Image coding method and apparatus for localized decoding at multiple resolutions

• US 6,763,139 B1
• Filed: 06/22/1999
• Issued: 07/13/2004
• Est. Priority Date: 07/03/1998
• Status: Expired due to Term

• Current Assignee: Canon Kabushiki Kaisha (Canon Inc.)
• Original Assignee: Canon Kabushiki Kaisha (Canon Inc.)
• Inventors: Andrew, James Philip
• Primary Examiner(s): Do, Anh Hong
• Application Number:
  US09/337,533
• Time in Patent Office: 1,848 Days
• Field of Search: 382/240, 382/232, 382/233, 382/248, 382/239, 341/67, 341/50, 345/420, 375/240.1
• US Class Current: 382/240
• CPC Class Codes: H04N 19/124 Quantisation
• CPC Class Codes: H04N 19/162 User input
• CPC Class Codes: H04N 19/17 the unit being an image region, e.g. an object
• CPC Class Codes: H04N 19/36 Scalability techniques involving formatting the layers as a function of picture distortion after decoding, e.g. signal-to-noise [SNR] scalability
• CPC Class Codes: H04N 19/63 using sub-band based transform, e.g. wavelets
• CPC Class Codes: H04N 19/645 by grouping of coefficients into blocks after the transform

Abstract

The method generates a compressed digital image from a original image. The compressed digital image allows random access to portions of the compressed image at a number of resolutions. The original image is first transformed (103) by a multi-level DWT to form a non redundant multiple resolution frequency domain representation of the image. The representation comprises a DC subband and a plurality of high frequency subbands arranged as levels, where each level represents a frequency contribution between adjacent resolutions and where each subband comprises a plurality of tiles. The DC subband is then entropy encoded (104) into the bitstream. The high frequency subbands are next entropy encoded (108,109, and 110) into the bitstream in level order (105,113,114) and tile order (107,111).

Claims

1. A method of encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said method including the steps of:

a) dividing each subband into a plurality of tiles;

b) entropy encoding each tile;

c) selecting a plurality of desired resolutions from said multiple resolutions for inclusion in a bitstream; and

d) arranging encoded tiles into the bitstream such that, for each level between each pair of adjacent selected resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

2. The method as claimed in claim 1, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

3. The method as claimed in claim 1, wherein the subbands are arranged in levels of decreasing order.

4. The method as claimed in claim 1, wherein said entropy encoding step further includes a quantization step.

5. The method as claimed in claim 1, wherein each tile comprises a plurality of transform coefficients.

6. The method as claimed in claim 5, wherein the step or steps of arranging tiles further includes arranging transform coefficients into the bitstream in a predetermined order.

7. The method as claimed in claim 6, wherein the predetermined order is a raster order of the coefficients in each tile.

8. The method as claimed in claim 6, wherein the predetermined order is an interleaving of binary bits of the coefficients in each tile.

9. A method of encoding a digital image to provide substantially random access to portions of the image at a plurality of nominated resolutions, said method including the steps of:

applying a linear transform to the image to produce a plurality of transform coefficients in a frequency domain;

grouping the transform coefficients into frequency subbands, each subband representing a range of frequencies of the image, wherein said grouping step is characterized by one low frequency subband and a plurality of high frequency subbands arranged in levels, and wherein each level represents frequency contributions between adjacent nominated resolutions of the image;

dividing each frequency subband into a plurality of tiles, each tile comprising at least one of the transform coefficients;

quantizing and entropy coding each tile; and

arranging the encoded tiles into a bitstream such that, for each level, those encoded tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

10. A method of encoding a digital image into a bitstream to provide substantially random access to portions of the image at a plurality of nominated resolutions, said method including the steps of:

applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

dividing each frequency subband into a plurality of tiles;

quantizing and entropy coding each said tile;

nominating desired resolutions of the digital image; and

arranging encoded tiles into a bitstream such that, for each level between nominated resolutions, those tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

11. A method of encoding a digital image including the steps of:

applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

dividing the non-redundant multiple resolution frequency domain representation into a plurality of tiles;

quantizing and entropy coding each tile;

nominating desired resolutions of the digital image; and

arranging in a contiguous manner, for each level between nominated resolutions, those tiles which substantially correspond to the same portion of the image.

