Estimating of Fractal and Correlation Dimension from 2D and 3D-Images

Ari M. Vepsalainen; Jun Ma

doi:10.1117/12.970053

1 November 1989 Estimating of Fractal and Correlation Dimension from 2D and 3D-Images

Ari M. Vepsalainen, Jun Ma

Proceedings Volume 1199, Visual Communications and Image Processing IV; (1989) https://doi.org/10.1117/12.970053
Event: 1989 Symposium on Visual Communications, Image Processing, and Intelligent Robotics Systems, 1989, Philadelphia, PA, United States

Abstract

If the recursive algorithm or the dynamical system that generate the fractal shape is known, then the fractal dimension can be calculated. Many natural shapes are fractals. However, one can usually not estimate exactly the corresponding dimension from images, because the images are formed of finite amount of values at discrete points. In here, one algorithm to estimate fractal dimension and two algorithms to estimate the correlation dimension, which is a lower bound of fractal dimension, from a 2D or 3D image are introduced. The calculated dimension could be used in order to solve many practical problems. For example, one could use the dimension image on icebreakers in order to determine the type of ice and in order to find cracks in the ice using satellite images. Also one can use dimension image in image compression and in pattern recognition.

Citation Download Citation

Ari M. Vepsalainen and Jun Ma "Estimating of Fractal and Correlation Dimension from 2D and 3D-Images", Proc. SPIE 1199, Visual Communications and Image Processing IV, (1 November 1989); https://doi.org/10.1117/12.970053

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