② Image Encoding ③ Image Decoding [34] Y. Linde, A. Buzo, R. Gray, “Algorithm for Vector Quantizer Design”, IEEE Transactions on Communications, vol. 28, no. 1, pp: 84 -95, 1980. 3

Introduction --- Vector Quantization (VQ) �Image Encoding ◦ Partition the grayscale image into non-overlapped image blocks ◦ Find the closest codeword in the codebook for each image block x ◦ The index of the closest codeword of x is recorded. �Image Decoding ◦ Reconstruct each block by the codeword in the codebook of its index. 4

Introduction --- Vector Quantization (VQ) Codebook 5

Introduction --- Side Match Vector Quantization(SMVQ) �Goal: ◦ Cut down the bit rate of VQ �Bit rate of VQ is log 2(Nc)/(n*n) bit per pixel (bpp) �An example: 0. 5 bpp when Nc=256 and block size is 4*4 �Processing Rules: ◦ Employ the encoded left and up blocks to generate a smallsized state codebook (SC). ◦ Use the state codebook to encode the current image block. [20] T. Kim, “Side match and overlap match vector quantizers for Images”, IEEE Transactions on Image Processing, vol. 1, no. 2, pp: 170 -185, 1992. 6

Introduction --- Side Match Vector Quantization(SMVQ) State Codebook (SC) 0 135, …, 135, 134 1 136, …, 136, 135 2 . 3 . 31 . 7

Introduction --- Locally adaptive data compression scheme (LAS) u The locally adaptive scheme (LAS) as a general-purpose data compression method. u Short decimal values could be compressed efficiently. Data string: a a b b b c d b b a c J. L. Bentley, D. D. Sleator, R. E. Tarjan, V. K. Wei, “ A locally adaptive data compression scheme”, 8

Introduction --- Locally adaptive data compression scheme (LAS) Data string: a a b b b c d b b a c Input characters a Character list 4 3 2 1 a 1 a Output characters a b b b c a a b a b 1 2 b 1 1 d b b a c a b c d a c d b a c 3 c 4 d 3 1 4 4 a b c 9

Proposed method Construction of the mapping table Embedding secret data Construction of the mapping LAS’s way table Embedding secret data SMVQ’s way VQ 102 139 140 219 103 140 92 219 164 136 92 219 92 92 251 104 Index Table 10

Proposed method-SMVQ index Sorting the VQ’s codebook by SMVQ 102 139 140 92 219 164 136 92 219 92 251 140 1 . 2 . 3 . 40 SMVQ . . 39 . . 253 . 254 . 255 . 219 103 92 0 104 Index Table 47 47 48 49 Codebook 39 39 140 State Codebook 11

Proposed method-Construction of the mapping table k c(k) w(k) lb(k) ub(k) 0 6 64 0 63 1 5 32 64 95 5 32 96 127 3 4 16 128 143 w(k): the width of the interval k. 4 4 16 144 159 lb(k): the start position of the interval k. 5 4 16 160 175 6 3 8 176 183 ub(k): the end position of the interval k. 7 3 8 184 191 8 6 64 192 255 k: the interval number (0 k t). c(k): the assigned capacity to the interval k, 2 in bits. 12

Proposed method-Embedding Secret bit: 10001010011 SMVQ 29 Index table 0 186 1 29 2 131 . . 80 230 k c(k) w(k) lb(k) ub(k) 0 6 64 0 63 1 5 32 64 95 81 66 2 5 32 96 127 82 119 3 4 16 128 143 4 4 16 144 159 . . 5 4 16 160 175 . . 6 3 8 176 183 . . 7 3 8 184 191 8 6 64 192 255 79 SCB(State Codebook) ① k = 1 ② c(k) = 5 ③ Secret bit: 10001 ④ = 17 ⑤ lb(1) + 17 64 + 17 = 81 66 SCB(81) = 66 13