12. A method of encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said method including the steps of:

a) dividing each subband into a plurality of tiles;

b) selecting a predetermined number of the levels from the multiple resolutions;

c) entropy encoding each tile;

d) processing the selected levels in a predetermined sequential order; and

e) arranging in a contiguous manner, for each level in the sequence to a current level not processed in step d), each entropy encoded tile representing substantially the same portion of image into a bitstream.

13. A method of encoding a digital image into a bitstream, said method including the steps of:

applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

dividing each frequency subband into a plurality of tiles;

quantizing and entropy coding each tile;

arranging into the bitstream in a predetermined order each entropy tile of a DC subband; and

arranging in a contiguous manner each set of three encoded tiles belonging to each of three AC subbands respectively, which substantially correspond to the same portion of the image at each level, into the bitstream.

14. A method of encoding a digital image into a bitstream, said method including the steps of:

applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a DC subband and a plurality of AC subbands arranged in a hierarchical structure having a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

dividing each frequency subband into a plurality of tiles;

grouping each tile, substantially corresponding to a same portion of the digital image, at each level of the AC subbands into tile triplets;

entropy coding each tile of a DC subband and each tile triplet of the AC subbands;

arranging in a predetermined order each entropy encoded tile of a DC subband and each entropy encoded tile triplet into the bitstream.

15. The method as claimed in claim 14, wherein the levels are arranged in a hierarchical structure comprising the DC subband and the AC subbands, which AC subbands are arranged in decreasing level order substantially according to their increasing subband frequency.

16. The method as claimed in claim 15, wherein said arranging step of arranging tiles of the AC subbands is further performed in decreasing level order.

17. A method of encoding a sequential stream of data for providing substantially random access to portions of an image at a plurality of predetermined resolutions, the stream including a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each subband is divided into a plurality of tiles and each level represents frequency contributions between adjacent resolutions of the image, and wherein each tile represents a frequency contribution to a portion of the image at a predetermined resolution, said method including:

inserting at most one pointer in the sequential stream for each set of tiles which correspond to substantially a same spatial portion of the image for each level to access a portion of the digital image.

18. An apparatus for encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said apparatus including:

means for dividing each subband into a plurality of tiles;

means for entropy encoding each tile;

means for selecting a plurality of desired resolutions from the multiple resolutions for inclusion in a bitstream; and

means for arranging encoded tiles into the bitstream, such that, for each level between each pair of adjacent selected resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

19. The apparatus as claimed in claim 18, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

20. The apparatus as claimed in claim 18, wherein the subbands are arranged in levels of decreasing order.

21. The apparatus as claimed in claim 18, wherein the entropy encoding means further includes quantization means.

22. The apparatus as claimed in claim 18, wherein each tile comprises a plurality of transform coefficients.

23. The apparatus as claimed in claim 22, wherein the arranging means further includes means for arranging transform coefficients into the bitstream in a predetermined order.

24. The apparatus as claimed in claim 23, wherein the predetermined order is a raster order of the coefficients in each tile.

25. The apparatus as claimed in claim 23, wherein the predetermined order is an interleaving of binary bits of the coefficients in each tile.

