Image transforms of Image compression - PowerPoint PPT Presentation

About This Presentation
Title:

Image transforms of Image compression

Description:

Image transforms of Image compression Presenter: Cheng-Jin Kuo Advisor: Jian-Jiun Ding, Ph. D. Professor Digital Image & Signal Processing Lab – PowerPoint PPT presentation

Number of Views:320
Avg rating:3.0/5.0
Slides: 31
Provided by: djjEeNtu9
Category:

less

Transcript and Presenter's Notes

Title: Image transforms of Image compression


1
Image transforms of Image compression
  • Presenter Cheng-Jin Kuo ???
  • Advisor Jian-Jiun Ding, Ph. D.
  • Professor ?????
  • Digital Image Signal Processing Lab
  • Graduate Institute of Communication Engineering
  • National Taiwan University, Taipei, Taiwan, ROC

2
Outline
  • Introduction
  • Image compression scheme
  • Image Transform
  • Orthogonal Transform
  • DCT transform
  • Subband Transform
  • Haar Wavelet transform

3
Introduction
  • Image types
  • bi-level image
  • grayscale image
  • color image e.g. RGB, YCbCr
  • continuous-tone image
  • -natural scene
  • -image noise
  • -clouds, mountains, surface of lakes

4
Introduction
  • discrete-tone image(graphical image or synthetic
    image)
  • -artificial image
  • -sharp and well-defined edges
  • -high contrasted from the background
  • cartoon-like image
  • -uniform color

5
Introduction
  • The principle of Image compression
  • removing the redundancy
  • -the neighboring pixels are highly correlated
  • -the correlation is called spatial redundancy

6
Image compression scheme


  • Arithmetic coding,


  • Huffman coding,
  • 1.Orthogonal
    transform(Walsh-Hamadard transform,
    RLE, .

  • DCT, )
  • 2.Subband
    transform(wavelet transform, )


  • quantization error





image
transform
quantizer
encoder
Compressed image file
decoder
Inverse transform
image
7
Image transform
  • Two properties and main goals
  • -to reduce image redundancy
  • -to isolate the various freq. of the image
  • (identify the important parts of the image)

8
Image transform
  • Two main types
  • -orthogonal transform
  • e.g. Walsh-Hdamard transform, DCT
  • -subband transform
  • e.g. Wavelet transform

9
Orthogonal transform
  • Orthogonal matrix W
  • ? CW.D
  • Reducing redundancy
  • Isolating frequencies

10
Orthogonal transform
  • One choice of W
  • (Walsh-Hadamard
    transform)
  • CW.D
  • W should be Invertible (for inverse transform)
  • Other properties?

11
Orthogonal transform
  • Reducing redundancy (Energy weighted)
  • example d5 6 7 8
  • after multiply by W/2? c13 -2 0 -1
  • energy of d energy of c 174
  • energy ratio of the first index
  • d25/174 14
  • c169/174 97

12
Orthogonal transform
  • Reducing redundancy (Energy weighted)
  • d4 6 5 2 c8.5 1.5 -2.5 0.5 E81
  • In general, we ignore several smallest
    elements in d, and get c8.5 0 -2.5 0
  • quantize it and get the inverse
  • c3 5.5 5.5 3
  • E81.75
  • Property 1 should be large while others,
    small.

13
Orthogonal transform
  • Isolating frequencies (freq. weighted)
  • example
  • d1 0 0 1?c2 0 2 0 W
  • d0.51 1 1 10.51 -1 -1 1
  • d0 0.33 -0.33 -1?c0 2.66 0 1.33
  • d0.661 1 -1 -10.331 -1 1 -1

14
Orthogonal transform
  • Isolating frequencies (freq. weighted)
  • Property 2 should correspond to zero freq.
    while other coefficients correspond to higher and
    higher freq.
  • W , W
  • (Walsh-Hadamard transform)

15
Orthogonal transform
  • So how do we choose W?
  • Invertible matrix
  • Coefficients in the first row are all positive
  • Each row represents the different freq.
  • Orthogonal matrix

16
Orthogonal transform

17
Discrete Cosine Transform
  • W matrix of DCT
  • W

18
Discrete Cosine Transform
  • 1D DCT ,
    for f07

  • , f0

  • 1 , fgt0
  • Inverse DCT(IDCT)

19
Discrete Cosine Transform
  • 2D DCT
  • Inverse DCT(IDCT)

20
Discrete Cosine Transform

21
Subband Transform
  • Separate the high freq. and the low freq. by
    subband decomposition

22
Subband Transform

  • Filter each row and downsample the filter output
    to obtain two N x M/2 images.
  • Filter each column and downsample the filter
    output to obtain four N/2 x M/2 images



23
Haar wavelet transform

  • Haar wavelet transform
  • Average resolution
  • Difference detail
  • Example for one dimension



24
Haar wavelet transform
  • Example data(5 7 6 5 3 4 6 9)
  • -average(57)/2, (65)/2, (34)/2, (69)/2
  • -detail coefficients
  • (5-7)/2, (6-5)/2, (3-4)/2, (6-9)/2
  • n (6 5.5 3.5 7.5 -1 0.5 -0.5 -1.5)
  • n (23/4 22/4 0.25 -2 -1 0.5 -0.5
    -1.5)
  • n (45/8 1/8 0.25 -2 -1 0.5 -0.5 -1.5)

25
Haar wavelet transform
26
Subband Transform
27
Subband Transform
  • The standard image wavelet transform
  • The Pyramid image wavelet transform

28
Subband Transform

29
Subband Transform
30
Reference
  • David Salomon, Coding for Data and Computer
    Communication, Springer, 2005.
  • A. Uhl, A. Pommer, Image and Video Encryption,
    Springer, 2005
  • David Salomon, Data Compression - The Complete
    Reference 3rd Edition, Springer, 2004.
  • Khalid Sayood, Introduction to Data Compression
    2nd Edition, Morgan Kaufmann, 2000.
  • J.Goswami, A.Chan, Fundamentals of Wavelets
    Theory, Algorithms, and Application, Wiley
    Interscience, 1999
  • C.S. Burrus, R. A. Gopinath, H. Guo, Introduction
    to Wavelets and Wavelet Transforms A Primer,
    Prentice-Hall, 1998
Write a Comment
User Comments (0)
About PowerShow.com