## Abstract

This paper proposes a fast encoding algorithm for iterated function system (IFS) coding of gray-level homogeneous fractal images. In order to realize IFS coding of high order fractal images, it is necessary to solve a set of simultaneous equations with many unknowns. Solving the simultaneous equations using a multi-dimensional, numerical root-finding method is however very time consuming. As preprocessing of numerical computation, the proposed algorithm employs univariate polynomial manipulation, which requires less computation time than multivariate polynomial manipulation. Moreover, the symmetry'of the simultaneous equations with respect to the displacement coefficients enables us to derive an equation with a single unknown from the simultaneous equations using univariate polynomial manipulation. An experimental result is presented to illustrate that the encoding time of the proposed algorithm is about 5 seconds on a personal computer with a 400 MHz Pentium II processor.

Original language | English |
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Pages (from-to) | 1435-1442 |

Number of pages | 8 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E82-A |

Issue number | 8 |

Publication status | Published - 1999 Aug |

Event | Proceedings of the 1998 13th Digital Signal Processing Symposium - Niigata, Japan Duration: 1998 Nov 12 → 1998 Nov 13 |

## Keywords

- Fractal
- Intelligent signal processing
- Inverse problem
- Iterated function system
- Polynomial manipulation

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics