5. What is JPEG2000?
JPEG2000 is a new compression standard for still images intended to overcome the shortcomings of the existing JPEG standard.
The standardization process is coordinated by the Joint Technical Committee on Information technology of the International Organization for Standardization (ISO)/ International Electrotechnical Commission (IEC).
JPEG2000 makes use of the wavelet and sub-band technologies. Some of the markets targeted by the JPEG2000 standard are Internet, printing, digital photography, remote sensing, mobile, digital libraries and E-commerce.
The core compression algorithm is primarily based on the Embedded Block Coding with Optimized Truncation (EBCOT) of the bit-stream. The EBCOT algorithm provides a superior compression performance and produces a bit- stream with features such as resolution and SNR scalability and random access.
© V. Sanchez & A. Basu, University of Alberta

6. Features of JPEG2000
);; Lossless and lossy compression: the standard provides lossy compression with a superior performance at low bit-rates. It also provides lossless compression with progressive decoding. Applications such as digital libraries/databases and medical imagery can benefit from this feature.
);; Protective image security: the open architecture of the JPEG2000 standard makes easy the use of protection techniques of digital images such as watermarking, labeling, stamping or encryption
);; Region-of-interest coding: in this mode, regions of interest (ROI’s) can be defined. These ROI’s can be encoded and transmitted with better quality than the rest of the image .
);; Robustness to bit errors: the standard incorporate a set of error resilient tools to make the bit-stream more robust to transmission errors.
© V. Sanchez & A. Basu, University of Alberta

7. Features of JPEG2000 (cont’d)
Example of region of interest coding.
A region of interest in the Barbara image is reconstructed with quality scalability. The region of interest is decoded first before any background information.
Region of interest
© V. Sanchez & A. Basu, University of Alberta

8. The JPEG 2000 Compression Engine
Source Image Data
Encoder
Pre- processing
Forward Quantization Entropy
Transform Encoding
Bit stream
Storage or transmission
Inverse Transform
Inverse Quantization
Entropy Decoding
Bit stream
Reconstructed
Decoder
Image Data
© V. Sanchez & A. Basu, University of Alberta

9. Pre-processing Three steps:
1. Image tiling (optional)-7 for each image component.
DWT on Each Tile
Tiling DC
Level Shifting
Component
Transformati on
Image Component
DC level shifting -7 samples of each tile are subtracted the same quantity (i.e. component depth).
Color transformation (optional) -7 from RGB to Y Cb Cr
© V. Sanchez & A. Basu, University of Alberta

10. Forward Transform
Discrete Wavelet Transform (DWT) is used to decompose each tile component into different sub-bands.
The transform is in the form of dyadic decomposition and use bi- orthogonal wavelets.
© V. Sanchez & A. Basu, University of Alberta

11. Forward Transform (cont’d)
DWT can be irreversible or reversible.
);; Irreversible transform -7Daubechies 9-tap/7-tap filter
);; Reversible transform -7 Le Gall 5-tap/3-tap filter
Two filtering modes are supported:
);; Convolution based
);; Lifting based
© V. Sanchez & A. Basu, University of Alberta

12. Analysis and Synthesis Filter Coefficients
Le Gall 5/3
© V. Sanchez & A. Basu, University of Alberta

13. Analysis and Synthesis Filter Coefficients
Daubchines 9/7
© V. Sanchez & A. Basu, University of Alberta

14. 2D-Forward Transform
1-D sets of samples are decomposed into low-pass and high-pass samples.
Low-pass samples represent a down-sampled, low resolution version of the original set.
High pass samples represent a down-sampled residual version of the original set (details).
Low frequency information
High frequency information
(horizontal details)
High frequency
High frequency information (diagonal details)
information (vertical details)
© V. Sanchez & A. Basu, University of Alberta

