Fractal Image Coding by pKpFpjI9

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									Fractal Image Coding
                       Po-kai Chen
                              Liz Li
                            3/13/07
                           EE398A

          Fractal Image Coding         1
Overview
   Fractal Coding Algorithm
   Sample Images and Results
   Trade-offs
   Rate-distortion Comparison with JPEG and
    JPEG-2000
   Conclusion



                    Fractal Image Coding       2
Fractal Coding Algorithm
   Redundancy can be
    coded using self-
    transformability
   Finite iterations of
    transformations results in
    fractal image
    approximating original

    Based on work by Jacquin
                       Fractal Image Coding   3
Image Partitions
   Parent blocks BxB
   Children blocks B/2xB/2
   Perform transformations on these

                 Split if distortion
                 measure too big




                      Fractal Image Coding   4
Domain Block Pools
   Shade
       Smooth, uniform block
       Only apply DC shift
   Midrange
     Textured block
     Apply scaling and DC shift

   Edge
       Apply scaling, DC shift, and
         shuffling transformation
                          Fractal Image Coding   5
Transformations - Geometric
   Mapping from domain
    block 2Bx2B to range
    block (parent or child)




                          Fractal Image Coding   6
Transformations - Massic
   Changing of pixel values
       Contrast scaling
       DC shift
   Shuffling of pixels
       Identity
       Reflections
       Rotations



                           Fractal Image Coding   7
Transmission
   Location of domain block
   Whether to split into child blocks
       Child block data
   Type of domain block
       Scaling factor and DC shift level
       If edge block, type of shuffling transformation




                           Fractal Image Coding           8
Sample Images - Lena 128x128




    3 iterations, CPU time = 261.05s, Compression
     Ratio = 1.9, rms error = 4.8145 (PSNR = 34.5)

                          Fractal Image Coding       9
Sample Images - Flower
128x128




    3 iterations, CPU time= 475.15s, Compression
     Ratio = 1.4, rms error = 6.3111 (PSNR = 32.1)
                         Fractal Image Coding        10
Sample Images - 1up NES
256x256




   1 iteration, CPU time = 4.26s, Compression Ratio =
    81.1, rms error = 0.3388 (PSNR = 57.5)

                            Fractal Image Coding         11
Trade-offs
   Trade-off between encoding time,
    compression ratio, and image quality
    (measured with rms error)




                     Fractal Image Coding   12
Rate Distortion Curves
(Lena 128x128)
   For the same
    PSNR ~ 35,
       Fractal rate =
        4.8 bpp
       JPEG rate =
        1.5 bpp
       JPEG2000
        rate = 1.25
        bpp

                         Fractal Image Coding   13
Conclusion
   Fractal coding performs well, especially for uniform
    CG images (compression and image quality)
   No noticeable difference between coding fractal
    images and photos

   Fractal coding can be good but not worth it
    because of
       Prohibitive encoding time
       Less than stellar compression ratio for ‘good’ image
        reconstruction


                            Fractal Image Coding               14
References
   A. E. Jacquin, "A novel fractal block-coding
    technique for digital images," International
    Conference on Acoustics, Speech, and
    Signal Processing, 1990.”
   A. E. Jacquin, "Fractal image coding: a
    review," Proceedings of the IEEE, vol. 81, no.
    10, pp. 1451-1465, October 1993.


                      Fractal Image Coding       15

								
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