Hausdorff (Box-Counting) Fractal Dimension

バージョン 1.2.0.0 (1.82 KB) 作成者: Alceu Costa
Returns the Haussdorf fractal dimension of an object represented by a binary image.
ダウンロード: 6.1K
更新 2013/12/18

ライセンスの表示

Returns the Haussdorf fractal dimension D of an object represented by the binary image I. Nonzero pixels belong to an object and 0 pixels constitute the background.

Algorithm:

1 - Pad the image with background pixels so that its dimensions are a power of 2.
2 - Set the box size 'e' to the size of the image.
3 - Compute N(e), which corresponds to the number of boxes of size 'e' which contains at least one object pixel.
4 - If e > 1 then e = e / 2 and repeat step 3.
5 - Compute the points log(N(e)) x log(1/e) and use the least squares method to fit a line to the points.
6 - The returned Haussdorf fractal dimension D is the slope of the line.

In this blog post I show how this code can be used to compute the fractal dimension:

http://www.alceufc.com/2013/11/fractal-dimension-from-image.html

引用

Alceu Costa (2024). Hausdorff (Box-Counting) Fractal Dimension (https://www.mathworks.com/matlabcentral/fileexchange/30329-hausdorff-box-counting-fractal-dimension), MATLAB Central File Exchange. 取得済み .

MATLAB リリースの互換性
作成: R2009a
すべてのリリースと互換性あり
プラットフォームの互換性
Windows macOS Linux
カテゴリ
Help Center および MATLAB AnswersFractals についてさらに検索

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
バージョン 公開済み リリース ノート
1.2.0.0

Updated the description to include a link to a blog post explaining how the code can be used.

1.1.0.0

Corrected a typo in the file title .

1.0.0.0