4. 1 Joint Photographic
Experts Group
o
o
Introduction
Discrete Cosine Transformation
o Algorithm
o Compression Results
5. Joint Photographic Experts Group
Introduction
Bitmap Image, JPEG Compressed,
150KB 14KB
Based on discrete cosine transformation
Lossy compression method
Mostly used by digital cameras and web usage
6. Joint Photographic Experts Group
Discrete Cosine Transformation
Time Domain Frequency Domain
DCT is a time to frequency domain transformation.
7. Joint Photographic Experts Group
Algorithm
8x8 Zig-zag Huffman
pixel DCT Quantization RLE
scan Encoding
blocks
Quantization Output
Table
Quantization results in loss of information .
Compressed output is losslessly stored .
9. 2 Region Of Interest
o Introduction
o Compression Results
o Comparison with JPEG
10. Region Of Interest
Introduction
Original Image ROI
Portion of image containing the significant information is selected
as ROI and compressed at a higher quality .
13. 3 Embedded Zerotree
Wavelet
o
o
Introduction
Discrete Wavelet Transformation
o Zerotree Concept
o An Example
14. Embedded Zerotree Wavelet
Introduction
Embedded – The EZW encoder is based on
progressive encoding. Progressive encoding is also
known as embedded encoding.
Zerotree – A data structure called zero-tree is used in
EZW algorithm to encode the data.
Wavelet – The EZW encoder is specially designed to
work with wavelet transform. It was originally designed
to operate on images.
15. Embedded Zerotree Wavelet
Discrete Wavelet Transformation
Original First Second Third
Image Level Level Level
Lower sub-band has higher resolution and contains higher frequency
information.
16. Embedded Zerotree Wavelet
Zerotree Concept
Quad-tree An
Structure Example
A zerotree is a quad-tree having all its descendents less than the current
threshold.
17. Embedded Zerotree Wavelet
An Example
63 -34 49 10 7 13 -12 7
P N P T Z Z
Dominant Pass 1
-31 23 14 -13 3 4 6 -1
Z T T T Z Z
Threshold = 32
15 14 3 -12 5 -7 3 9
Output =
T Z
PNZTPTTTTZTTZZZZZ
-9 -7 -14 8 4 -2 3 2 PZZ
T T
-5 9 -1 47 4 6 -2 2
Subordinate Pass 1
Z P
3 0 -3 2 3 -2 0 4 List = {63 34 49 47 }
Z Z
Output = 1 0 1 0
2 -3 6 -4 3 6 3 6
5 11 5 6 0 3 -4 4
18. 4 Unit Embedded
Zerotree Wavelet *
o
o
Drawback of existing algorithm
Concept of Unit Cell
o Formation of Unit Cell
o Comparison with existing
algorithm
* Paper under Review process
19. Unit Embedded Zerotree Wavelet *
Drawback of existing algorithm
Dimensions Children Descendents
8x8 284 378
32 x 32 6,859 8,564
128 x 128 1,10,576 1,36,407
256 x 256 4,43,492 5,67,959
Existing algorithm needs to check a large number of children and descendents.
* Paper under Review process
20. Unit Embedded Zerotree Wavelet *
Concept of Unit Cell
2
n
2
n
Smallest possible square matrix generated from the wavelet
decomposed image, having the same level of wavelet
decomposition structure as the original image.
* Paper under Review process
21. Unit Embedded Zerotree Wavelet *
Formation of Unit Cell
Decomposition Unit Cell
Level Order
1 2
2 4
3 8
n 2n
Smallest possible square matrix generated from the wavelet
decomposed image, having the same level of wavelet
decomposition structure as the original image.
* Paper under Review process
22. Unit Embedded Zerotree Wavelet *
Comparison to Existing Algorithm
Original algorithm Proposed algorithm
Image
32 64 128 256 32 64 128 256
× × × × × × × ×
32 64 128 256 32 64 128 256
LENA 1.092 4.540 20.062 210.617 0.952 3.479 13.120 52.073
BARBARA 1.108 4.477 19.407 213.425 0.983 3.572 13.915 54.632
CAMRAMAN 1.139 4.618 20.639 200.960 0.998 3.588 13.463 53.867
GOLDHILL 1.136 4.680 20.779 216.670 0.996 3.510 13.541 54.226
PEPPERS 1.186 4.524 19.812 214.626 1.030 3.650 14.258 54.632
Table showing coding time (seconds) for original and proposed
algorithm.
* Paper under Review process
23. Unit Embedded Zerotree Wavelet *
Comparison to Existing Algorithm
Percent
Image
32 64 128 256
× × × × 80
32 64 128 256 70
60
LENA 12.821 23.370 34.603 75.276
50
Percent
40
BARBARA 11.282 20.214 28.299 74.402 30
20
10
CAMRAMAN 12.379 22.304 34.769 73.195
0
32 × 32 64 × 64 128 × 128 256 × 256
GOLDHILL 12.324 25.000 34.833 74.973 Image Dimensions (pixels)
LENA BARBARA CAMRAMAN GOLDHILL PEPPERS
PEPPERS 13.153 19.319 28.034 74.545
Table showing percentage improvement in coding time using
proposed algorithm over original algorithm.
* Paper under Review process