Fractal dimension is a mathematical concept used to measure the geometrical complexity of fractal set. It is defined for fractal geometric images, and considered as global features for them. There are many methods to estimate the fractal dimension of an object. The box counting dimension is an easier and a widely used one, while the escape time dimension is another method used to estimate the dimension of fractals generated using escape time algorithm. These methods are used to calculate the dimension for monochrome images (2Dimages). The necessity to generalize these concepts to be applicable for real world application (e.g. gray scale image, or colored images) has motivating us to introducing the concepts of fuzzy sets. Fuzzy fractal dimension is proposed as the fractal feature for n-dimensional image. In this paper, a new approach to determine fractal dimension is proposed and a new local fuzzy fractal dimension based on this approach is proposed also. It will help to extend this feature to be used in many real world applications that cannot be served based on traditional fractal dimension. By this new approach, the FD is estimated with a reduced number of computational processes. This will helps to improve the complexity of the escape time algorithm that is considered as an NP-Hard problem, and with high precision results.

One of the main disadvantages of fractal image data compression is a loss time in the process of image compression (encoding) and conversion into a system of iterated functions (IFS). In this paper, the idea of the inverse problem of fixed point is introduced. This inverse problem is based on collage theorem which is the cornerstone of the mathematical idea of fractal image compression. Then this idea is applied by iterated function system, iterative system functions and grayscale iterated function system down to general transformation. Mathematical formulation form is also provided on the digital image space, which deals with the computer. Next, this process has been revised to reduce the time required for image compression by excluding some parts of the image that have a specific milestone. The neural network algorithms have been applied on the process of compression (encryption). The experimental results are presented and the performance of the proposed algorithm is discussed. Finally, the comparison between filtered ranges method and self-organizing method is introduced.

No abstract

No abstract

No abstract