//Initializing centroids to random points in the image, points are different from each others.
    
    for(int j=0; j<c; j++) {
        vertex pixel = vertices[rand()%n];
        while(!far(pixel, assigned)) pixel = vertices[rand()%n];
        add_element_list(assigned, pixel);
        centers[j].r = pixel.r; centers[j].g = pixel.g; centers[j].b = pixel.b;
        centers[j].a = pixel.a;
    }

//Updating clusters centers
        
        for(int j = 0; j < c; j++) {

            double numeratorR = 0.0, numeratorG = 0.0, numeratorB = 0.0, numeratorA = 0.0;
            double denominator = 0.0;

            for(int i = 0; i < n; i++) {

                double weight = fmax(pow(U[i][j], FUZZINESS), EPSILON);

                numeratorR += weight * (vertices[i].r);
                numeratorG += weight * (vertices[i].g);
                numeratorB += weight * (vertices[i].b);
                numeratorA += weight * (vertices[i].a);
                denominator += weight;
            }
            
            denominator = fmax(denominator, EPSILON);

            centers[j].r = numeratorR / denominator;
            centers[j].g = numeratorG / denominator;
            centers[j].b = numeratorB / denominator;
            centers[j].a = numeratorA / denominator;
        }

//Initialize each point membership to each cluster, this is done before updating the clusters

void initialize_membership_matrix(double** U, int n, int c) {

  srand(time(NULL));

    for(int i = 0; i<n; i++) {
        double sum = 0.0;

        for(int j = 0; j<c; j++) {
          
            U[i][j] = (double) rand() / RAND_MAX;
            sum += U[i][j];
        }

        for(int j = 0; j<c; j++) {
            U[i][j] /= sum;
        }
    }
}