15. © V. Sanchez & A. Basu, University of Alberta

16. Quantization  a (u, v)  q (u , v)  sign (a (u , v))     b 
After transformation, all coefficients are quantized using scalar quatization.
Quantization reduces coefficients in precision. The operation is lossy unless the quatization step is 1 and the coefficients integers (e.g. reversible integer 5/3 wavelet).
The process follows the formula:
Largest integer not
exceeding ab
 a (u, v) 
q (u , v)  sign (a (u , v))  b  
b b 
 b
Quantized value
Transform coefficient of sub-band b
Quantization step
© V. Sanchez & A. Basu, University of Alberta

17. Modes of Quantization Two modes of operation:
);; Integer mode-7 integer-to-integer transforms are employed. Quantization step are fixed to one. Lossy coding is still achieved by discarding bit-planes.
);; Real mode-7 real-to-real transforms are employed. Quantization steps are chosen in conjunction with rate control. In this mode, lossy compression is achieved by discarding bi-planes or changing the size of the quantization step or both.
© V. Sanchez & A. Basu, University of Alberta

18. Code-blocks, precincts and packets1 2
Precinct: each sub-band is divided into rectangular blocks called precincts.
Packets: three spatially consistent rectangles comprise a packet.
Code-block: each precinct is further divided into non-overlapping rectangles called code-blocks.
Each code-block forms the input to the entropy encoder and is encoded independently.
Within a packet, code-blocks are visited in raster order. 3 4 5 6
9 10 7 8 11 12
Packet
Code-block
Precinct
Sub-band
© V. Sanchez & A. Basu, University of Alberta

19. Entropy Coding: Bit-planes
The coefficients in a code block are separated into bit-planes. The individual bit-planes are coded in 1-3 coding passes.
Code-block
Bit-plane representation
MSB
LSB 15 1 6 3 11 15 6 3 11
Coding passes
Bit-plane context based arithmetic coder
Encoded data
© V. Sanchez & A. Basu, University of Alberta

20. Entropy Coding: Coding Passes
Each of these coding passes collects contextual information about the bit- plane data. The contextual information along with the bit-planes are used by the arithmetic encoder to generate the compressed bit-stream.
The coding passes are:
);; Significance propagation pass -7 coefficients that are insignificant and have a certain preferred neighborhood are coded.
);; Magnitude refinement pass -7 the current bits of significant coefficients are coded.
);; Clean-up pass -7 the remaining insignificant coefficients for which no information has yet been coded are coded.
© V. Sanchez & A. Basu, University of Alberta

21. JPEG2000 Bit-stream
For each code-block, a separate bit-stream is generated.
The coded data of each code-block is included in a packet.
If more that one layer is used to encode the image information, the code-block bit-streams are distributed across different packets corresponding to different layers. H
JPEG2000 bit-stream
Main Header
Layer H
Packet
Packet Header
Coded code-block
© V. Sanchez & A. Basu, University of Alberta

22. How to tell if 2 Images are same?
Pixel by pixel comparison?
Makes sense only if pictures taken from same angle, same lighting, etc
Noise, quantization, etc introduces differences
Human may say images are same even with numerical differences

23. Comparing Images Better approach: Template matching Applications?
Identify similar sub‐images (called template) within 2 images
Applications?
Match left and right picture of stereo images
Find particular pattern in scene
Track moving pattern through image sequence

24. Template Matching Basic idea
Move given pattern (template) over search image
Measure difference between template and sub‐images at different positions
Record positions where highest similarity is found
SubImage
Template

25. Template Matching Difficult issues?
What is distance (difference) measure?
What levels of difference should be considered a match?
How are results affected when brightness or contrast changes?
SubImage
Template

26. Template Matching in Intensity Images
Consider problem of finding a template (reference image) R within a search image
Can be restated as Finding positions in which contents of R are most similar to the corresponding subimage of I
If we denote R shifted by some distance (r,s) by

27. Template Matching in Intensity Images
We can restate template matching problem as:
Finding the offset (r,s) such that the similarity between the shifted reference image Rr,s and corresponding subimage I is a maximum
Solving this problem involves solving many sub‐problems

28. Distance between Image Patterns
Many measures proposed to compute distance between the shifted reference image Rr,s and corresponding subimage I

