影像辨識

1. Image Compression
Standards

2. Image Compression Standards
• JPEG Standard
• JPEG2000 Standard
• JPEG-LS Standard
• Bilevel Image Compression Standards

3. JPEG History
• Joint Photographic Experts Group was
organized in 1986.
– ISO and CCITT (now ITU-T)
• Standard was issued in 1992.
• Approved as ISO 10918-1 in 1994.

4. Observations
• Useful image contents change relatively
slowly across the image.
• Psychophysical experiments suggest that
humans are less likely to notice the loss of
high-spatial-frequency components than
lower-frequency components.
• The accuracy in distinguishing closely
spaced lines is much greater for gray than
for color.

5. Block Diagram

6. Main Steps
• Color space transform and downsampling
– RGB  YCbCr
• DCT
• Quantization
• Zigzag ordering and run-length encoding
• Entropy coding

7. RGB Color Model

8. Luminance and chrominance

9. Color Selection in Photoshop

10. YUV,YIQ, and YCbCr Color Models
• YIQ:
– U and V rotates 33o.

11. Color Space Downsampling
• Human eyes are more sensitive to
luminance than chrominance.
• The resolution of the chrominance data is
reduced by a factor of 2.
– 4:4:4
• No downsampling
– 4:2:2
• Reduce by factor of 2 in horizontal direction
– 4:2:0
• Reduce by factor of 2 in horizontal and vertical
directions

12. DCT
• Divide by blocks.
• Level shifted by .
is the number of bits used to represent each
pixel.
– 8-bit image
• [0, 255]  [-128, 127]
– By subtracting the mean, the DC coefficient
can be significantly reduced.
• 2D DCT

13. Block Effect

14. Quantization
• Uniform midtread quantizers with different
step sizes
Luminance Quantization Table Chrominace Quantization Table

15. Quantization
• Larger step sizes at high frequency
– More quantization error in high frequency.
– More likely that a high-frequency coefficient
will be zero.
• Change compression ratio
– Multiply a scaling factor to the quantization
table.

16. Example

17. Example

18. Example

19. Example

20. Zigzag Scan
(32, 6, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, …, 0)

21. Coding of DC Coefficients
• DPCM
– Input: 150,155,149,152,144
– Output: 150, 5, -6, 3, -8
– Represent by (SIZE, AMPLITUDE)
• (8, 10010110), (3, 101), (3, 001), (2, 11), (4, 0111)
• Negative value is represented as one’s complement.
– SIZE is Huffman coded.
• Only 12 values.

22. Coding of AC Coefficients:
Run Length Coding
• Replace coefficient sequence by
(RUNLENGTH, VALUE)
– RUNLENGTH is the number of zeroes
– VALUE is the next nonzero coefficient
– A special EOB pair (0,0) indicates that all the
coefficients after it are zeroes.
• Example:
– (32, 6, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, …, 0)
– (0,6) (0,-1) (0,-1) (1,-1) (3,-1) (2,1) (0,0)

23. Entropy Coding of RLC
• In (RUNLENGTH, VALUE), VALUE is
further represented by (SIZE, AMPLITUDE).
– (RUNLENGTH, SIZE, AMPLITUDE)
– Divide into 2 symbols.
– Symbol 1:
• (RUNLENGTH, SIZE)
– 8 bits total, 4 bits each.
• 4-bit RUNLENGTH can represent 15 zeroes max.
– Special extension code ZRL: (15,0).
– Symbol 2:
• (AMPLITUDE)
– Symbol 1 is Huffman coded. Symbol 2 is not.

24. JPEG Modes
• Sequential Mode
– Default
– Encoded in a single left-to-right, top-to-bottom scan.
• Progressive Mode
– DCT coefficients are sent in multiple passes.
• Hierarchical Mode
– Image is encoded in a hierarchy of several different
resolutions.
• Lossless Mode

25. Progressive Mode
• Spectral Selection
– Scan 1: AC1, AC2.
– Scan 2: AC3, AC4, AC5.
– …
– Scan k: AC61,AC62, AC63.
• Successive Approximation
– Scan 1: Bits 7,6,5,4.
– Scan 2: Bit 3.
– …
– Scan m: Bit 0.

