# 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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