1. 1 Image Transcoding in the block DCT Space Jayanta Mukhopadhyay Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur, 721302, India jay@cse.iitkgp.ernet.in

2. 2 Transcoding DWT to DCT

3. 3 Analysis Synthesis Forward DWT and Inverse DWT Discrete Wavelet Transform

4. 4 2-D DWT  1D DWT applied to vertical and horizontal direction.  For Multilevel DWT:-  The LL band is recursively decomposed, vertically and horizontally.  Filtering is performed in time domain. Image in spatial domain LH HL HH 2LL2HL 2LH2HH LL LH HL HH Decomposition 1 st Level 2 nd Level

5. 5 DCT domain Upsampling with Zero Insertion Type-II DCT of upsampled signal as obtained through zero insertion of signal x(n) is computed by: Note:- DCT obtained is referred as upsampled DCT.

6. 6 A typical conversion matrix 4x4 block to 8x8 upsampled type-II DCT For even sample xoxoxoxo… For odd sample oxoxoxox…

7. 7 Computation of upsampled DCT

8. 8 Wavelet synthesis in the DCT domain  Result is transcoded type-II DCT coefficients.  Operation is equivalent to IDWT + DCT.

9. 9 Transcoding in the DCT domain Composite Operation

10. 10 Wavelet to DCT Transcoding (WDT) Viswanath, Mukherejee and Biswas (2009), Springer Journal on SIVP,

11. 11  WDT computes DCT blocks of larger size.  By decomposing, 8x8 blocks are obtained.  Cost of transcoding increases.  To reduce the cost, smaller blocks are to be considered. WBDT: * Three blocks of NxN size are used in a wavelet subband of size WxW. * Blocks are Upsampled, composed, filtered and decomposed. * The transcoded blocks of size 2Nx2N. Note:- N=4 for JPEG based applications. Wavelet to Block DCT Transcoding (WBDT) This work is published in Springer Journal on SIVP, Jan 2009

12. 12 T L, T H are pre-computed Let and Wavelet to Block DCT Transcoding (WBDT)

13. 13  WBDT computes DCT blocks of size 8x8,  Uses composing and decomposing of DCT blocks.  Requires Type-I DCT of filter and Type-II DCT of data.  Linear Filtering in the DCT domain:  Requires only Type-II DCT.  Blocks are processed separately and added together. The WBDTL, * Three adjacent NxN size subband blocks are used. * Upsampled blocks filtered separately and the results are added. * Computes the transcoded blocks of size 2Nx2N. Note:- For JPEG based applications, N=4. Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

14. 14 Where and are the even upsampled DCT blocks of wavelet approximation subband blocks and DCT matrices of the lowpass synthesis filter. are the odd upsampled DCT blocks of wavelet detail subband blocks and DCT matrices of the highpass synthesis filter. Where and Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

15. 15 Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

16. 16 Transcoding with Multilevel DWT LH HL HHLH HL HH 2LL2HL 2LH2HH LL 2LL2HL 2LH2HH 2 nd level Transcoding LH HL HH LL 1 st level Transcoding Reconstructed image DCT Blocks

17. 17 For a tile size of 64 x 64 In JPEG2000 For blocks of size 8 x 8 Cost of Multilevel Transcoding Hybrid Approach

18. 18 JPEG2000 9/7 wavelet filters Analysis Filter Coefficients Synthesis Filter Coefficients i Lowpass H(i) Highpass G(i) Lowpass H ’ (i) Highpass G ’ (i) 0 0.6029 -1.11511.1151-0.6029 0.2669 0.5913 0.2669 -0.0782 0.0575-0.0575 0.0782 -0.0169 -0.0913 -0.0169 0.0267-0.0267

19. 19 Analysis Filters

20. 20 Synthesis Filters

21. 21 Wavelet filters and responses

22. 22 Wavelet filters and responses

23. 23 Other wavelet filters

24. 24 Results PSNR close to ~300 dB

25. 25 Results: Quantization of wavelet subbands For Lena image Large number of coefficients are zeros No. of zero coefficients

26. 26 Observations  The proposed new algorithms for transcoding the DCT coefficients from wavelet coefficients are computationally efficient.  Both the approaches (WBDT and WBTL) are found to be equivalent.  Proposed transcoding achieves PSNR performances as same as the spatial domain technique.

27. 27 Block DCT to wavelet transcoding  The technique is based on the combined step of block filtering and downsampling directly in the DCT domain.  Filtering matrices are computed using wavelet analysis filters.  Three adjacent DCT blocks are used in transcoding.

28. 28 Block DCT to wavelet transcoding Composite operation

29. 29 For LL subband For LH subband Downsampling from block DCT

30. 30 Block DCT to Wavelet Transcoding (BWT) H L and H H are computed from Type-I DCT of the analysis filters. In 1-D: In 2-D:

31. 31 Transcoding with Linear Filtering

32. 32 Block DCT to Wavelet Transcoding with Linear Convolution (BWTL) This work is Accepted in IEEE ICIP 2009

33. 33 T L Matrices using 9/7 analysis lowpass filter

34. 34 DCT to Wavelet: Complexity

35. 35 Results: DCT to Wavelet transcoding PSNR close to 300 dB Ref: ST subbands Almost equal Almost equal

36. 36 Results: DCT Quantization effect on transcoding

37. 37 Results: DCT Quantization effect on transcoding

38. 38 Quantization effect on transcoded subbands More degradation of quality in lower frequency subbands This work is under revision in Springer Journal on SIVP

39. 39 Performance comparison with spatial transcoding Reference: Original Image

40. 40  Spatial transcoding and the BWTL transcoding techniques perform at par.  However, the BWT technique perform the best among them.  This is due to the fact that the rounding errors are accumulating in spatial domain transcoding and the BWTL techniques.  But the BWT technique operates with three blocks simultaneously, and thereby rounding errors are reduced. Observations

41. 41 JPEG2000 to JPEG

42. 42 JPEG2000 Compression Standard  JPEG2000 is an emerging image compression standard  Uses Discrete wavelet transform (DWT) as transform.  Transform coefficients are quantized an encoded.