26. Progressive Transmission vs
Raster Scan

27. Hierarchical Mode

28. JPEG Bitstream

29. Image Compression Standards
• JPEG Standard
• JPEG2000 Standard
• JPEG-LS Standard
• Bilevel Image Compression Standards

30. JPEG2000 Features
• Low-bitrate compression
• Lossless and lossy compression
• Large images
• Single decompression architecture
• Transmission in noisy environments
• Progressive transmission
• Region-of-interest coding
• Computer-generated imagery
• Compound documents

31. EBCOT
• Embedded Block Coding with Optimized
Truncation by Taubman
– Partitioning each subband LL, LH, HL, HH
into small block called code blocks.
– Each code block is coded independently.
– A separate, scalable bitstream is generated
for each code block.
• Quality and resolution scalability
• Improve error resilience.
• Random access.

32. Block Diagram
• For region-of-interest encoding and multiple
access, an image is spatially partitioned into tiles.
• Tiles are rectangular partitions of the image which
are coded independently allowing for random
access as well as editing functions.

33. Wavelet Transform and
Quantization
• 2 types of wavelet filters are included:
– Reversible wavelet transform
• Filters generate integer coefficients
• Lossless compression
– Irreversible wavelet transform
• Cohen-Daubechies-Feaveau (4,4) (CDF(4,4)) biorthogonal wavelets
• Dead zone quantizer:
– Sign and magnitude are separated.

34. Tier I Coding: Block Coding
• Each subband is partitioned into small code blocks
of size 32x32 or 64x64.
• A scalable bitstream is generated for each code
block. Each bitstream can be independently
truncated.

35. Bitplane Coder
• The most significant bit is coded first for all
samples in the code block.
• The next significant bitplane follows until
all bitplanes have been coded.
• Each code block is coded independently.
– Relationship between code blocks cannot be
used.
– Context information is used to code the
bitplane.

36. Bitstream Optimization
• Post compression rate distortion (PCRD)
optimization
– Produce an optimal truncation of each code
block’s bitstream such that distortion is
minimized given the bit-rate constraint.
• Layer formation and representation
– EBCOT offers both resolution and quality
scalability.
– Other scalable image compression algorithms
(EZW, SPIHT) offer only quality scalability.

37. Region-of-Interest Coding
(a) 0.4bpp (b) 0.5bpp (c) 0.6bpp (d) 0.7bpp

38. Performance Comparison
JPEG JPEG2000
0.75bpp

39. Performance Comparison
JPEG JPEG2000
0.25bpp

40. Performance Comparison
• For natural image

41. Performance Comparison
• For computer generated image

42. Performance Comparison
• For medical image

43. Image Compression Standards
• JPEG Standard
• JPEG2000 Standard
• JPEG-LS Standard
• Bilevel Image Compression Standards

44. CALIC
• Context Adaptive Lossless Image
Compression
• Proposed by Wu in 1995.
• Two modes
– Gray-scale
– Bi-level

45. Concept
• Context modeling
– A pixel has a value close to one of its neighbors.
• Depend on the direction of the edge.
– Models by conditional probabilities of the neighboring
pixel values.
– If the input source contains substantial structure, we
could potentially compress it using fewer bits than
0th-order entropy.
• Order-0 model
– Symbols were treated singly.
• Order-k model
– k preceding symbols were examined each time.

46. Context Modeling
• P(0)=0.4, P(1)=0.6
– 0th-order Entropy=-0.4log2(0.4)-
0.6log2(0.6)=0.97
• P(0|0)=0.8, P(1|0)=0.2
P(0|1)=0.1, P(1|1)=0.9
– Entropy for context 0
• -0.8log2(0.8)-0.2log2(0.2)=0.72
– Entropy for context 1
• -0.1log2(0.1)-0.9log2(0.9)=0.47
– 1st-order Entropy=0.72X0.4+0.47X0.6=0.57

47. Prediction
• Gradient adjusted predictor
ℎ
𝑣
• Prediction
𝑋 𝑁 𝑑 𝑑 80
𝑋 𝑌 𝑁 /2 80 𝑑 𝑑 32
𝑋 𝑌 𝑁 /4 32 𝑑 𝑑 8
𝑋 𝑊 𝑑 𝑑 80
𝑋 𝑌 𝑊 /2 80 𝑑 𝑑 32
𝑋 𝑌 𝑊 /4 32 𝑑 𝑑 8
𝑋 𝑌 Otherwise
𝑌
𝑁 𝑊
2
𝑁𝐸 𝑁𝑊
4
𝑁𝑁 𝑁𝑁𝐸
𝑁𝑊 𝑁 𝑁𝐸
𝑊𝑊 𝑊 𝑋

48. Prediction Error Context
• Error energy estimator
– Divide into 8 regions
– Encoding prediction error in these 8 contexts.