Proposed method-Embedding Secret bit: 10001010011 SMVQ 70 0 129 1 . 27 59 28 70 29 220 k c(k) w(k) lb(k) ub(k) 0 6 64 0 63 1 5 32 64 95 . 2 5 32 96 127 210 113 3 4 16 128 143 4 4 16 144 159 211 49 5 4 16 160 175 212 119 6 3 8 176 183 . 7 3 8 184 191 8 6 64 192 255 . ① k = 8 ② c(k) = 6 ③ Secret bit: 010011 ④ = 19 49 ⑤ lb(6) + 19 192 + 19 = 211 SCB(211) = 49 . 17 14

Proposed method-Decoding Input indices: …, 66, 49, 70, … SMVQ 66 0 186 1 29 2 131 . . k c(k) w(k) lb(k) ub(k) . . 0 6 64 0 63 1 5 32 64 95 80 230 2 5 32 96 127 81 66 3 4 16 128 143 82 119 4 4 16 144 159 . . 5 4 16 160 175 6 3 8 176 183 . . 7 3 8 184 191 . . 8 6 64 192 255 79 ① 64≤ 81 ≤ 95 ② k = 1 ③ lb(1) = 64 ④ c(1) = 5 ⑤ 81 – 64 = 17 = 29 ⑥SCB(1) = 29 15

Proposed method-Decoding Input indices: …, 66, 49, 70, … SMVQ 49 0 129 1 . 27 59 28 70 29 220 k c(k) w(k) lb(k) ub(k) 0 6 64 0 63 1 5 32 64 95 . 2 5 32 96 127 210 113 3 4 16 128 143 4 4 16 144 159 211 49 5 4 16 160 175 212 119 6 3 8 176 183 . 7 3 8 184 191 8 6 64 192 255 . ① 192≤ 211 ≤ 255 ② k = 8 ③ lb(8) = 192 ④ c(8) = 6 ⑤ 211 – 192 = 19 = 70 ⑥∵k = 8 ⑦∴SCB(k) = 70 . 17 16

Proposed method-Construction of the mapping table Total hiding capacity of the VQ index table should be maximized. The sum of the interval widths should not exceed the codebook size. 17

Experimental results Naïve : Mapping table in which the interval widths assigned equally. Generic : Constructed based on the SMVQ histogram or LAS histogram – of the Lena image Specific : Constructed based on the SMVQ histogram or LAS histogram – of each image itself 18

Experimental results Image Airplane Baboon Boat Gold hill Lena Peppers Mapping t   5 Table Type t   1 t   3 Bit rate Capacity Efficienc Bit rate y Capacity efficiency Bit rate Capacity efficiency 0. 613 64, 516 0. 27 48, 387 0. 22 32, 258 0. 16 Generic 81, 295 0. 40 72, 937 0. 40 64, 474 0. 41 Specific 81, 527 0. 40 73, 294 0. 41 64, 817 0. 42 64, 516 -0. 02 48, 387 0. 05 32, 258 0. 12 Generic 77, 561 0. 08 56, 622 0. 11 37, 732 0. 16 Specific 83, 778 0. 13 63, 179 0. 16 42, 548 0. 19 64, 516 0. 21 48, 387 0. 19 32, 258 0. 15 Generic 82, 687 0. 35 71, 390 0. 36 61, 625 0. 38 Specific 82, 697 0. 35 72, 022 0. 37 61, 998 0. 38 64, 516 0. 23 48, 387 0. 24 32, 258 0. 21 Generic 74, 223 0. 31 60, 340 0. 33 52, 275 0. 36 Specific 74, 908 0. 31 61, 894 0. 35 52, 595 0. 36 64, 516 0. 27 48, 387 0. 24 32, 258 0. 20 Generic 78, 999 0. 38 69, 429 0. 40 60, 759 0. 41 Specific 78, 999 0. 38 69, 429 0. 40 60, 759 0. 41 64, 516 0. 28 48, 387 0. 24 32, 258 0. 19 Generic 78, 831 0. 39 69, 984 0. 40 61, 496 0. 41 Specific 79, 011 0. 39 70, 210 0. 40 61, 722 0. 41 Naïve Naïve 0. 756 0. 640 0. 630 0. 610 0. 608 0. 577 0. 662 0. 590 0. 563 0. 564 0. 566 Table 1. Performance of the proposed SMVQ-based method. 0. 542 0. 565 0. 546 0. 519 0. 525 0. 528 19