43. 43 Advantages:  JPEG 2000 permits high compression ratios (CR’s) with little degradation in image quality.  An image can either be compressed without any distortion or data loss, ( “reversible” or “lossless” ), or it can be compressed so that there are slight perceptible differences from the original under normal viewing conditions ( “lossy” ).  An image can contain multiple embedded image quality layers  ROI Certain parts of image can be coded in better quality than others and many other functionalities.  JPEG2000 likely to become the technology of choice in image servers, medical imaging, digital cinema, security systems and digital photography.  JPEG 2000 will be used in other areas like mobile imaging applications. JPEG 2000

44. 44 JPEG Compression Standard  JPEG divides up the image into 8 by 8 pixel blocks, calculates the DCT of each block.  A quantizer rounds off the DCT coefficients according to the quantization matrix. This step produces the "lossy" nature of JPEG, but allows for large compression ratios.  Uses a variable length code on these coefficients, and then writes the compressed data stream to an output file (*.jpg).  For decompression, JPEG recovers the quantized DCT coefficients from the compressed data stream, takes the inverse transforms and displays the image.

45. 45 Transcoding JPEG2000 to JPEG  Encoding of JPEG2000 usually gives 2-4 dB higher PSNR values at the same compression level.  Average decoding time for JPEG2000 is almost five times higher compared to JPEG  Current web browsers do not support JPEG 2000 natively.  Since JPEG is the most common compression standard and has very low complexity, transcoding to JPEG provides a smooth upgrade path.

46. 46 Spatial transcoding

47. 47 Transform Domain Transcoder

48. 48  Since impulse responses of JPEG2000 wavelet filters are symmetric, DCT domain filtering can be used.  JPEG2000 encoded using 2-D wavelet transforms by incorporating 9-7 analysis filters.  The wavelet coefficients are encoded with different quantization levels to achieve different compression rate. Tanscoding…

49. 49 Tanscoding… Quantization in JPEG2000[25,28] Where Quantized coefficients are given by -is the coefficient at subband b -is the quantization step, depends on the number of bits allocated for encoding (15) ‏

50. 50 Tanscoding… Dequantizing in Decoding  Encoder encodes M b bit planes, we can decode N b bit planes.  Remaining bit planes are set to zero Instead of performing IDWT on the denormalized coefficients, TBFCD algorithm is used for transcoding. (16) ‏

51. 51 Transcoding… Inputs  Wavelet coefficients bands LL,LH,HL,HH each of size WxW  L, M are two numbers N=8;  L =2(Width of wavelet band)/N  M=2(Height of wavelet band)/N  Type-I DCT of filter response for the corresponding band Output: NxN block type-II DCT coefficients of the reconstructed image.

52. 52 Tanscoding… Begin{  Get the four decompositions-a low resolution approximation of image in approximation (LL) band, horizontal (HL), vertical (LH) and diagonal (HH) bands.  Compute the upsampled block type-II DCT for each band of size B LNxNM.  Get the filtered block of each band by point-wise multiplication of H and B.  Add the four filtered blocks to get transcoded type-II DCT block.  Decompose the transcoded DCT block to 8x8 DCT blocks. }End  Quantize the DCT blocks by quantization matrix and entropy encode to get JPEG image.  Here scaling the quantization matrix can vary the compression rates and reconstructed image quality.

53. 53 Transform domain Transcoding

54. 54 Computational complexity

55. 55  Spatial Transcoding  IDWT cost  DCTcost  Transform Domain  Upsampled DCT cost  DCT domain Filtering cost  DCT block Decomposing cost Computational complexity

56. 56 IDWT cost for filter length FL1 and FL2 IDWT Complexity depends on the length of the wavelet filter FL. Requires FL multiplications and (FL-1) additions.

57. 57 Spatial domain cost 8x8 block DCT cost : Per pixel complexity: IDWT cost per pixel: Total cost

58. 58 Computational Complexity comparison

59. 59 Computational Complexity comparison

60. 60 JPEG2000 Decoding Original Image PSNR=41.5460 at 1.044 bpp

61. 61 Transcoding Results Spatial Domain bpp=0.720, PSNR=35.77 Transform Domain bpp=0.7208, PSNR=35.77

62. 62 IMAGE to JPEG bpp=0.712 PSNR=35.8082Original Image

63. 63 Transcoder Performance evaluation

64. 64  Guaranteed PSNR(M g ): The minimum PSNR value with respect to the JPEG2000 decoded image to be achieved by the transcoder. Here we used a typical value of 40 dB.  Equivalent rate (ρ eq ): The minimum compression rate of the transcoded JPEG image providing at least the guaranteed PSNR with respect to the JPEG2000 decoded image. The equivalent rate is obtained at 40 dB point with respect to JPEG2000 decoded image.  Equivalent PSNR (M eq ): The transcoder PSNR with respect to the original image at the equivalent rate. We have defined three measures as follows:

65. 65 JPEG2000 to JPEG Transcoder Performance

66. 66 Transcoder Performance

67. 67 Equivalent PSNR comparison

68. 68 Thanks

69. 69 where, Type I 2D-DCT Type-I 2-D DCT of a block

70. 70       1,0,cos,)‏( ( 2, 1 0 1 0 2 12 2 12         Nk nmxk N kX N m N n N n N km II   where, Type II 2D-DCT Type-II 2-D DCT of a block