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The LOCO-I Lossless image Compression Algorithm: Principles and Standardization into JPEG-LS

The LOCO-I Lossless image Compression Algorithm: Principles and Standardization into JPEG-LS. Authors: M. J. Weinberger, G. Seroussi, G. Sapiro Source : IEEE Transactions on Image Processing, Vol. 9, No. 8, August 2000, 1309-1324 Speaker: Chia-Chun Wu ( 吳佳駿 )

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The LOCO-I Lossless image Compression Algorithm: Principles and Standardization into JPEG-LS

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  1. The LOCO-I Lossless imageCompression Algorithm: Principlesand Standardization into JPEG-LS • Authors: M. J. Weinberger, G. Seroussi, G. Sapiro • Source : IEEE Transactions on Image Processing, Vol. 9, No. 8, August 2000, 1309-1324 • Speaker: Chia-Chun Wu (吳佳駿) • Date : 2004/10/20 NCHU

  2. Outline • 1. Introduction • 2. Example • 3. Modeler • 4. Regular mode • 5. Run mode • 6. Coded data • 7. Result • 8. Conclusion • 9. Comments NCHU

  3. 1. Introduction (1/2) LOCO-I (LOw COmplexity LOssless COmpression for Image) is the standard for lossless and near-lossless compression of continuous-tone images, such as JPEG-LS. NCHU

  4. 1. Introduction (2/2) 1100 0000… Fig.1 JPEG-LS：Block diagram NCHU

  5. 補 0 2. Example Fig.2 4 x 4 Example image data NCHU

  6. 3. Modeler • 3.1 Compute local gradients • 3.2 Local gradient quantization • 3.3 Quantized gradient merging • 3.4 Select the mode NCHU

  7. 3.1 Compute local gradients • Ix is the value of current sample in the image. • Three gradients g1, g2, g3. g1 = Rd – Rb g2 = Rb – Rc g3 = Rc – Ra • Example 1Example 2 (g1,g2,g3)=( 0,81,-36) (g1,g2,g3)=( 0, 0, 0) NCHU

  8. 3.2 Local gradient quantization • Q1, Q2, Q3 are region numbers of quantized local gradients. • Example 1Example 2 (g1,g2,g3) ⇒ (Q1,Q2,Q3) (g1, g2, g3)=( 0,81,-36) ⇒ (Q1,Q2,Q3)=( 0, 4, -4) (g1, g2, g3)=( 0, 0, 0) ⇒ (Q1,Q2,Q3)=( 0, 0, 0) NCHU

  9. 3.3 Quantized gradient merging • If the first non-zero element of vector (Q1,Q2,Q3) is negative, then (Q1,Q2,Q3) ⇒ (-Q1,-Q2,-Q3) and SIGN set to –1, otherwise it set to +1. • Example 1Example 2 (Q1, Q2, Q3)=( 0, 4, -4) ⇒ SIGN = +1 (Q1, Q2, Q3)=( 0, 0, 0) ⇒ SIGN = +1 NCHU

  10. 3.4 Select the mode • If quantized local gradients are not all zero, choose the regular mode. • If Q1=Q2=Q3=0, go to the run mode. • Example 1Example 2 (Q1, Q2, Q3)=( 0, 4, -4) ⇒ Reqular mode (Q1, Q2, Q3)=( 0, 0, 0) ⇒ Run mode NCHU

  11. 4. Regular model • 4.1 Compute the fixed prediction • 4.2 Adaptive correction • 4.3 Compute the prediction error • 4.4 Modulo reduction of the error • 4.5 Error mapping • 4.6 Compute the Golomb coding parameter k • 4.7 Golomb Code • 4.8 Mapped-error encoding • 4.9 Update the variables NCHU

  12. 4.1 Compute the fixed prediction • Ra, Rb, Rc used to predict Ix. • Px is predicted value for the sample Ix. • Example 1 { min(Ra,Rb), if Rc ≧ max(Ra,Rb). max(Ra,Rb), if Rc ≦ min(Ra,Rb). Ra+Rb–Rc, otherwise. Px = Rc = 64≦min(100,145)≦100 ⇒ Px = max(100,145) = 145 NCHU

  13. { Px + C, if SIGN = +1. Px ─ C, if SIGN = ─1. Px = [ ] [ ] -1 2 B N 4.2 Adaptive correction • C = , C is the prediction of correction value. • Example 1 B = -1, N = 2 ⇒ C = = -1 Px = 145, SIGN = +1 ⇒ Px = Px + C = 145 + (-1) = 144 To P23 NCHU

  14. 4.3 Compute the prediction error • Errval is the prediction error. • Example 1 1. Errval = Ix – Px. 2. Errval = ─ Errval, if SIGN = ─1. Ix = 145 Px = 144 SIGN = +1 ⇒ Errval = Ix - Px = 145 ─ 144 = 1 NCHU