Experimental results Efficiency= ( Compressionachievement + Hidingcapacity ) / Sizeofthe. VQindextable Compressionachievement = Sizeofthe. VQindextable − Sizeoftheembeddedcode Bit rate Airplane Naïve 0. 613 Capacity Efficienc y 64, 516 0. 27 Compressionachievement = 128*8 – 512*0. 613 = -29622. 272 Efficiency = (-29622. 272 + 64516) / 128*8 = 0. 27 20

Experimental results Image Airplane Baboon Boat Gold hill Lena Peppers Mapping t   5 Table Type Naïve Generic Specific Naïve Generic Specific t   1 t   3 Bit rate Capacity efficiency 0. 713 64, 516 89, 040 89, 321 64, 516 91, 257 94, 068 64, 516 93, 839 93, 991 64, 516 92, 276 93, 004 64, 516 93, 385 64, 516 95, 631 48, 387 78, 494 80, 075 48, 387 72, 123 82, 576 48, 387 85, 655 87, 165 48, 387 74, 348 78, 600 48, 387 85, 103 48, 387 85, 026 86, 314 32, 258 55, 962 58, 998 32, 258 44, 776 55, 852 32, 258 62, 186 64, 244 32, 258 44, 200 49, 619 32, 258 63, 563 32, 258 62, 239 63, 671 0. 824 0. 729 0. 773 0. 693 0. 734 0. 07 0. 25 0. 26 − 0. 16 0. 05 0. 07 0. 03 0. 26 − 0. 05 0. 16 0. 11 0. 33 0. 02 0. 26 0. 680 0. 779 0. 705 0. 716 0. 661 0. 699 Table 2. Performance of the proposed LAS-based method. 0. 01 0. 24 0. 25 − 0. 19 − 0. 01 0. 07 − 0. 04 0. 26 − 0. 06 0. 14 0. 17 0. 05 0. 33 − 0. 03 0. 25 0. 26 0. 582 0. 671 0. 603 0. 577 0. 560 0. 600 0. 08 0. 26 0. 29 − 0. 10 0. 08 0. 04 0. 27 0. 28 0. 09 0. 18 0. 22 0. 13 0. 36 0. 05 0. 27 0. 29 21