26. An apparatus for encoding a digital image, to provide substantially random access to portions of the image at a plurality of nominated resolutions, said apparatus including:

means for applying a linear transform to the image to produce a plurality of transform coefficients in a frequency domain;

means for grouping the transform coefficients into frequency subbands, each subband representing a range of frequencies of the image, wherein the grouping is characterised by one low frequency subband and a plurality of high frequency subbands arranged in levels, and wherein each level represents frequency contributions between adjacent nominated resolutions of the image;

means for dividing each frequency subband into a plurality of tiles, each tile comprising at least one of the transform coefficients;

means for quantizing and entropy coding each tile; and

means for arranging the encoded tiles into a bitstream such that, for each level, those encoded tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

27. An apparatus for encoding a digital image into a bitstream, to provide substantially random access to portions of the image at a plurality of nominated resolutions, said apparatus including:

means for applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

means for dividing each frequency subband into a plurality of tiles;

means for quantizing and entropy coding each tile;

means for nominating desired resolutions of the digital image; and

means for arranging encoded tiles into a bitstream such that, for each level between nominated resolutions, those tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

28. An apparatus for encoding a digital image including:

means for applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

means for dividing the non-redundant multiple resolution frequency domain representation into a plurality of tiles;

means for quantizing and entropy coding each tile;

means for nominating desired resolutions of the digital image; and

means for arranging in a contiguous manner, for each level between nominated resolutions, those tiles which substantially correspond to the same portion of the image.

29. An apparatus for encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said apparatus including:

means for dividing each subband into a plurality of tiles;

means for selecting a predetermined number of the levels from the multiple resolutions;

means for entropy encoding each tile;

means for processing the selected levels in a predetermined sequential order; and

means for arranging in a contiguous manner, for each level in the sequence to a current level not processed by said processing means, each entropy encoded tile representing substantially the same portion of image into a bitstream.

30. An apparatus for encoding a digital image into a bitstream, said apparatus including:

means for applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

means for dividing each frequency subband into a plurality of tiles;

means for quantizing and entropy coding each tile;

means for arranging into the stream bitstream in a predetermined order each entropy tile of a DC subband; and

means for arranging in a contiguous manner each set of three encoded tiles belonging to each of three AC subbands respectively, which substantially correspond to the same portion of the image at each level, into the bitstream.

31. An apparatus for encoding a digital image into a bitstream, said apparatus including:

means for applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a DC subband and a plurality of AC subbands arranged in a hierarchical structure having a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

means for dividing each frequency subband into a plurality of tiles;

means for grouping each tile, substantially corresponding to a same portion of the digital image, at each level of the AC subbands into tile triplets;

means for entropy coding each tile of a DC subband and each tile triplet of the AC subbands;

means for arranging in a predetermined order each entropy encoded tile of a DC subband and each entropy encoded tile triplet into the bitstream.

32. The apparatus claimed in claim 31, wherein the levels are arranged in a hierarchical structure comprising the DC subband and the AC subbands, which AC subbands are arranged in decreasing level order substantially according to their increasing subband frequency.

33. The apparatus as claimed in claim 32, wherein the arranging means arranges the AC subbands in decreasing level order.

34. An apparatus for encoding a sequential stream of data for providing substantially random access to portions of an image at a plurality of predetermined resolutions, the stream including a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each subband is divided into a plurality of tiles and each level represents frequency contributions between adjacent resolutions of the image, and wherein each tile represents a frequency contribution to a portion of the image at a predetermined resolution, said apparatus including:

means for inserting at most one pointer in the sequential stream for each set of tiles which correspond to substantially a same spatial portion of the image for each level to access a portion of the digital image.

35. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said computer program product including:

code for a division step, of dividing each subband into a plurality of tiles;

code for an entropy encoding step, of entropy encoding each tile;

code for a selection step, of selecting a plurality of desired resolutions from the multiple resolutions for inclusion in a bitstream; and

code for an arrangement step, of arranging encoded tiles into the bitstream such that, for each level between each pair of adjacent selected resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

36. The computer program product as claimed in claim 35, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

37. The computer program product as claimed in claim 35, wherein the subbands are arranged in levels of decreasing order.

38. The computer program product as claimed in claim 35, wherein said entropy encoding step further includes a quantization step.

47. The computer program product as claimed in claim 35, wherein each tile comprises a plurality of transform coefficients.

48. The computer program product as claimed in claim 47, wherein said arranging step further includes code for a second arranging step, of arranging transform coefficients into the bitstream in a predetermined order.

