Directional Property of Fractal-Isotropic or Anisotropic

Abstract

The fractal concept has been widely applied to analyze the image with different textural pattern. This is based on that the value of fractal dimension of an image with homogenous textural pattern should keep consistent. However several studies show identical values of fractal dinebsion of the images which are conveived as different textural pattern by human vision. It was found that the fractal dimension could not distinguish the texture with or without directional preference. With the question of the necessity of assuming isotropy of fractal, we examine the directional property of fractal dimension as a function of angle, F(a), of the image with 3 different textures. The results show a different pattern of F(a) with each image. In addition, this pattern is independent to the image orientation. This may suggest a new feature to represent a textural pattern.