29. Distance between Image Patterns
Many measures proposed to compute distance between the shifted reference image Rr,s and corresponding subimage I
Sum of absolute differences:
Maximum difference:
Sum of squared differences (also called N‐dimensional Euclidean distance):

30. Distance and Correlation
Best matching position between shifted reference image Rr,s and subimage I minimizes square of dE which can be expanded as
B term is a constant, independent of r, s and can be ignored
A term is sum of squared values within subimage I at current offset r, s

31. Distance and Correlation
C(r,s) term is linear cross correlation between I and R defined as
Since R and I are assumed to be zero outside their boundaries
Note: Correlation is similar to linear convolution
Min value of d2 (r,s) corresponds to max value of E

32. Normalized Cross Correlation
Unfortunately, A term is not constant in most images
Thus cross correlation result varies with intensity changes in image I
Normalized cross correlation considers energy in I and R
CN (r,s) is a local distance measure, is in [0,1] range
CN (r,s) = 1 indicates maximum match
CN (r,s) = 0 indicates images are very dissimilar

33. Correlation Coefficient
Correlation coefficient: Use differences between I and R and their average values
where the average values are defined as
K is number of pixels in reference image R
CL(r,s) can be rewritten as

34. Correlation Coefficient Algorithm

35. Correlation Coefficient Java Implementation

36. Correlation Coefficient Java Implementation

37. Examples and Discussion
We now compare these distance metrics
Original image I: Repetitive flower pattern
Reference image R: one instance of repetitive pattern extracted from I
Now compute various distance measures for this I and R

38. Examples and Discussion
Sum of absolute differences: performs okay but affected by global intensity changes
Maximum difference: Responds more to lighting intensity changes than pattern similarity

39. Examples and Discussion
Sum of squared (euclidean) distances: performs okay but affected by global intensity changes
Global cross correlation: Local maxima at true template position, but is dominated by high‐intensity responses in brighter image parts

40. Examples and Discussion
Normalized cross correlation: results similar to euclidean distance (affected by global intensity changes)
Correlation coefficient: yields best results. Distinct peaks produced for all 6 template instances, unaffected by lighting

41. Effects of Changing Intensity
To explore effects of globally changing intensity, raise intensiy of reference image R by 50 units
Distinct peaks disappear in Euclidean distance
Correlation coefficient unchanged, robust measure in realistic lighting conditions

42. Euclidean Distance under Global Intensity Changes
Distance function for original template R
Distance function with intensity increased by 25 units
Distance function with intensity increased by 50 units
Local peaks disappear as template intensity (and thus distance) is increased

43. Shape of Template Template does not have to be rectangular
Some applications use circular, elliptical or custom‐shaped templates
Non‐rectangular templates stored in rectangular array, but pixels in template marked using a mask
More generally, a weighted function can be applied to template elements

44. Matching under Rotation and Scaling
Simple Approach:
Store multiple rotated and scaled versions of template
Computationally prohibitive
Alternate approaches:
Matching in logarithmic‐polar space (complicated!)
Affine matching use local statistical features invariant under affine image transformations (including rotation and scaling)

45. Matching Binary Images
Direct Comparison:
Count the number of identical pixels in search image and template
Small total difference when most pixels are same
Problem: Small shift, rotation or distortion of image create high distance
Need a more tolerant measure

47. - 17 Mbps data rate through 1994, 20
- 17 Mbps data rate through 1994, 20.4 Mbps from 1995 to 2004, 16 bit from 2005 onward
- 10 bit data encoding through 1994, 12 bit from 1995
- Silicon (Si) detectors for the visible range, indium gallium arsenide (InGaAr) for the NIR, and indium-antimonide (InSb) detectors for the SWIR
- "Whisk broom" scanning
- 12 Hz scanning rate
- Liquid Nitrogen (LN2) cooled detectors
- 10 nm nominal channel bandwidth, calibrated to within 1 nm
- 34 degrees total field of view (full 677 samples)
- 1 milliradian Instantaneous Field Of View (IFOV, one sample), calibrated to within 0.1 mrad
- 76GB hard disk recording medium

54. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

55. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

56. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

57. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

58. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

59. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

60. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

61. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

62. First, what kind of models can be represented by the shape descriptor?
On one end of the spectrum, there are the shape descriptors that can be defined for any point set, independent of any connectivity or topology information. Since every 3D model can be point sampled, this type of shape descriptor allows us to match a very broad class of models.
On the other end of the spectrum are shape descriptors that can only be defined for water-tight, genus-0 objects. These types of shape descriptors can only be used for much more restricted databases, but they can take advantage of these geometric restrictions to generate more discriminating representations of 3D models.

63. Introduction --Classification
Shape
Contour
Region
Structural
Non-Structural
Area
Euler Number
Eccentricity
Geometric Moments
Zernike Moments
Pseudo-Zernike Mmts
Legendre Moments
Grid Method
Syntactic
Graph
Tree
Model-driven
Data-driven
Perimeter
Compactness
Eccentricity
Fourier Descriptors
Wavelet Descriptors
Curvature Scale Space
Shape Signature
Chain Code
Hausdorff Distance
Elastic Matching

64. Boundary Descriptors
There are several simple geometric measures that can be useful for describing a boundary.
The length of a boundary: the number of pixels along a boundary gives a rough approximation of its length.
Curvature: the rate of change of slope
To measure a curvature accurately at a point in a digital boundary is difficult
The difference between the slops of adjacent boundary segments is used as a descriptor of curvature at the point of intersection of segments

65. Representation
Skeletons
Skeletons: produce a one pixel wide graph that has the same basic shape of the region, like a stick figure of a human. It can be used to analyze the geometric structure of a region which has bumps and “arms”.

66. One application of skeletonization is for character recognition.
Representation
Skeletons: Example
One application of skeletonization is for character recognition.
A letter or character is determined by the center-line of its strokes, and is unrelated to the width of the stroke lines.

67. Topological Descriptors
Regional Descriptors
Topological Descriptors
Topological property 1:
the number of holes (H)
Topological property 2:
the number of connected
components (C)

68. Topological Descriptors
Regional Descriptors
Topological Descriptors
Topological property 3:
Euler number: the number of connected components subtract the number of holes
E = C - H
E=0
E= -1

69. Topological Descriptors
Regional Descriptors
Topological Descriptors
Topological
property 4:
the largest
connected
component.

70. Regional Descriptors
Texture

71. There are two types of texture: random and regular.
Regional Descriptors
Texture
Texture is usually defined as the smoothness or roughness of a surface.
In computer vision, it is the visual appearance of the uniformity or lack of uniformity of brightness and color.
There are two types of texture: random and regular.
Random texture cannot be exactly described by words or equations; it must be described statistically. The surface of a pile of dirt or rocks of many sizes would be random.
Regular texture can be described by words or equations or repeating pattern primitives. Clothes are frequently made with regularly repeating patterns.
Random texture is analyzed by statistical methods.
Regular texture is analyzed by structural or spectral (Fourier) methods.

72. Statistical Approaches
Regional Descriptors
Statistical Approaches
Let z be a random variable denoting gray levels and let p(zi), i=0,1,…,L-1, be the corresponding histogram, where L is the number of distinct gray levels.
The nth moment of z:
The measure R:
The uniformity:
The average entropy:

73. Statistical Approaches
Regional Descriptors
Statistical Approaches
Smooth
Coarse
Regular

75. Regional Descriptors
Spectral Approaches

76. Regional Descriptors
Spectral Approaches

77. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
For a 2-D continuous function f(x,y), the moment of order (p+q) is defined as
The central moments are defined as

78. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
If f(x,y) is a digital image, then
The central moments of order up to 3 are

79. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
The central moments of order up to 3 are

80. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
The normalized central moments are defined as

81. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
A seven invariant moments can be derived from the second and third moments:

82. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
This set of moments is invariant to translation, rotation, and scale change.

83. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions

84. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
Table Moment invariants for the images in Figs (a)-(e).

85. The End