Fractals in nature: from characterization to simulation
The Science of Fractal Images
Algorithms for random fractals
The Science of Fractal Images
Estimating the fractal dimension of synthetic topographic surfaces
Computers & Geosciences - Special issue on computers, geoscience and geocomputation
Computer rendering of stochastic models
Communications of the ACM
Suboptimal Minimum Cluster Volume Cover-Based Method for Measuring Fractal Dimension
IEEE Transactions on Pattern Analysis and Machine Intelligence
An improved algorithm for computing local fractal dimension using the triangular prism method
Computers & Geosciences
New features using fractal multi-dimensions for generalized Arabic font recognition
Pattern Recognition Letters
Estimation of fractal dimension according to optical density of cell nuclei in papanicolaou smears
ITIB'12 Proceedings of the Third international conference on Information Technologies in Biomedicine
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Fractal geometry has been actively researched in a variety of disciplines. The essential concept of fractal analysis is fractal dimension. It is easy to compute the fractal dimension of truly self-similar objects. Difficulties arise, however, when we try to compute the fractal dimension of surfaces that are not strictly self-similar. A number of fractal surface dimension estimators have been developed. However, different estimators lead to different results. In this paper, we compared five fractal surface dimension estimators (triangular prism, isarithm, variogram, probability, and variation) using surfaces generated from three surface generation algorithms (shear displacement, Fourier filtering, and midpoint displacement). We found that in terms of the standard deviations and the root mean square errors, the triangular prism and isarithm estimators perform the best among the five methods studied.