49. Prediction Error Adjustment
• Prediction vector
– 𝑁, 𝑊, 𝑁𝑊, 𝑁𝐸, 𝑁𝑁, 𝑊𝑊, 2𝑁 𝑁𝑁, 2𝑊 𝑊𝑊
– Compare each component with initial prediction 𝑋
• If component < prediction, replace component with 1.
• Otherwise, replace component with 0.
– 256 possible vectors
• Because the dependence of various components, only
144 possible vectors.
• Error energy estimator 𝛿/2
– Divide 𝛿 into 4 intervals
• Total number of contexts
– 576
• Adjusted prediction value
– Keep track of the prediction errors of the 576 contexts and offset 𝑋
by that amount.

50. Recursive Indexing
• How to represent a number larger than
.
– Example:
.
.
• Recursively subtracting from the
value until the remainder is in .
• This method followed by entropy coding is
optimal for geometric distribution.

51. CALIC Summary
• Find initial prediction
• Compute prediction context
• Refine prediction by removing the
estimated bias in that context
• Update bias estimate
• Remap prediction error to
• Find the coding context
• Code the prediction error

52. JPEG-LS
• Based on LOCO-I
– LOw COmplexity LOssless COmpression for
Images
– Proposed by HP in 1998.
– Standardized in 1999.
– Motivation
• Low complexity is more important than small
increase in compression.

53. Components
• Prediction
• Context determination
• Residual coding

54. Prediction
• Causal context
• Median adaptive prediction
– Detect vertical and horizontal edges.
• Better prediction uses adaptive model based on
calculation of the local edge direction.

55. Context Determination
• Prediction error is considered under
context model.
– Prediction error is called “residual”.
• Context model uses three-component
vector
2
– Capture local smoothness or edge contents
surrounding current sample.

56. Context Model and Residual
Coding
• Q are quantized with the following outputs:
– -4,-3,-2,-1,0,1,2,3,4
– First element of 𝑸 must be positive.
• If first element of 𝑸 is negative, replace 𝑸 by 𝑸.
– The total number of context 9 9 4.5 365.
– Vector 𝑸 is mapped into a number between 0 and 364.
• The residuals are encoded using adaptively selected
codes based on Golomb code.

57. Golomb Code
• Encode integers with the assumption that
the larger an integer, the lower its
probability.
• Unary code
– For positive integer n, its code is n 1s followed
by a 0.
• 4: 11110
• 7: 11111110
– It is a Huffman code.

58. Comparison

59. Near-Lossless Mode
• Residuals are quantized using a uniform
quantizer.

60. Comparison with Lossless JPEG
• JPEG-LS is a single-pass algorithm.
Lossless JPEG needs to compare the
results from 8 different predictors.
• JPEG-LS is adaptive and performs well on
compound documents. Lossless JPEG is
not.

61. Image Compression Standards
• JPEG Standard
• JPEG2000 Standard
• JPEG-LS Standard
• Bilevel Image Compression Standards

62. Facsimile Encoding
• CCITT (ITU-T)
– Group 1
• Transmit an A4 document in about 6 minutes.
• Standardized in recommendation T.2.
– Group 2
• Transmit an A4 document in about 3 minutes.
• Standardized in recommendation T.3.
– Group 3
• Transmit an A4 document in about 1 minute.
• Standardized in recommendation T.4.
– Group 4
• Same speed as Group 3.
• Standardized in recommendations T.6, T.503, T.521, and
T.563.
– Group 1 and Group 2 are analog and without
compression.

63. Group 3 and Group 4 Fax
• Two coding schemes
– One-dimensional scheme
– Two-dimensional scheme
• One-dimensional scheme
– Run-length coding
• Each line is a series of alternating white runs and
black runs.
• The first run is always a white run.

64. Coding the Run Length
• Modified Huffman (MH) scheme
• To accommodate extremely long run
– For run length ,
• 𝑟 64 𝑚 𝑡
• Codes for 𝑚 are called make-up codes.
• Codes for 𝑡 are called terminating codes.
– Can represent lengths of 1728 (number of
pixels per line in an A4 document)

65. Two-Dimensional Scheme
• Report transition times when move from one state to
another state.
– Runs
• 0, 2, 3, 3, 8
0, 1, 8, 3, 4
– Transitions
• 1, 3, 6, 9
• 1, 2, 10, 13
• Relative Element Address Designate (READ)
– Rows of a FAX image are heavily correlated.
– Code the transition points with reference to the previous line.

