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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.8 pp.1435-1442

- Publication Date
- 1999/08/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Digital Signal Processing)

- Category

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Toshimizu ABIKO, Masayuki KAWAMATA, "An Encoding Algorithm for IFS Coding of Homogeneous Fractal Images Using Univariate Polynomial Manipulation" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 8, pp. 1435-1442, August 1999, doi: .

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_8_1435/_p

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@ARTICLE{e82-a_8_1435,

author={Toshimizu ABIKO, Masayuki KAWAMATA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={An Encoding Algorithm for IFS Coding of Homogeneous Fractal Images Using Univariate Polynomial Manipulation},

year={1999},

volume={E82-A},

number={8},

pages={1435-1442},

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.},

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - An Encoding Algorithm for IFS Coding of Homogeneous Fractal Images Using Univariate Polynomial Manipulation

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1435

EP - 1442

AU - Toshimizu ABIKO

AU - Masayuki KAWAMATA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 1999

AB - 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.

ER -