资源简介
从国外下的代码,可以计算1D,2D,3D的分形盒维数,很好用
代码片段和文件信息
function [nr] = boxcount(cvarargin)
%BOXCOUNT Box-Counting of a D-dimensional array (with D=123).
% [N R] = BOXCOUNT(C) where C is a D-dimensional array (with D=123)
% counts the number N of D-dimensional boxes of size R needed to cover
% the nonzero elements of C. The box sizes are powers of two i.e.
% R = 1 2 4 ... 2^P where P is the smallest integer such that
% MAX(SIZE(C)) <= 2^P. If the sizes of C over each dimension are smaller
% than 2^P C is padded with zeros to size 2^P over each dimension (e.g.
% a 320-by-200 image is padded to 512-by-512). The output vectors N and R
% are of size P+1. For a RGB color image (m-by-n-by-3 array) a summation
% over the 3 RGB planes is done first.
%
% The Box-counting method is useful to determine fractal properties of a
% 1D segment a 2D image or a 3D array. If C is a fractal set with
% fractal dimension DF < D then N scales as R^(-DF). DF is known as the
% Minkowski-Bouligand dimension or Kolmogorov capacity or Kolmogorov
% dimension or simply box-counting dimension.
%
% BOXCOUNT(C‘plot‘) also shows the log-log plot of N as a function of R
% (if no output argument this option is selected by default).
%
% BOXCOUNT(C‘slope‘) also shows the semi-log plot of the local slope
% DF = - dlnN/dlnR as a function of R. If DF is contant in a certain
% range of R then DF is the fractal dimension of the set C.
%
% The execution time depends on the sizes of C. It is fastest for powers
% of two over each dimension.
%
% Examples:
%
% % Plots the box-count of a vector containing randomly-distributed
% % 0 and 1. This set is not fractal: one has N = R^-2 at large R
% % and N = cste at small R.
% c = (rand(12048)<0.2);
% boxcount(c);
%
% % Plots the box-count and the fractal dimension of a 2D fractal set
% % of size 512^2 (obtained by BOXDIV) with fractal dimension
% % DF = 2 + log(P) / log(2) = 1.68 (with P=0.8).
% c = randcantor(0.8 512 2);
% boxcount(c);
% figure boxcount(c ‘slope‘);
%
% F. Moisy
% Revision: 2.00 Date: 2006/11/22
% History:
% 2006/11/22: joins into a single file boxcountn (n=123).
% control input argument
error(nargchk(12nargin));
% check for true color image (m-by-n-by-3 array)
if ndims(c)==3
if size(c3)==3 && size(c1)>=8 && size(c1)>=8
c = sum(c3);
end;
end;
warning off
c = logical(squeeze(c));
warning on
dim = ndims(c); % dim is 2 for a vector or a matrix 3 for a cube
if dim>3
error(‘Maximum dimension is 3.‘);
end
% transpose the vector to a 1-by-n vector
if length(c)==numel(c)
dim=1;
if size(c1)~=1
c = c‘;
end
end
width = max(size(c)); % largest size of the box
p = log(width)/log(2); % nbre of generations
% remap the array if the sizes are not all equal
% or if they are not power of two
% (this slows down the computation!)
if p~=round(p) || any(size(c)~=width)
p = ceil(p);
width = 2^p
属性 大小 日期 时间 名称
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文件 37254 2006-11-14 13:04 box-counting\Apollonian_gasket.gif
文件 5587 2006-11-21 12:43 box-counting\boxcount.m
文件 198 2006-11-21 12:40 box-counting\Contents.m
文件 4998 2006-11-21 12:50 box-counting\demo.m
文件 30608 2006-11-21 00:00 box-counting\dla.gif
文件 1125602 2006-11-20 17:03 box-counting\fractal_tree.jpg
文件 15947 2006-11-21 12:57 box-counting\html\demo.html
文件 1541 2006-11-21 12:57 box-counting\html\demo.png
文件 17927 2006-11-21 12:57 box-counting\html\demo_01.png
文件 4913 2006-11-21 12:57 box-counting\html\demo_02.png
文件 5947 2006-11-21 12:57 box-counting\html\demo_03.png
文件 4489 2006-11-21 12:57 box-counting\html\demo_04.png
文件 8783 2006-11-21 12:57 box-counting\html\demo_05.png
文件 5058 2006-11-21 12:57 box-counting\html\demo_06.png
文件 4576 2006-11-21 12:57 box-counting\html\demo_07.png
文件 347480 2006-11-21 12:57 box-counting\html\demo_08.png
文件 19070 2006-11-21 12:57 box-counting\html\demo_09.png
文件 4738 2006-11-21 12:57 box-counting\html\demo_10.png
文件 15346 2006-11-21 12:57 box-counting\html\demo_11.png
文件 4383 2006-11-21 12:57 box-counting\html\demo_12.png
文件 5297 2006-11-21 12:57 box-counting\html\demo_13.png
文件 2329 2006-11-21 12:57 box-counting\html\demo_14.png
文件 4747 2006-11-21 12:57 box-counting\html\demo_15.png
文件 3714 2006-11-21 12:57 box-counting\html\demo_16.png
..A.SH. 45056 2008-05-27 10:59 box-counting\html\Thumbs.db
..AD... 0 2006-11-21 12:57 box-counting\html
文件 5221 2006-11-21 12:42 box-counting\randcantor.m
目录 0 2008-05-24 21:46 box-counting
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............此处省略2个文件信息
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