A quadsection algorithm for grammar-based image compression

Authors:
Morihiro Hayashida;Peiying Ruan;Tatsuya Akutsu
Affiliations:
Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan
Venue:
Integrated Computer-Aided Engineering - Anniversary Volume: Celebrating 20 Years of Excellence
Year:
2012

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Abstract

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 On^{4/3}, where an input image data is of size On × On. Furthermore, we practically improve the proposed algorithm by adding several rules concerning sub-images. We also present results on computational experiments on the proposed algorithms.