1 / 30

Image transforms of Image compression

Image transforms of Image compression. Presenter: Cheng-Jin Kuo 郭政錦 Advisor: Jian-Jiun Ding, Ph. D. Professor 丁建均教授 Digital Image & Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University, Taipei, Taiwan, ROC. Outline. Introduction

baker-harmon
Télécharger la présentation

Image transforms of Image compression

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Image transforms of Image compression Presenter: Cheng-Jin Kuo 郭政錦 Advisor: Jian-Jiun Ding, Ph. D. Professor 丁建均教授 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 image’ Inverse transform decoder

  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 C=W．D • Reducing redundancy • Isolating frequencies

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

  11. Orthogonal transform • Reducing redundancy (Energy weighted) • example: d=[5 6 7 8] after multiply by W/2 c=[13 -2 0 -1] energy of d = energy of c= 174 • energy ratio of the first index: d:25/174 =14% c:169/174 =97%

  12. Orthogonal transform • Reducing redundancy (Energy weighted) • d=[4 6 5 2] ; c=[8.5 1.5 -2.5 0.5] ; E=81 In general, we ignore several smallest elements in d’, and get c=[8.5 0 -2.5 0] quantize it and get the inverse c=[3 5.5 5.5 3] E=81.75 • Property 1: should be large while others, small.

  13. Orthogonal transform • Isolating frequencies (freq. weighted) • example: d=[1 0 0 1]c=[2 0 2 0] W= d=0.5[1 1 1 1]+0.5[1 -1 -1 1] d=[0 0.33 -0.33 -1]c=[0 2.66 0 1.33] d=0.66[1 1 -1 -1]+0.33[1 -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 f=0~7 = , f=0 1 , f>0 • 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:(5+7)/2, (6+5)/2, (3+4)/2, (6+9)/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

More Related