A simple method for estimating the fractal dimension from digital images: The compression dimension |
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| Affiliation: | 1. College of Information Science and Technology, Beijing Normal University, China;2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, China;3. IBM Research, China;4. School of Computer Science and Engineering, University of Electronic Science and Technology of China, China;1. Mathematical Sciences Institute, Australian National University, Canberra, Australia;2. Departmento de Matemática Aplicada, Escuela de Ingeniería y Arquitectur, Universidad de Zaragoza, C/ María de Luna 3, Zaragoza 50018, Spain;1. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China;2. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China |
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| Abstract: | The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem. |
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