  15. 4.4 Modulo reduction of the error • The prediction error will be reduced to the range relevant for coding,-127~+128. • Example 1 1. Errval = Errval + 256, if Errval < 0. 1. Errval = Errval ─ 256, if Errval ≧ 128. Errval = 1 (1 > 0 and 1 ≦ 128) ⇒ Errval = 1 NCHU

  16. { 2*Errval, if Errval ≧ 0. ─2*Errval-1, if Errval < 0. MErrval = 4.5 Error mapping (1/2) • The prediction error, Errval will be mapped to a non-negative value. • MErrval is the Errval mapped to non-negative integers in regular mode. • Example 1 Errval = 1 (1 ≧ 0) ⇒ MErrval = 2 * 1 = 2 NCHU

  17. 127 -128 0 0 255 4.5 Error mapping (2/2) Prediction error 0 -1 1 -2 2 -3 3 … 127 -128 ↓ ↓ ↓ ↓ ↓↓ ↓ ↓ ↓ 0 1 2 3 4 5 6 … 254 255 Mapped value NCHU

  18. 4.6 Compute the Golomb coding parameter k • K is the Golomb coding parameter for regular mode. k= min {k’|2k’*N≧A} • Example 1 N = 2, A = 64 ⇒2k’ * 2 ≧ 64 ⇒ 2k’ ≧ 32 ⇒ k = 5 NCHU

  19. 4.7 Golomb Code (1/3) • A formula： MErrval = q * m + r • A parameter：m (m = 2k) • Two parts：unary code (q) and modified binary code (r) • Example： MErrval = 13, k = 2 ⇒ m = 22 = 4 ⇒ 13 = 3 x 4 + 1 ⇒ q = 3, r = 1 ⇒ unary code=3, modified binary code=1 ⇒ unary code=000, modified binary code=01 ⇒ 000101 NCHU

  20. 4.7 Golomb Code (2/3) Table.Ⅰ Golomb code for m = 4 (k=2). NCHU

  21. 0 255 4.7 Golomb Code (3/3) • Properties - n↓⇒ code length↓ - one pass encoding - without to store the code tables - Golomb code are optimal for one sided geometric distributions of nonnegative integers NCHU

  22. 4.8 Mapped-error encoding • Example 1 k = 5 ⇒ m = 2k = 25 = 32 MErrval = 2 ⇒ 2 = q * m + r = 0 * 32 + 2 ⇒ q = 0, r = 2 ⇒ unary code= 0, modified binary code=2 ⇒ unary code= null, modified binary code=00010 ⇒100010 NCHU

  23. { A = A + | Errval | B = B + Errval N = N + 1 4.9 Update the variables (1/2) • The variables A, B and N are updated according to the current prediction error. • A, B are counters for the accumulated prediction error. • N is counter for frequency of occurrence of the context. NCHU

  24. 4.9 Update the variables (2/2) • The variables before encoding are： A = 64, B = -1, N = 2 . • The variables after updating are： Example 1: Errval = 1 ⇒A = A + | Errval | = 64 + 1 = 65. B = B + Errval = -1 + 1 = 0. N = N + 1 = 2 + 1 = 3. To P13 NCHU

  25. 5. Run model • 5.1 Run scanning • 5.2 Run-length coding NCHU

  26. 5.1 Run scanning • RUNval is the value of repetitived sample. • RUNcnt is the value of repetitived sample count for run mode. • Example 2 RUNval = Ra = 145 Ix = 145 = RUNval ⇒RUNcnt = 2 { RUNval = Ra; while (Ix == RUNval) { RUNcnt = RUNcnt + 1; } NCHU

  27. 5.2 Run-length coding • RUNcnt is the value represents the run-length. • Example 2 RUNcnt = 2 ⇒11 { while (RUNcnt >0) { Append 1 to bit stream; RUNcnt = RUNcnt ─ 1; } NCHU

  28. 6. Coded data Table.Ⅱ Coded segment. PS:The last five bits in the above table are padding with 0. NCHU

  29. 7. Results (1/2) Table Ⅲ Compression Results On ISO/IEC 10918-1 Image Test Set (In Bits/Sample) NCHU

  30. 7. Results (2/2) Table Ⅳ Compression Results On New Image Test Set (In Bits/Sample) NCHU

  31. 8. Conclusion • LOCO-I/JPEG-LS significantly outperforms other schemes of comparable complexity (e.g.,JPEG-Huffman), and it attains compression rations similar or superior to those of higher complexity schemes based on arithmetic coding (e.g.,JPEG-Arithm, CALIC Arithm). • LOCO-I performed within a few percentage points of the best available compression ratios (given, in practice, by CALIC), at a much lower complexity level. NCHU

  32. 9. Comments • 找出一個方法去修改JPEG-LS的壓縮演算法，使其具有資訊隱藏的功能。 NCHU

  33. The end Thank you!! NCHU

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