A generalized fractal dimension as an image feature

In the real life, many phenomenon cannot be described by the traditional geometry; fractal objects are one of these phenomenon. They have irregular shapes and complex structures. The concept of fractal dimension (FD)is used as an indicator of the complexity and irregularity of these objects. Texture analysis plays an important role in image processing. Fractal dimension is utilized in texture segmentation and classification and has proved to be an interesting parameter to characterize image roughness and extract image features. But, in some complex and irregular scenes, it becomes ineffective for feature extraction and classification. Therefore, a more general approach known as fuzzy fractal dimension can be used to model such types of scenes effectively. A new fuzzy fractal dimension method is proposed in this paper. It is verified by the experiment on a set of natural texture images to show its efficiency and accuracy, and a satisfactory result is found. It also offers promising performance when it is tested on some types of noises to show a good robustness to them.

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