Directional Fractal Dimension by Extended Box Counting Method

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  • Box Counting法の拡張による方向別フラクタル次元
  • Box Countingホウ ノ カクチョウ ニ ヨル ホウコウベツ フラクタル ジゲン

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Abstract

The conventional Fractal Dimension is scalar-valued and cannot contain sufficient image information for image analysis. For example, spatial information such as the pixels direction and relative arrangement of the pixels are not represented by the Fractal Dimension. Overcoming these defects, in this paper, a new type of fractal feature, which we call the Directional Fractal Dimension, is proposed and applied to texture analysis. The Directional Fractal Dimension is refinement of the Box Dimension, and is consisted of three Fractal Dimensions, considering directional cosine on which the pixels are placed. The Directional Fractal Dimension contains directional information for pixel placement. The recognition experiment is carried out for 10 texture images, and is obtained correct result 95.8%. Also, Directional Multi-Fractal Dimension is defined and the usefulness for image analysis is examined. The proposed new features are useful for image analysis and recognition.

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