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Distortion estimators for bitplane image coding

Distortion estimators for bitplane image coding. Francesc Aulí -Llinàs. Department of Information and Communications Engineering Universitat Autònoma de Barcelona, Spain. Distortion estimation Code-stream transcoding Interactive image and video transmission. Applications.

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Distortion estimators for bitplane image coding

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  1. Distortion estimators for bitplane image coding Francesc Aulí-Llinàs Department of Information and Communications Engineering UniversitatAutònoma de Barcelona, Spain

  2. Distortion estimation Code-stream transcoding Interactive image and video transmission Applications TABLE OF CONTENTS 1. INTRODUCTION 2. PDF-BASED DISTORTION ESTIMATORS 3. EXPERIMENTS 4. CONCLUSIONS

  3. Distortion estimation Code-stream transcoding Interactive image and video transmission Applications TABLE OF CONTENTS 1. INTRODUCTION 2. PDF-BASED DISTORTION ESTIMATORS 3. EXPERIMENTS 4. CONCLUSIONS

  4. INTRODUCTION BITPLANE CODING STRATEGY MOST SIGNIFICANT BITPLANE (MSB) mid-point reconstruction significance coding 1 1 1 0 0 0 0 0 0 0 … original coefficients recovered coefficients

  5. INTRODUCTION BITPLANE CODING STRATEGY MSB - 1 significance coding 1 1 0 0 0 0 … original coefficients recovered coefficients

  6. INTRODUCTION BITPLANE CODING STRATEGY MSB - 1 refinement coding 1 0 0 0 original coefficients recovered coefficients

  7. Progressive refinement of image distortion Lossy-to-lossless coding Well-suited digital representation for computers Mid-point reconstructiondoes NOT correspond with the nature of the signal INTRODUCTION BITPLANE CODING STRATEGY original coefficients recovered coefficients

  8. distribution INTRODUCTION DISTRIBUTION OF WAVELET COEFFICIENTS wavelet coefficients in a subband

  9. INTRODUCTION DISTRIBUTION OF WAVELET COEFFICIENTS

  10. INTRODUCTION DISTRIBUTION OF WAVELET COEFFICIENTS Common model: generalized Laplacian distribution number of coefficients 0 - +

  11. INTRODUCTION DISTRIBUTION OF WAVELET COEFFICIENTS Common model: generalized Laplacian distribution number of coefficients 0 - +

  12. FAST COMPUTATION OF DISTORTION DECREASES TRANSCODING OPERATIONS DISTORTION ESTIMATION 1 1 1 0 0 0 0 ΔD INTRODUCTION MID-POINT RECONSTRUCTION 1) RECONSTRUCTION PROCEDURE CARRIED OUT IN THE DECODER 2) DETERMINATION OF DISTORTION DECREASES IN THE ENCODER 3) DISTORTION ESTIMATORS

  13. INTRODUCTION MID-POINT RECONSTRUCTION 1) RECONSTRUCTION PROCEDURE CARRIED OUT IN THE DECODER 2) DETERMINATION OF DISTORTION DECREASES IN THE ENCODER FAST COMPUTATION OF DISTORTION DECREASES TRANSCODING OPERATIONS 3) DISTORTION ESTIMATORS DISTORTION ESTIMATION RESEARCH PURPOSE: DETERMINATION OF DISTORTION ESTIMATORS THAT BETTER CAPTURE THE SIGNAL’S NATURE Application to the PCRD process of JPEG2000

  14. Distortion estimation Code-stream transcoding Interactive image and video transmission Applications TABLE OF CONTENTS 1. INTRODUCTION 2. PDF-BASED DISTORTION ESTIMATORS 3. EXPERIMENTS 4. CONCLUSIONS

  15. 2P* 2P*+1 δP*= 0.5 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - probability density function (pdf) 2P* PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS coefficients distribution within a subband ( 2P* + δP*· 2P* ) ΔDsigP* = ΔDrefP* = …

  16. 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 ζP* 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 mean of non- transmitted bits 2P*+1 δP*= ζP* / 2P* ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval transmitted bitplane P*

  17. p(x) 2P*+1 2P* 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval

  18. 2P*+1 ζP* ] [ ∫ )2 ( accumulated probability = 0.5 dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) 2P* 2P*+1

