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Fractal image compression

Published online by Cambridge University Press:  13 December 2013

C. E. MARTIN  and
S. A. CURTIS
C. E. MARTIN
Affiliation:
Oxford Brookes University, Oxford OX33 1HX, UK (e-mail: cemartin@brookes.ac.uk)
S. A. CURTIS
Affiliation:
Oxford University, Oxford OX3 7LF, UK (e-mail: sharon.curtis@ctsu.ox.ac.uk)
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Abstract

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This paper describes some experiences of using fractal image compression as the subject of an assignment for a functional programming course using Haskell. The students were fascinated by the reproduction of images from their encodings and engaged well with the exercise which involved only elementary functional programming techniques.

Information

Type
Educational Pearls
Information
Journal of Functional Programming , Volume 23 , Issue 6 , November 2013 , pp. 629 - 657
Copyright
Copyright © Cambridge University Press 2013 

References

Baelde, D. & Mimram, S. (2011) Fractal compressor. Accessed March 26, 2013. Available at: http://fractcompr.sourceforge.net/.Google Scholar
Barnes, C., Shechtman, E., Finkelstein, A. & Goldman, D. B. (2009) PatchMatch: a Randomized Correspondence Algorithm for Structural Image Editing. ACM Trans. Graph. 28, 3 (Article 24).Google Scholar
Barnsley, M. F. (1988) Fractals Everywhere. Waltham, MA: Academic Press.Google Scholar
Barnsley, M. F. (2011) Superfractals. Waltham, MA: Academic Press. Accessed March 20, 2013. Available at: http://www.superfractals.com/.Google Scholar
Barnsley, M. F. & Hurd, L. P. (1992) Fractal Image Compression. Natick, MA: AK Peters.Google Scholar
Bentley, J. (1975) Multidimensional binary search trees used for associative searching. Commun. ACM 18 (9), 509–517.Google Scholar
Cardinal, J. (1999) Faster fractal image coding using similarity search in a KL-transformed feature space. In Fractals: Theory and Applications in Engineering, Dekking, M. (eds). New York, NY: Springer, pp. 293–306.Google Scholar
Curtis, S. A. & Martin, C. E. (2005) Functional fractal image compression. In Proceedings of the 6th Symposium on Trends in Functional Programming (TFP 2005), Tallinn, Estonia, pp. 393–398.Google Scholar
Davoine, J. (1997) How to improve pixel-based fractal image coding with adaptive partitions. In Fractals in Engineering: From Theory to Industrial Applications, Lévy Véhel, J., Lutton, E. and Tricot, C. (eds). Berlin, Germany: Springer-Verlag, pp. 292–306.Google Scholar
Elliot, C. (2003) Functional images. In The Fun of Programming, Gibbons, J. & de Moor, O. (eds). Sydney Australia: Palgrave Macmillan, pp. 131–150.Google Scholar
Fisher, Y. (1995) Fractal Image Compression. Theory and Application. Nerw York, NY: Springer.Google Scholar
Fractal Foundation. (2011) Accessed March 14, 2013. Available at: http://www.fractalfoundation.org.Google Scholar
Frame, M. & Mandelbrot, B. B. (2002) Fractals, Graphics, and Mathematics Education, Mathematical Association of America Notes, vol. 58. Cambridge, UK: Cambridge University Press.Google Scholar
Ghosh, S. K., Mukhopadhyay, J., Chowdary, V. M. & Jeyaram, A. (2002) Relative fractal coding and its application in satellite image compression. In Proceedings of the Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP), India.Google Scholar
GIMP (2012) The GNU Image Manipulation Program (version 2.8.2). Accessed October 23, 2013. Available at: http://www.gimp.org.Google Scholar
Hafner, U. (2000). Fiasco. Accessed February 21, 2013. Available at: http://github.com/megatherion/Fiasco/.Google Scholar
Hudak, P. (2000) The Haskell School of Expression. Cambridge, UK: Cambridge University Press.Google Scholar
Hugs (2006) The Hugs 98 System. Available at: http://haskell.org/hugs/.Google Scholar
Hutton, G. (2007) Programming in Haskell. Cambridge, UK: Cambridge University Press.Google Scholar
