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Digital Image Processing

Digital Image Processing. Jain-Yi Lu ( 呂健益 ) Visual Communications Laboratory Department of Communication Engineering National Central University ChungLi , Taiwan. Homework II Fast Discrete Cosine Transform. The Goal of This Homework. Implement Fast Discrete Cosine Transform

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Digital Image Processing

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  1. Digital Image Processing Jain-Yi Lu (呂健益)Visual Communications Laboratory Department of Communication Engineering National Central University ChungLi, Taiwan Homework II Fast Discrete Cosine Transform

  2. The Goal of This Homework • Implement Fast Discrete Cosine Transform • Implement Fast Discrete Cosine Inverse Transform

  3. p + - é ù 1 N ( 2 x 1 ) u å = C ( u ) a ( u ) f ( x ) cos ê ú ë 2 N û = 0 x Discrete Cosine Transform (DCT) N : 1-D Sequence Length : 0,1,2…N-1 (u=0 -> DC) f(x) : Spatial Domain Intensity C(u) : Frequency Domain intensity u

  4. Discrete Cosine Transform

  5. Discrete Cosine Transform (8 ×8 Blocks)

  6. Fast Discrete Cosine Transform(FDCT) • W. H. Chen, C. H. Smith and S. C. Fralick, “A Fast Computational Algorithm for the Discrete Cosine Transform,” IEEE Trans. Communications, Vol. COM-25, No. 9, September 1977

  7. Fast Discrete Cosine Transform 8×8 Block Stage1 Stage2 Stage3 Stage4 Initial Signal Result

  8. Fast Discrete Cosine Transform 8×8 Block Stage1 Stage1 Stage2 Stage3 Stage4

  9. Fast Discrete Cosine Transform 8×8 Block Stage2 Stage1 Stage2 Stage3 Stage4

  10. Fast Discrete Cosine Transform 8×8 Block Stage3 Stage1 Stage2 Stage3 Stage4

  11. Fast Discrete Cosine Transform 8×8 Block Stage4 Stage1 Stage2 Stage3 Stage4

  12. Result

  13. Note and Report • We will provide grayscale Lena 512×512 pixels image. • Your program (Image size, bugs, some questions) (2 points) • The accuracy (2 points) • Computation perplexity (Bonus) • Other comment (Bonus)

  14. Appendix-A

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