49. The computer program product as claimed in claim 48, wherein the predetermined order is a raster order of the coefficients in each tile.

50. The computer program product as claimed in claim 48, wherein the predetermined order is an interleaving of binary bits of the coefficients in each tile.

39. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image, to provide substantially random access to portions of the image at a plurality of nominated resolutions, said computer program product including:

code for an applying step, of applying a linear transform to the image to produce a plurality of transform coefficients in a frequency domain;

code for a grouping step, of grouping the transform coefficients into frequency subbands, each subband representing a range of frequencies of the image, wherein the grouping is characterized by one low frequency subband and a plurality of high frequency subbands arranged in levels, and wherein each level represents frequency contributions between adjacent nominated resolutions of the image;

code for a division step, of dividing each frequency subband into a plurality of tiles, each tile comprising at least one of the transform coefficients;

code for a quantizing and entropy step, of quantizing and entropy coding each tile; and

code for an arranging step, of arranging the encoded tiles into a bitstream such that, for each level, those encoded tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

40. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image into bitstream, to provide substantially random access to portions of the image at a plurality of nominated resolutions, said computer program product including:

code for an applying step, of applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

code for a division step, of dividing each frequency subband into a plurality of tiles;

code for a quantizing and entropy step, of quantizing and entropy coding each tile;

code for a nomination step, of nominating desired resolutions of the digital image; and

code for an arranging step, of arranging encoded tiles into a bitstream such that, for each level between nominated resolutions, those tiles which substantially correspond to the same portion of the image are contiguous in the bitstream.

41. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image, said computer program product including:

code for an applying step, of applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

code for a division step, of dividing the non-redundant multiple resolution frequency domain representation into a plurality of tiles;

code for a quantizing and entropy step, of quantizing and entropy coding each tile;

code for a nomination step, of nominating desired resolutions of the digital image; and

code for an arranging step, of arranging in a contiguous manner, for each level between nominated resolutions, those tiles which substantially correspond to the same portion.

42. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a coded representation of a digital image, wherein the coded representation includes a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said computer program product including:

code for a division step, of dividing each subband into a plurality of tiles;

code for a selection step, of selecting a predetermined number of the levels from the multiple resolutions;

code for an entropy encoding step, of entropy encoding each tile;

code for a processing step, of processing the selected levels in a predetermined sequential order; and

code for an arranging step, of arranging in a contiguous manner, for each level in the sequence to a current level not processed by said processing step, each entropy encoded tile representing substantially the same portion of image into a bitstream.

43. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image into a bitstream, said computer program product including:

code for an applying step, of applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

code for a division step, of dividing each frequency subband into a plurality of tiles;

code for a quantizing and entropy step, of quantizing and entropy coding each tile;

code for a first arranging step, of arranging into the bitstream in a predetermined order each entropy tile of a DC subband; and

code for a second arranging step, of arranging in a contiguous manner each set of three encoded tiles belonging to each of three AC subbands respectively, which substantially correspond to the same portion of the image at each level, into the bitstream.

44. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image into a bitstream, said computer program product including:

code for an applying step, of applying a discrete wavelet transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising a DC subband and a plurality of AC subbands arranged in a hierarchical structure having a plurality of levels, wherein each level represents frequency contributions between adjacent resolutions of the image;

code for an division step, of dividing each frequency subband into a plurality of tiles;

code for a grouping step, of grouping each tile, substantially corresponding to a same portion of the digital image, at each level of the AC subbands into tile triplets;

code for an entropy coding step, of entropy coding each tile of a DC subband and each tile triplet of the AC subbands;

code for an arranging step, of arranging in a predetermined order each entropy encoded tile of a DC subband and each entropy encoded tile triplet into the bitstream.

45. The computer program product as claimed in claim 44, wherein the levels are arranged in a hierarchical structure comprising the DC subband and the AC subbands, which AC subbands are arranged in decreasing level order substantially according to their increasing subband frequency.

46. The computer program product as claimed in claim 45, wherein said arranging step arranges AC subbands in decreasing level order.

51. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a sequential stream of data for providing substantially random access to portions of an image at a plurality of predetermined resolutions, the stream including a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each subband is divided into a plurality of tiles and each level represents frequency contributions between adjacent resolutions of the image, and wherein each tile represents a frequency contribution to a portion of the image at a predetermined resolution, said computer program product including:

code for an insertion step, of inserting at most one pointer in the sequential stream for each set of tiles which correspond to substantially a same spatial portion of the image for each level to access a portion of the digital image.

52. A method of encoding a digital image, the method including the steps of:

applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image and each subband comprises a plurality of tiles; and

entropy coding each tile into a bitstream, wherein said entropy coding step comprises the following sub-steps;

entropy encoding the tiles of the low frequency subband into the bitstream; and

entropy encoding tile triplets of the high frequency subbands into the bitstream in level and tile triplet order.

53. A method as claimed in claim 52, wherein the method further includes the step of:

nominating two or more levels as one level for the purposes of entropy encoding the tile triplets tiles of the high frequency subbands into the bitstream in level and tile triplet order.

54. The method as claimed in claim 52, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

55. The method as claimed in claim 52, wherein the high frequency subbands are entropy encoded in levels of decreasing order.

56. The method as claimed in claim 55, wherein the high frequency subbands of the same level are entropy encoded in tile triplets of increasing order.

57. The method as claimed in claim 52, wherein the entropy encoding step further includes a quantization step.

58. A method as claimed in claim 52, wherein said entropy encoding step of the tile triplets of the high frequency subbands comprises:

entropy encoding a tile triplet as a single unit.

59. A method as claimed in claim 52, wherein the tiles are of a constant size.

60. A method as claimed in claim 52, wherein each subband comprises an equal number of tiles.

61. An apparatus for encoding a digital image, the apparatus including:

means for applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image and each subband comprises a plurality of tiles; and

means for entropy coding each tile into a bitstream, wherein said entropy coding means comprises the following;

means for entropy encoding the tiles of the low frequency subband into the bitstream; and

means for entropy encoding tile triplets of the high frequency subbands into the bitstream in level and tile triplet order.

62. The apparatus as claimed in claim 61, wherein the apparatus further includes:

means for nominating two or more levels as one level for the purposes of entropy encoding the tile triplets of the high frequency subbands into the bitstream in level and tile triplet order.

63. The apparatus as claimed in claim 61, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

64. The apparatus as claimed in claim 61, wherein the high frequency subbands are entropy encoded in levels of decreasing order.

65. The apparatus as claimed in claim 64, wherein the high frequency subbands of the same level are entropy encoded in tile triplets of increasing order.

66. The apparatus as claimed in claim 61, wherein the entropy encoding means further includes a quantization means.

67. An apparatus as claimed in claim 61, wherein said means for entropy encoding the tile triplets of the high frequency subbands comprises means for entropy encoding a tile triplet as a single unit.

68. An apparatus as claimed in claim 61, wherein the tiles are of a constant size.

69. An apparatus as claimed in claim 61, wherein each subband comprises an equal number of tiles.

70. A computer program product comprising a computer readable medium having recorded thereon a computer program for encoding a digital image, the computer program product comprising:

code for an applying step, of applying a linear transform to the image to produce a non-redundant multiple resolution frequency domain representation of the image, the representation comprising one low frequency subband and a plurality of high frequency subbands arranged in levels, wherein each level represents frequency contributions between adjacent resolutions of the image and each subband comprises a plurality of tiles; and

code for an entropy coding step, of entropy coding each tile into a bitstream, wherein said entropy coding step comprises;

code for a first entropy encoding step, of entropy encoding the tiles of the low frequency subband into the bitstream; and

code for a second entropy encoding step, of entropy encoding tile triplets of the high frequency subbands into the bitstream in level and tile triplet order.

71. The computer program product as claimed in claim 70, wherein the computer program product further includes:

code for a nomination step, of nominating two or more levels as one level for the purposes of entropy encoding the tile triplets of the high frequency subbands into the bitstream in level and tile triplet order.