Jacquin, A. (1989) A Fractal Theory of Iterated Markov Operators with Applications to Digital Image Coding. PhD thesis, Georgia Institute of Technology, Atlanta, GA.Google Scholar
Jones, M. P. (2004) Composing Fractals. J. Funct. Program. 14 (6), 715–725.Google Scholar
Kanakarakis, I., Ntanasis, P. & Sarbinowski, P. (2011) Fractal image compression. Accessed March 26, 2013. Available at: http://github.com/c00kiemon5ter/Fractal-Image-Compression Google Scholar
Kaplan, K. (1997) Fractals are emerging as a shape of things to come. LA Times May 12, 1997. Accessed October 23, 2013. Available at: http://articles.latimes.com/1997-05-12/business/fi-58093_1_fractal-compression.Google Scholar
Lindenmayer, A. (1968) Mathematical models for cellular interaction in development, Parts I and II. J. Theor. Biol. 18, 280–315.Google Scholar
Liu, D. & Jimack, P. K. (2007) A survey of parallel algorithms for fractal image compression. J. Algorithms Comput. Technol. 1, 171–186.Google Scholar
Lu, N. (1997) Fractal Imaging. Waltham, MA: Academic Press.Google Scholar
Mandelbrot, B. B. (1977) Fractals, Form, Chance and Dimension. New York, NY: W. H. Freeman.Google Scholar
Mandelbrot, B. B. (1983) The Fractal Geometry of Nature. New York, NY: W. H. Freeman.Google Scholar
Microsoft (2009) Microsoft encarta. Accessed March 21, 2013. Available at: http://microsoft.com/uk/encarta/ Google Scholar
Munroe, R. (2006) Su Doku. xkcd. Accessed October 23, 2013. Available at: http://xkcd.com/74/ Google Scholar
Olson, C. F. (2006) Encouraging the development of undergraduate researchers in computer vision. In Proceedings of the 11th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education (ITICSE '06). New York, NY: ACM, pp. 255–259.Google Scholar
OnOne Software (2013) Perfect resize. Accessed February 21, 2013. Available at: http://www.ononesoftware.com/products/perfect-resize/ Google Scholar
Peitgen, H.-O., Jürgens, H. & Saupe, D. (1991) Fractals for the Classroom, Part One. New York, NY: Springer-Verlag.Google Scholar
Peitgen, H.-O., Jürgens, H. & Saupe, D. (1992) Fractals for the Classroom, Part Two. New York, NY: Springer-Verlag.Google Scholar
Peyton Jones, S. (ed) (2003) Haskell 98 Language and Libraries: The Revised Report. Cambridge, UK: Cambridge University Press.Google Scholar
Rasala, R. (2000, March) Toolkits in first year computer science: A pedagogical imperative. In Proceedings of the 31st SIGCSE Technical Symposium on Computer Science Education, 2000, (SIGCSE '00) Austin, Texas, Vol. 32 Issue 1. New York, NY: ACM, pp. 185–191.Google Scholar
Saupe, D. (1994) Breaking the Time Complexity of Fractal Image Compression. Technical Report 53, Institut für Informatik Freiburg, Freiburg, Germany.Google Scholar
Skiljan, I. (2012) IrfanView (version 4.33). Accessed October 23, 2013. Available at: http://www.irfanview.com Google Scholar
Stanford (2013) Nifty assignments. Accessed February 21, 2013 Available at: http://nifty.stanford.edu/ Google Scholar
Still, M. (2005) The Definitive Guide to ImageMagick. New York, NY: Apress.Google Scholar
Thalabard, S. & Zahariade, G. (2005) Compression Fractale d'Images. Lyon, France: TIPE, ENS.Google Scholar
Thompson, S. (2011) The Craft of Functional Programming, 3rd ed. Boston, MA: Addison-Wesley.Google Scholar
Ullrich, H. (1999) Low Bit-rate Image and Video Coding with Weighted Finite Automata. Berlin, Germany: Mensch & Buch.Google Scholar
Vaddella, V. R. P. & Inampudi, R. B. (2010) Fast fractal compression of satellite and medical images based on domain-range entropy. J. Appl. Comput. Sci. Math. 9 (4), 21–26.Google Scholar
Veenadevi, S. V. & Ananth, A. G. (2011) Fractal image compression of satellite imageries. Int. J. Comput. Appl. 30 (3), 33–36.Google Scholar
Welstead, S. (1999) Fractal and Wavelet Image Compression Techniques. Bellingham, WA: SPIE Press.Google Scholar
Wertheim, M. (2006) Field Guide to the Business Card Menger Sponge. Los Angeles, CA: The Institute for Figuring.Google Scholar
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