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Modified Haussdorf Fractal Dimension

version 1.6.0.0 (2.53 KB) by Reza Farrahi Moghaddam
A Modified version of the Haussdorf fractal dimension

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Updated 13 May 2015

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% 150507: Reza Farrahi Moghaddam (imriss@ieee.org) (May 7th, 2015)
% Modified Haussdorf Fractal Dimension
%
% Main features:
% 1. Valuing both White and Black pixels,
% 2. Probabilistically discarding boxes of less value.
%
% SYNTAX: [D, D_old, I, D_ref] = hausDim_Modified_R(I, method_flag)
% I: Input image (White pixels are assumed as information),
% method_flag: 'edg' to use edge of I, 'ske' to use skeleton of I, 'pre' to preprocess I, 'full' to preprocess and then use the edge and skeleton.
% D: Modified Haussdorf Fractal Dimension of I after preprocessing (if any),
% D_old: Haussdorf Fractal Dimension of I after preprocessing (if any),
% D_ref: Haussdorf Fractal Dimension of the unprocessed I,
% I: Processed output of I.
%
% Based on: http://www.mathworks.com/matlabcentral/fileexchange/30329-hausdorff--box-counting--fractal-dimension
%
% Requires:
% 1. Hausdorff (Box-Counting) Fractal Dimension (http://www.mathworks.com/matlabcentral/fileexchange/30329-hausdorff--box-counting--fractal-dimension)
% 2. inpaint_nans (http://www.mathworks.com/matlabcentral/fileexchange/4551-inpaint-nans)
% 3. Universal Color to Gray Conversion (http://www.mathworks.com/matlabcentral/fileexchange/27578-universal-color-to-gray-conversion)
%
% Examples:
% I = mat2gray(double(imread('http://4.bp.blogspot.com/-aHCfmDvyzFU/Un_U-Neo_GI/AAAAAAAAGpQ/DWzjztkh4HM/s1600/sierpinski.png')));
% [D, D_old, I, D_ref] = hausDim_Modified_R(I, 'edg'); % D = 1.5843, D_ref = 1.5999
%
% I = mat2gray(double(imread('http://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Sierpinski_carpet.png/480px-Sierpinski_carpet.png')));
% [D, D_old, I, D_ref] = hausDim_Modified_R(I, 'edg'); % D = 1.6794, D_ref = 1.8811
%
% I = mat2gray(double(imread('http://www.math.upenn.edu/~pstorm/images/round_Sierpinski_carpet.png')));
% [D, D_old, I, D_ref] = hausDim_Modified_R(I, 'edg'); % D = 1.6263, D_ref = 1.7129
%

Comments and Ratings (1)

Will this work for the mandelbrot set?

Updates

1.6.0.0

Minor update.

1.5.0.0

Bug fixed.

1.4.0.0

Bug fixed.

1.3.0.0

Bug fixed.

1.2.0.0

Bug fixed.

1.1.0.0

Added Computer Vision System Toolbox to the Requirements (for integralImage() function).

MATLAB Release Compatibility
Created with R2014b
Compatible with any release
Platform Compatibility
Windows macOS Linux