好的,以下是完整的代码:
% 读取bmp图片并转化为灰度图像 img = imread(‘example.bmp’); grayImg = rgb2gray(img);
% 定义分形维数计算函数 function [D, r2] = fractal_dimension(image)
% 将灰度图像二值化
bw = imbinarize(image);
% 计算图像中非零像素点的数量
n = sum(sum(bw));
% 滑动窗口计算覆盖该像素的长方形区域的线性尺寸
sizes = 2.^(0:floor(log2(size(bw, 1))))';
counts = zeros(length(sizes), 1);
for i = 1:length(sizes)
size = sizes(i);
counts(i) = 0;
for y = 1:size:size*(floor(size/bw(1))+1)
for x = 1:size:size*(floor(size/bw(2))+1)
if (bw(min(y+size-1,size*(floor(size/bw(1))+1)), min(x+size-1,size*(floor(size/bw(2))+1))) == 1)
counts(i) = counts(i) + 1;
end
end
end
end
% 线性拟合计算分形维数和R^2值
coeffs = polyfit(log(sizes), log(counts/n), 1);
D = -coeffs(1);
r2 = 1 - sum((log(counts/n) - polyval(coeffs, log(sizes))).^2)/sum((log(counts/n) - mean(log(counts/n))).^2);
end
% 计算进相和缺项分形维数和R^2值 [phaseD, phaseR2] = fractal_dimension(grayImg(1:end/2, :)); [gapD, gapR2] = fractal_dimension(grayImg(end/2+1:end, :));
% 输出结果 fprintf(‘进相分形维数: %.2f\n’, phaseD); fprintf(‘进相R^2值: %.2f\n’, phaseR2); fprintf(‘缺项分形维数: %.2f\n’, gapD); fprintf(‘缺项R^2值: %.2f\n’, gapR2);