Fuzzy transforms of monotone functions with application to image compression

This paper is focused on the special properties of functions (monotonicity, Lipschitz continuity) that are invariant with fuzzy transform. On the basis of the monotonicity invariance, we propose an efficient algorithm for improved image compression and reconstruction based on fuzzy transform.

[1]  Irina Perfilieva.  Fuzzy Transforms and Their Applications to Image Compression , 2005, WILF.

[2]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[3]  I. Perfilieva,et al.  Fuzzy transformation , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[4]  Irina Perfilieva.  Fuzzy Transform: Application to the Reef Growth Problem , 2004 .

[5]  Vilém Novák,et al.  On the semantics of perception‐based fuzzy logic deduction , 2004, Int. J. Intell. Syst..

[6]  Vilém Novák,et al.  Mining pure linguistic associations from numerical data , 2008, Int. J. Approx. Reason..

[7]  G. Klir,et al.  Fuzzy logic in geology , 2004 .

[8]  Salvatore Sessa,et al.  An image coding/decoding method based on direct and inverse fuzzy transforms , 2008, Int. J. Approx. Reason..

[9]  Vilém Novák,et al.  Fuzzy transform in the analysis of data , 2008, Int. J. Approx. Reason..

[10]  Witold Pedrycz,et al.  Logic-based fuzzy networks: A study in system modeling with triangular norms and uninorms , 2009, Fuzzy Sets Syst..

[11]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[12]  Vilém Novák,et al.  On the semantics of perception-based fuzzy logic deduction: Research Articles , 2004 .

[13]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[14]  Witold Pedrycz,et al.  Fuzzy relational compression , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[15]  Irina Perfilieva,et al.  Fuzzy Transforms: A Challenge to Conventional Transforms , 2007 .

[16]  Irina Perfilieva,et al.  Fuzzy transforms: Theory and applications , 2006, Fuzzy Sets Syst..

[17]  Bernard De Baets,et al.  Advanced Image Compression on the Basis of Fuzzy Transforms , 2008 .

[18]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.