Experimental results Image Airplane Baboon Boat Goldhill Lena Peppers Scheme Wang and Wang et al. Chang et al. Lee et al. 's Qin et al. 's Lee et al. 's Lin et al. 's The Lu's 's 's scheme [22] scheme [29] scheme [23] scheme [24] proposed scheme [40] scheme [44] scheme [7] scheme The proposed scheme Settings Path 2 3 bits per index – Size of state – codebooks: – Fixed bit rate 0. 5 LASbased t   0 SMVQbased t   0 Quality Capacity Bit rate Efficiency Quality Capacity Bit rate Efficiency 31. 49 47, 250 0. 682 − 0. 00 23. 84 47, 250 0. 721 − 0. 08 29. 12 47, 250 0. 696 − 0. 03 29. 48 47, 250 0. 683 − 0. 01 31. 66 47, 250 0. 667 0. 03 31. 90 47, 250 0. 662 0. 04 31. 49 49, 149 0. 604 0. 17 23. 84 49, 149 0. 723 − 0. 07 29. 12 49, 149 0. 611 0. 15 29. 48 49, 149 0. 569 0. 24 31. 66 49, 149 0. 661 0. 05 31. 90 49, 149 0. 637 0. 10 31. 49 47, 473 0. 548 0. 27 23. 84 34, 311 0. 656 − 0. 05 29. 12 43, 920 0. 559 0. 22 29. 48 37, 377 0. 529 0. 23 31. 66 41, 684 0. 539 0. 24 31. 90 43, 911 0. 537 0. 26 31. 49 57, 927 0. 518 0. 41 23. 84 16, 991 0. 541 0. 05 29. 12 39, 252 0. 521 0. 26 29. 48 35, 763 0. 523 0. 23 31. 66 46, 362 0. 519 0. 32 31. 90 45, 477 0. 522 0. 30 31. 49 32, 171 0. 432 0. 38 23. 84 29, 980 0. 539 0. 15 29. 12 36, 753 0. 494 0. 29 29. 48 31, 851 0. 513 0. 22 31. 66 38, 491 0. 485 0. 32 31. 90 39, 731 0. 479 0. 35 31. 49 47, 326 0. 500 0. 36 23. 84 12, 327 0. 500 0. 09 29. 12 29, 821 0. 500 0. 23 29. 48 33, 207 0. 500 0. 25 31. 66 47, 611 0. 500 0. 36 31. 90 44, 758 0. 500 0. 34 31. 49 74, 488 0. 655 0. 26 23. 84 75, 645 0. 751 0. 08 29. 12 82, 556 0. 690 0. 25 29. 48 71, 406 0. 689 0. 17 31. 66 78, 888 0. 635 0. 33 31. 90 80, 277 0. 667 0. 28 31. 49 70, 453 0. 564 0. 41 23. 84 55, 661 0. 626 0. 17 29. 12 68, 236 0. 574 0. 37 29. 48 58, 071 0. 544 0. 36 31. 66 66, 107 0. 549 0. 41 31. 90 66, 867 0. 551 0. 41 31. 49 26, 321 0. 500 0. 20 23. 84 5481 0. 500 0. 04 29. 12 24, 363 0. 500 0. 19 29. 48 15, 269 0. 500 0. 12 31. 66 21, 632 0. 500 0. 17 31. 90 10, 421 0. 500 0. 08 22

Experimental results [40]J. X. Wang, Z. M. Lu, A path optional lossless data hiding scheme based on VQ joint neighboring coding Inf. Sci. (Ny), 179 (19) (2009), pp. 3332 -3348 [44]Z. H. Wang, C. C. Chang, K. N. Chen, M. C. Li, An encoding method for both image compression and data lossless information hiding J. Syst. Softw. , 83 (11) (2010), pp. 2073 -2082 [7]C. C. Chang, C. Y. Lin, Y. P. Hsieh, Data hiding for vector quantization images using mixed-base notation and dissimilar patterns without loss of fidelity [22]J. D. Lee, Y. H. Chiou, J. M. Guo, Lossless data hiding for VQ indices based on neighboring correlation Inf. Sci. (Ny), 221 (2013), pp. 419 -438 [29]C. Qin, C. C. Chang, Y. C. Chen, Efficient reversible data hiding for VQ-compressed images based on index mapping mechanism Signal Process. , 93 (9) (2013), pp. 2687 -2695 [23]J. D. Lee, Y. H. Chiou, J. M. Guo, Information hiding based on block match coding for vector quantizationcompressed images IEEE Syst. J. , 8 (3) (2014), pp. 737 -748 [24]C. C. Lin, X. L. Liu, S. M. Yuan, Reversible data hiding for VQ-compressed images based on search-order coding and state-codebook mapping 23 Inf. Sci. (Ny), 293 (2015), pp. 314 -326

Conclusions �This paper presented a VQ-based reversible data hiding scheme including two methods (SMVQ、LAS). �SMVQ-based scheme has a better efficiency. �LAS-based scheme has a better capacity. 24

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