72. The computer program product as claimed in claim 70, wherein the coded representation is a multiple level discrete wavelet transform of the digital image.

73. The computer program product as claimed in claim 70, wherein the high frequency subbands are entropy encoded in levels of decreasing order.

74. The computer program product as claimed in claim 73, wherein the high frequency subbands of the same level are entropy encoded in tile triplets of increasing order.

75. The computer program product as claimed in claim 70, wherein the entropy coding step further includes a code for a quantization step.

76. The computer program product as claimed in claim 70, wherein said entropy encoding step of, entropy encoding the tile triplets of the high frequency subbands includes entropy encoding a tile triplet as a single unit.

77. The computer program product as claimed in claim 70, wherein the tiles are of a constant size.

78. The computer program product as claimed in claim 70, wherein each subband comprises an equal number of tiles.

79. A method of encoding a coded representation of a digital image, wherein the coded representation comprises a non redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said method comprising the steps of:

dividing each subband into a plurality of tiles;

entropy encoding each tile; and

arranging entropy encoded tiles into a bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

80. A method of encoding a digital image into a bitstream, said method comprising the steps of:

linear transforming the image to produce a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image;

dividing each subband into a plurality of tiles;

entropy encoding each tile; and

arranging entropy encoded tile into the bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

81. A method of encoding a coded representation of a digital image, wherein the coded representation comprises a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image and each subband comprises a plurality of tiles, said method comprising the step of:

entropy encoding the tiles of the high frequency subbands into the bitstream according to a predetermined level order and the tiles of each level according to a predetermined tile order, wherein spatially corresponding tiles are arranged contiguously in the bitstream.

82. An apparatus for encoding a coded representation of a digital image, wherein the coded representation comprises a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said apparatus comprising:

means for dividing each subband into a plurality of tiles;

means for entropy encoding each tile; and

means for arranging entropy encoded tiles into a bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

83. An apparatus for encoding a digital image into a bitstream, said apparatus comprising:

means for linear transforming the image to produce a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image;

means for dividing each subband into a plurality of tiles;

means for entropy encoding each tile; and

means for arranging entropy encoded tiles into the bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

84. An apparatus for encoding a coded representation of a digital image, wherein the coded representation comprises a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image and each subband comprises a plurality of tiles, said apparatus comprising:

means for entropy encoding the tiles of the high frequency subbands into the bitstream according to a predetermined level order and the tiles of each level according to a predetermined tile order, wherein spatially corresponding tiles are arranged contiguously in the bitstream.

85. A computer readable medium comprising a computer program for encoding a coded representation of a digital image, wherein the coded representation comprises a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image, said computer program comprising:

code for a division step, of dividing each subband into a plurality of tiles;

code for an entropy encoding step, of entropy encoding each tile; and

code for an arranging step, of arranging the entropy encoded tiles into a bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

86. A computer readable medium comprising a computer program for encoding a digital image into a bitstream, said computer program comprising:

code for a transforming step, of linear transforming the image to produce a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image;

code for a division step, of dividing each subband into a plurality of tiles;

code for an entropy encoding step, of entropy encoding each tile; and

code for an arranging step, of arranging the entropy encoded tiles into the bitstream such that, for each level between each pair of resolutions of two or more predetermined resolutions of the multiple resolutions, the entropy encoded tiles representing substantially the same portion of the image are contiguous in the bitstream.

87. A computer readable medium comprising a computer program for encoding a coded representation of a digital image, wherein the coded representation comprises a non-redundant hierarchical code, having one low frequency subband and a plurality of high frequency subbands arranged in levels, which levels combine to represent multiple resolutions of the image and each subband comprises a plurality of tiles, said computer program comprising:

code for an entropy encoding step, of entropy encoding the tiles of the high frequency subbands into the bitstream according to a predetermined level order and the tiles of each level according to a predetermined tile order, wherein spatially corresponding tiles are arranged contiguously in the bitstream.