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Approximate resolutions and box-counting dimension

open access: yesApproximate resolutions and box-counting dimension
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An improved box-counting method for image fractal dimension estimation

Pattern Recognition, 2009
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Li, Jian, Du, Qian, Sun, Caixin
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Box-counting dimensions of popcorn subsets

Journal of Mathematical Analysis and Applications, 2023
Let \(S\) be a subset of \(\mathbb N\).
Du, Yali, Wei, Chun, Wen, Shengyou
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BOX-COUNTING DIMENSION COMPUTED BY α-DENSE CURVES

Fractals, 2017
We introduce a method to reduce to the real case the calculus of the box-counting dimension of subsets of the unit cube [Formula: see text], [Formula: see text]. The procedure is based on the existence of special types of [Formula: see text]-dense curves (a generalization of the space-filling curves) in [Formula: see text] called [Formula: see text ...
García Macías, Gonzalo   +2 more
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Efficient box-counting determination of generalized fractal dimensions

Physical Review A, 1990
An alternative algorithm for the numerical analysis of fractal structures and measures is presented, which consumes computer time and memory only quasiproportionally to the size of the input data set. This efficient tool is applied to various deterministic and random multifractals, in particular to the growth probability measures of diffusion-limited ...
, Block, , von Bloh W, , Schellnhuber
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Box-Counting Dimension of Fractal Urban Form

International Journal of Artificial Life Research, 2012
The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in ...
Shiguo Jiang, Desheng Liu
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Functional Box-Counting and Multiple Elliptical Dimensions in Rain

Science, 1987
Many physical systems that have interacting structures that span wide ranges in size involve substantial scale invariant (or scaling) subranges. In these regimes, the large and small scales are related by an operation that involves only the scale ratio. The system has no intrinsic characteristic size.
S, Lovejoy, D, Schertzer, A A, Tsonis
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Fractional box-counting approach to fractal dimension estimation

Proceedings of 13th International Conference on Pattern Recognition, 1996
The estimation of the fractal dimension is essential in fractal-based image segmentation, classification and shape analysis. The most popular estimation approach is based on box-counting. However, the partition and counting methods used in the regular box-counting scheme produces inaccurate results.
null Jie Feng   +2 more
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