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This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.8 pp.1575-1581

- Publication Date
- 2000/08/25

- Publicized

- Online ISSN

- DOI

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

- Category
- Image/Visual Signal Processing

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Toshimizu ABIKO, Masayuki KAWAMATA, "IFS Coding of Non-Homogeneous Fractal Images Using Grobner Basis Techniques" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 8, pp. 1575-1581, August 2000, doi: .

Abstract: This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_8_1575/_p

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@ARTICLE{e83-a_8_1575,

author={Toshimizu ABIKO, Masayuki KAWAMATA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={IFS Coding of Non-Homogeneous Fractal Images Using Grobner Basis Techniques},

year={2000},

volume={E83-A},

number={8},

pages={1575-1581},

abstract={This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - IFS Coding of Non-Homogeneous Fractal Images Using Grobner Basis Techniques

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1575

EP - 1581

AU - Toshimizu ABIKO

AU - Masayuki KAWAMATA

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E83-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2000

AB - This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256

ER -