matlab计算图像分形维数代码

计算图像分形维数是利用分形理论中的盒计数法，通过不断缩小分形图形并计算其所覆盖的单位长度内的盒子数目，从而得出分形维数。在Matlab中，可以通过以下代码实现图像分形维数的计算：

1. 读入图像并二值化处理

img = imread('test.png');
img = rgb2gray(img); %转换为灰度图像
bw = imbinarize(img); %二值化处理

2. 构造递归函数求所需参数

function [N,S] = recur_box(IA,theta,step,box_dim,W,dim_num)
    if step>=5
        N(1:dim_num) = 0;
        box_size(1:dim_num) = (1/box_dim).^((1:dim_num)-1);
        box_position = zeros(dim_num,1);
        for I = 1:size(IA,2)
            box_index = ceil(IA(:,I)./box_size);
            for J = 1:dim_num
                if box_index(J)>0 && box_index(J)<=box_dim
                    box_position(J) = (box_index(J)-1)*box_size(J);
                else
                    box_position(1) = 0;
                end
            end
            if theta>0
                area = prod((box_size.^theta));
            else
                area = 1;
            end
            S(1:dim_num) = 0;
            for J = 1:dim_num
                S(J) = S(J) + prod((1./box_size(1:J-1)))*(box_size(J).^theta)*area;
            end
            N(1:dim_num) = N(1:dim_num) + S(1:dim_num);
        end
    else
        [A1,T1] = ismeas(IA,W(1),W(2:dim_num+1,:));
        N1 = recur_box(A1,theta,step+1,box_dim,W,dim_num);
        [A2,T2] = ismeas(T1,W(1),W(2:dim_num+1,:));
        N2 = recur_box(A2,theta,step+1,box_dim,W,dim_num);
        N = N1 + N2;
    end
end

3. 基于递归函数计算盒子数目与分形维数

W = [ones(dim_num+1,1),zeros(dim_num+1,dim_num)];
for k = 1:dim_num
    W(k+1,k+1) = 1;
end
IA = find(bw);
box_dim = 32;
N_0 = recur_box(IA,0,0,box_dim,W,dim_num);
N_1 = recur_box(IA,1,0,box_dim,W,dim_num);
fd = (log(N_1)-log(N_0))/log(1/box_dim);

其中，`IA`代表图像中所有像素的位置，`step`为递归的深度，`box_dim`为盒子的数目，`dim_num`为图像的维数，`N`为对于某个theta下的总盒子数目，`S`为每个盒子中覆盖区域的数目。最后，计算图像的分形维数fd即可。