matlab C均值聚類演算法FCM用影象分割的徹底解析

1

首先，你要知道什麼是C均值聚類演算法，就是那個公式，你最好要能推出來，其次，要明白matlab中自帶FCM 的程式碼含義 ，在命令窗中輸入 edit fcm; 會在M檔案中開啟，前面是註釋

function [center, U, obj_fcn] = fcm(data, cluster_n, options)

%FCM Data set clustering using fuzzy c-means clustering.

%%   [CENTER, U, OBJ_FCN] = FCM(DATA, N_CLUSTER) finds

N_CLUSTER number of

%   clusters in the data set DATA. DATA is size M-by-N, where M is

the number of

%   data points and N is the number of coordinates for each data point. The

%   coordinates for each cluster center are returned in the rows of the matrix

%   CENTER. The membership function matrix U contains the grade of membership of

%   each DATA point in each cluster. The values 0 and 1 indicate no membership

%   and full membership respectively. Grades between 0 and 1 indicate that the

%   data point has partial membership in a cluster. At each iteration, an

%   objective function is minimized to find the best location for the clusters

%   and its values are returned in OBJ_FCN.%

%   [CENTER, ...] = FCM(DATA,N_CLUSTER,OPTIONS) specifies a vector of options

%   for the clustering process:%       OPTIONS(1): exponent for the matrix U             (default: 2.0)%       OPTIONS(2): maximum number of iterations          (default: 100)%       OPTIONS(3): minimum amount of improvement         (default: 1e-5)

%       OPTIONS(4): info display during iteration         (default: 1)

%   The clustering process stops when the maximum number of iterations

%   is reached, or when the objective function improvement between two

%   consecutive iterations is less than the minimum amount of improvement

%   specified. Use NaN to select the default value.%

%   Example

%       data = rand(100,2);

%       [center,U,obj_fcn] = fcm(data,2);

%       plot(data(:,1), data(:,2),'o');

%       hold on;

%       maxU = max(U);

%       % Find the data points with highest grade of membership in cluster 1

%       index1 = find(U(1,:) == maxU);

%       % Find the data points with highest grade of membership in cluster 2

%       index2 = find(U(2,:) == maxU);

%       line(data(index1,1),data(index1,2),'marker','*','color','g');

%       line(data(index2,1),data(index2,2),'marker','*','color','r');

%       % Plot the cluster centers

%       plot([center([1 2],1)],[center([1 2],2)],'*','color','k')%       hold off;%

%   See also FCMDEMO, INITFCM, IRISFCM, DISTFCM, STEPFCM.

%   Roger Jang, 12-13-94, N. Hickey 04-16-01

%   Copyright 1994-2002 The MathWorks, Inc.

%   $Revision: 1.13 $  $Date: 2002/04/14 22:20:38 $

%  %後是說明部分，從此處開始是函數定義

if nargin ~= 2 & nargin ~= 3,

 error('Too many or too few input arguments!');

end

data_n = size(data, 1);

in_n = size(data, 2);

% Change the following to set default options

default_options = [2; % exponent for the partition matrix U

  100; % max. number of iteration

  1e-5; % min. amount of improvement

  1]; % info display during iteration

if nargin == 2,

 options = default_options;

else

 % If "options" is not fully specified, pad it with default values.

 if length(options) < 4,

  tmp = default_options;

  tmp(1:length(options)) = options;

  options = tmp;

 end

 % If some entries of "options" are nan's, replace them with defaults.

 nan_index = find(isnan(options)==1);

 options(nan_index) = default_options(nan_index);

 if options(1) <= 1,

  error('The exponent should be greater than 1!');

 end

end

expo = options(1);  % Exponent for U

max_iter = options(2);  % Max. iteration

min_impro = options(3);  % Min. improvement

display = options(4);  % Display info or not

obj_fcn = zeros(max_iter, 1); % Array for objective function

U = initfcm(cluster_n, data_n);   % Initial fuzzy partition

% Main loop

for i = 1:max_iter,

 [U, center, obj_fcn(i)] = stepfcm(data, U, cluster_n, expo);

 if display,

  fprintf('Iteration count = %d, obj. fcn = %fn', i, obj_fcn(i));

 end

 % check termination condition

 if i > 1,

  if abs(obj_fcn(i) - obj_fcn(i-1)) < min_impro, break; end,

 end

end

iter_n = i; % Actual number of iterations

obj_fcn(iter_n+1:max_iter) = [];

英文看起來比較鬱悶的看中文如下

2

關於初始化子函數　　function U = initfcm(cluster_n, data_n)，  程式碼全解如下

3

下一個疊代子函數 function [U_new, center, obj_fcn] = stepfcm(data, U, cluster_n, expo)

4

下一個計算距離子函數 function out = distfcm(center, data)

5

所以這些函數都是用matlab 自帶的函數，包括子函數，你可以把所有的函數放在一個M檔案中  下面將貼出我自己的關於FCM的全碼，都是在自帶函數基礎上改的，

6

接著進行影象分割，呼叫程式碼如下，可以直接輸入在命令視窗中，這段程式碼大家要好好研究

7

下面展示下效果圖，有疊代次數，聚類中心，還有分割後的影象。大家研究下吧