A Quadsection Algorithm for Grammar-Based Image Compression

  • Morihiro Hayashida
  • Peiying Ruan
  • Tatsuya Akutsu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6485)


Grammar-based compression is to find a small grammar that generates a given data and has been well-studied in text compression. In this paper, we apply this methodology to compression of rectangular image data. We first define a context-free rectangular image grammar (CFRIG) by extending the context-free grammar. Then we propose a quadsection type algorithm by extending a bisection type algorithm for grammar-based compression of text data. We show that our proposed algorithm approximates in polynomial time the smallest CFRIG within a factor of O(n 4/3), where an input image data is of size O(n) ×O(n). We also present results on computational experiments on the proposed algorithm.


Bisection Context-free Rectangular Image Grammar 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bamsley, M.F., Demko, S.: Iterated function systems and the global construction of fractals. Proc. of Royal Society of London A399, 243–275 (1985)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Charikar, M., Lehman, E., Liu, D., Panigrahy, R., Prabhakaran, M., Sahai, A., Shelat, A.: The smallest grammar problem. IEEE Transactions on Information Theory 51, 2554–2576 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Drewes, F.: Grammatical picture generation: A tree-based approach. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  4. 4.
    Huffman, D.A.: A method for the construction of minimum-redundancy codes. In: Proceedings of the Institute of Radio Engineers, vol. 40, pp. 1098–1101 (1952)Google Scholar
  5. 5.
    Jacquin, A.E.: Image coding based on a fractal theory of iterated contractive image transformations. IEEE Transactions on Image Processing 1, 18–30 (1992)CrossRefGoogle Scholar
  6. 6.
    Kieffer, J.C., Yang, E.H.: Grammar-based codes: A new class of universal lossless source codes. IEEE Transactions on Information Theory 46, 737–754 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Polvere, M., Nappi, M.: A feature vector technique for fast fractal image coding. Tech. rep., University of Salerno (1998)Google Scholar
  8. 8.
    Rytter, W.: Application of lempel-ziv factorization to the approximation of grammar-based compression. Theoretical Computer Science 302, 211–222 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Subramanian, K.G., Ali, R.M., Geethalakshmi, M., Nagar, A.K.: Pure 2d picture grammars and languages. Discrete Applied Mathematics 157, 3401–3411 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory 24, 530–536 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Morihiro Hayashida
    • 1
  • Peiying Ruan
    • 1
  • Tatsuya Akutsu
    • 1
  1. 1.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityUjiJapan

Personalised recommendations