I have a Fuzzy-C means function, is there a pro to explain it to me?

function [ Unow, center, now_obj_fcn ] = FCMforImage( img, clusterNum)

% demo

% img = double(imread('brain.tif'));

% clusterNum = 3;

% [ Unow, center, now_obj_fcn ] = FCMforImage( img, clusterNum );

% figure;

% subplot(2,2,1); imshow(img,[]);

% for i=1:clusterNum

% subplot(2,2,i+1);

% imshow(Unow(:,:,i),[]);

% end

if nargin < 2

clusterNum = 8; % number of cluster

end

[row, col] = size(img);

expoNum = 2; % fuzzification parameter

epsilon = 0.001; % stopping condition

mat_iter = 100; % number of maximun iteration

rng('default');

Upre = rand(row, col, clusterNum);

dep_sum = sum(Upre, 3);

dep_sum = repmat(dep_sum, [1,1, clusterNum]);

Upre = Upre./dep_sum;

center = zeros(clusterNum,1);

for i=1:clusterNum

center(i,1) = sum(sum(Upre(:,:,i).*img))/sum(sum(Upre(:,:,i)));

end

pre_obj_fcn = 0;

for i=1:clusterNum

pre_obj_fcn = pre_obj_fcn + sum(sum((Upre(:,:,i) .*img - center(i)).^2));

end

fprintf('Initial objective fcn = %f\n', pre_obj_fcn);

for iter = 1:mat_iter

Unow = zeros(size(Upre));

for i=1:row

for j=1:col

for uII = 1:clusterNum

tmp = 0;

for uJJ = 1:clusterNum

disUp = abs(img(i,j) - center(uII));

disDn = abs(img(i,j) - center(uJJ));

tmp = tmp + (disUp/disDn).^(2/(expoNum-1));

end

Unow(i,j, uII) = 1/(tmp);

end

end

end

now_obj_fcn = 0;

for i=1:clusterNum

now_obj_fcn = now_obj_fcn + sum(sum((Unow(:,:,i) .*img - center(i)).^2));

end

fprintf('Iter = %d, Objective = %f\n', iter, now_obj_fcn);

if max(max(max(abs(Unow-Upre))))<epsilon || abs(now_obj_fcn - pre_obj_fcn)<epsilon

break;

else

Upre = Unow.^expoNum;

for i=1:clusterNum

center(i,1) = sum(sum(Upre(:,:,i).*img))/sum(sum(Upre(:,:,i)));

end

pre_obj_fcn = now_obj_fcn;

end

end

Answer 1

[埃博拉酱]

This MATLAB code implements the Fuzzy C-Means (FCM) algorithm for image segmentation. Here's an explanation of what the code does:

1. The function `FCMforImage` takes an input image and the number of clusters as parameters.
2. It initializes variables such as the fuzzification parameter, stopping condition, and maximum number of iterations.
3. The code starts by randomly initializing the membership matrix `Upre` .
4. It then calculates initial cluster centers based on the membership matrix and image data.
5. The main loop of the FCM algorithm begins, which iterates until convergence or the maximum number of iterations is reached: It updates the membership matrix `Unow` based on the distances between pixels and cluster centers. It calculates the objective function value for the current iteration. It checks for convergence by comparing the change in membership matrix and objective function value with the stopping condition. If not converged, it updates the cluster centers and continues to the next iteration.
6. The function returns the final membership matrix `Unow` , cluster centers, and the final objective function value.
7. There's also a commented-out demo section at the beginning, showing how to use the function and display the results.

This algorithm is used for fuzzy clustering of image data, where each pixel can belong to multiple clusters with different degrees of membership.