66. Modified READ Code
• 𝑎
– The last pixel whose value is known
to both encoder and decoder.
• 𝑎
– The first transition pixel to the right
of 𝑎 .
• 𝑎
– The second transition pixel to the
right of 𝑎 .
• 𝑏
– The first transition pixel on the line
above to the right of 𝑎 whose color
is the opposite of 𝑎 .
• 𝑏
– The first transition pixel to the right
of 𝑏 .

67. Modified READ Code
• Pass mode (code 0001)
and lie between and .
– From to the pixel right below , all pixels
are of the same color.
– Update to pixel right below .

68. Modified READ Code
• Vertical mode
– If the distance between 𝑎 and 𝑏 is 3, send the
location of 𝑎 with respect to 𝑏 and move 𝑎 to 𝑎 .
• Horizontal mode
– If the distance between 𝑎 and 𝑏 is 3, send
modified Huffman codewords corresponding to the
run length from 𝑎 to 𝑎 , and 𝑎 to 𝑎 .

69. Differences between
Group 3 and Group 4
• Each line is based on the previous line, an error in
one line will propagate to the other lines.
– To prevent this, Group 3 requires that after each one-
dimensional coded line, at most 𝐾 1 lines can be
coded using two-dimensional algorithm.
– 𝐾 2 or 4.
• Group 4 does not have a one-dimensional coding
algorithm.
– Modified Modified READ (MMR)

70. JBIG (T.82)
• Joint Bi-level Image Processing Group
• Three steps:
– Resolution reduction (progressive mode)
– Redundancy removal
– Arithmetic coding of the residuals

71. Resolution Reduction
• Instead of simply taking the average of
every block, JBIG provides a table-
based method for resolution reduction.
• The table is indexed by the neighboring
pixels shown the figure
– The circles represent the
lower-resolution layer pixels.
– The squares represent the
higher-resolution layer pixels.

72. Redundancy Removal
• Typical prediction:
– In regions of constant color, pixels in both high
resolution and low resolution images have the same
color.
– If the low resolution pixels are available, the high
resolution pixels need not be transmitted.
• Deterministic prediction:
– Only used in images encoded using a progressive
mode.
– Because the resolution reduction is
carried out using a table-based
algorithm, it is sometimes possible to
determine the exact value of a high
resolution pixel given the values of
the pixels already encoded.

73. Arithmetic Coding
• Context Modeling +
Arithmetic Coding (QM Coder)
• For progressive mode 

74. QM Coder
• Track 𝑙𝑜𝑤 and 𝑟𝑎𝑛𝑔𝑒.
• Only two symbols
– More probable symbol (MPS)
• Map to lower subinterval
– Less probable symbol (LPS)
• Probability of LPS 𝑞
• Interval update
– MPS occurs
• 𝑙𝑜𝑤 is the same.
• 𝑟𝑎𝑛𝑔𝑒 𝑟𝑎𝑛𝑔𝑒 1 𝑞
– LPS occurs
• 𝑙𝑜𝑤 𝑙𝑜𝑤 𝑟𝑎𝑛𝑔𝑒 1 𝑞
• 𝑟𝑎𝑛𝑔𝑒 𝑟𝑎𝑛𝑔𝑒 𝑞

75. JBIG2 (T.88)
• A bi-level images usually consists of
– Texts on background
– Halftone images
• Divide into 3 types of regions
– Symbol regions
• Dictionary-based coding
– Halftone regions
• Dictionary-based coding
– Generic regions
• MMR or variation of JBIG.
• Applications
– PDF

76. T.44 for Mixed Raster Content
(MRC)
• For color document.
• Separate document into elements that can be compressed
using available techniques.
– JPEG (T.81), JBIG (T.82), T.6, …
• Divides a page into slices.
– The width of the slice is equal to the width of the entire page.
• In the base mode, each slice is represented by 3 layers:
– Background layer
– Foreground layer
– Mask layer.
• These layers are used to effectively represent three basic
data types:
– Color images
– Bi-level data
– Multilevel (multicolor) data.

77. Slices
• 2 slices:

78. Layers
Background layer
Mask layer  Foreground layer 