  19. 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) 2P* 2P*+1 ζP*

  20. 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) 2P* 2P*+1 ζP*

  21. 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) 2P* 2P*+1 ζP*

  22. 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) 2P* 2P*+1 ζP*

  23. 2P*+1 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* ( 2P* + δP*· 2P* ) ΔDsigP* = PDF-BASED DISTORTION ESTIMATORS DETERMINATION OF THE ESTIMATORS to minimize the average distortion coefficients have to be reconstructed as the centroid of the quantization interval p(x) CENTROIDS ARE NOT COMMONLY AVAILABLE IN PRACTICE 2P* 2P*+1 ζP*

  24. PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition

  25. PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition HL1 LH1 HH1

  26. Portrait image - 5 wavelet levels (9/7 DWT) PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition LL2 HL2 HL1 LH2 HH2 LH1 HH1

  27. PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition Portrait image - 5 wavelet levels (9/7 DWT) LL2 HL2 HL1 LH2 HH2 LH1 HH1

  28. PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition Portrait image - 5 wavelet levels (9/7 DWT) LL2 HL2 HL1 LH2 HH2 LH1 HH1

  29. ) ( Kb – P log10 Kb Practical advantage: implementations can use pre-computed lookup tables for and δP,b = + 0.475 5 ΔDsigP ΔDrefP PDF-BASED DISTORTION ESTIMATORS CENTROIDS ESTIMATION dyadic wavelet decomposition Portrait image - 5 wavelet levels (9/7 DWT) LL2 HL2 HL1 LH2 HH2 LH1 HH1

  30. core coding system ORIGINAL IMAGE MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000

  31. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  32. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  33. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  34. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  35. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  36. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE

  37. MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM QUANTIZATION TIER-1 CODING TIER-2 CODING PCRD JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE final codestream

  38. D MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM convex hull QUANTIZATION TIER-1 CODING TIER-2 CODING PCRD R JP2 codestream PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE R1,D1 R4,D4 R2,D2 R3,D3 R5,D5 1 2 3 4 5 generalized Lagrange multiplier

  39. D MULTI-COMPONENT TRANSFORM WAVELET TRANSFORM convex hull QUANTIZATION TIER-1 CODING TIER-2 CODING PCRD R JP2 codestream D = ΔDsigP · #S + ΔDrefP· #R PDF-BASED DISTORTION ESTIMATORS APPLICATION TO JPEG2000 core coding system ORIGINAL IMAGE R1,D1 R4,D4 R2,D2 R3,D3 R5,D5 1 2 3 4 5 generalized Lagrange multiplier

  40. Distortion estimation Code-stream transcoding Interactive image and video transmission Applications TABLE OF CONTENTS 1. INTRODUCTION 2. PDF-BASED DISTORTION ESTIMATORS 3. EXPERIMENTS 4. CONCLUSIONS

  41. “Portrait” image 5 DWT levels 9/7 filter-taps 64x64 codeblocks EXPERIMENTS LOSSY MODE

  42. EXPERIMENTS LOSSLESS MODE “Portrait” image 5 IWT levels 5/3 filter-taps 64x64 codeblocks

  43. Distortion estimation Code-stream transcoding Interactive image and video transmission Applications TABLE OF CONTENTS 1. INTRODUCTION 2. PDF-BASED DISTORTION ESTIMATORS 3. EXPERIMENTS 4. CONCLUSIONS

  44. Penalization on the performance of distortion estimators RESEARCH PURPOSE: DETERMINATION OF DISTORTION ESTIMATORS THAT BETTER CAPTURE THE SIGNAL’S NATURE CONCLUSIONS • MID-POINT RECONSTRUCTION DOES NOT • CORRESPOND WITH THE NATURE OF THE SIGNAL

  45. 2P* 2P*+1 ζP* 2P*+1 • APPLICATION TO THE PCRD PROCESS OF JPEG2000 ] [ ∫ )2 ( dx p(x) x - x2 - 2P* When both the coder and decoder use pdf-based reconstruction, gains of 1 dB are achieved in the lossless mode ( 2P* + δP*· 2P* ) ΔDsigP* = CONCLUSIONS centroid

  46. Distortion estimation Codestream transcoding Interactive image and video transmission Applications CONCLUSIONS • FUTURE RESEARCH

  47. EXPERIMENTS LOSSLESS MODE “Portrait” image 5 IWT levels 5/3 filter-taps 64x64 codeblocks

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