Fractal Matrix Model and Its Application to Texture Analysis

Hiroshi KANEKO

Fractal Matrix Model and Its Application to Texture Analysis

Hiroshi KANEKO

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Fractals have been widely applied to picture processings and related fields. They have been particularly successful as computer graphics tools. However, fractal applications to image analysis have not been successful. Because,conventional fractal feature--fractal dimension (F-dim)--is scalar valued, and it is difficult to characterize various image information using the conventional F-dim. In this paper, a new concept of a fractal feature is proposed to overcome the above drawback. The conventional F-dim satisfies a kind of scaling equation. The new fractal feature is a generalization of the conventional F-dim and is defined as a matrix (F-matrix) satisfying the vector scaling equation. The parameter estimation procedure for the F-matrix is also discussed. Texture image analysing experiments were conducted to investigate effectiveness of the F-matrix as an image feature. The main results show that: (1) many texture images fit the F-matrix model well, (2) the F-matrix contains various information that characterize texture images, (3) the F-matrix was useful for texture classification, a 93.8% recognition rate is obtained for 65 samples in 13 categories.

Publication: IEICE TRANSACTIONS on transactions Vol.E71-E No.12 pp.1221-1228

Publication Date: 1988/12/25

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Type of Manuscript: Special Section PAPER (Special Issue on CAS Karuizawa Workshop)

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Hiroshi KANEKO

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Hiroshi KANEKO, "Fractal Matrix Model and Its Application to Texture Analysis" in IEICE TRANSACTIONS on transactions, vol. E71-E, no. 12, pp. 1221-1228, December 1988, doi: .
Abstract: Fractals have been widely applied to picture processings and related fields. They have been particularly successful as computer graphics tools. However, fractal applications to image analysis have not been successful. Because,conventional fractal feature--fractal dimension (F-dim)--is scalar valued, and it is difficult to characterize various image information using the conventional F-dim. In this paper, a new concept of a fractal feature is proposed to overcome the above drawback. The conventional F-dim satisfies a kind of scaling equation. The new fractal feature is a generalization of the conventional F-dim and is defined as a matrix (F-matrix) satisfying the vector scaling equation. The parameter estimation procedure for the F-matrix is also discussed. Texture image analysing experiments were conducted to investigate effectiveness of the F-matrix as an image feature. The main results show that: (1) many texture images fit the F-matrix model well, (2) the F-matrix contains various information that characterize texture images, (3) the F-matrix was useful for texture classification, a 93.8% recognition rate is obtained for 65 samples in 13 categories.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e71-e_12_1221/_p

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@ARTICLE{e71-e_12_1221,
author={Hiroshi KANEKO, },
journal={IEICE TRANSACTIONS on transactions},
title={Fractal Matrix Model and Its Application to Texture Analysis},
year={1988},
volume={E71-E},
number={12},
pages={1221-1228},
abstract={Fractals have been widely applied to picture processings and related fields. They have been particularly successful as computer graphics tools. However, fractal applications to image analysis have not been successful. Because,conventional fractal feature--fractal dimension (F-dim)--is scalar valued, and it is difficult to characterize various image information using the conventional F-dim. In this paper, a new concept of a fractal feature is proposed to overcome the above drawback. The conventional F-dim satisfies a kind of scaling equation. The new fractal feature is a generalization of the conventional F-dim and is defined as a matrix (F-matrix) satisfying the vector scaling equation. The parameter estimation procedure for the F-matrix is also discussed. Texture image analysing experiments were conducted to investigate effectiveness of the F-matrix as an image feature. The main results show that: (1) many texture images fit the F-matrix model well, (2) the F-matrix contains various information that characterize texture images, (3) the F-matrix was useful for texture classification, a 93.8% recognition rate is obtained for 65 samples in 13 categories.},
keywords={},
doi={},
ISSN={},
month={December},}

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TY - JOUR
TI - Fractal Matrix Model and Its Application to Texture Analysis
T2 - IEICE TRANSACTIONS on transactions
SP - 1221
EP - 1228
AU - Hiroshi KANEKO
PY - 1988
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E71-E
IS - 12
JA - IEICE TRANSACTIONS on transactions
Y1 - December 1988
AB - Fractals have been widely applied to picture processings and related fields. They have been particularly successful as computer graphics tools. However, fractal applications to image analysis have not been successful. Because,conventional fractal feature--fractal dimension (F-dim)--is scalar valued, and it is difficult to characterize various image information using the conventional F-dim. In this paper, a new concept of a fractal feature is proposed to overcome the above drawback. The conventional F-dim satisfies a kind of scaling equation. The new fractal feature is a generalization of the conventional F-dim and is defined as a matrix (F-matrix) satisfying the vector scaling equation. The parameter estimation procedure for the F-matrix is also discussed. Texture image analysing experiments were conducted to investigate effectiveness of the F-matrix as an image feature. The main results show that: (1) many texture images fit the F-matrix model well, (2) the F-matrix contains various information that characterize texture images, (3) the F-matrix was useful for texture classification, a 93.8% recognition rate is obtained for 65 samples in 13 categories.
ER -