% This function BCFCM3D, segments (clusters) an imagevolume in object classes,
% and estimates the bias field.
%
% It's an implementation of the paper of M.N. Ahmed et. al. "A Modified Fuzzy
% C-Means Algorithm for Bias Field estimation and Segmentation of MRI Data"
% 20002, IEEE Transactions on medical imaging.
%
% [B,U]=BCFCM3D(Y,v,Options)
%
% Inputs,
% Y : The 3D greyscale input image of data-type Single
% v : Class prototypes. A vector with approximations of the greyscale
% means of all image classes. It is also possible to set values
% further away from the mean to allow better class separation.
% Options : A struct with options
% Options.epsilon : The function stops if difference between class means
% of two itterations is smaller than epsilon
% Options.alpha : Scales the effect of neighbours, must be large if
% it is a noisy image, default 1.
% Options.maxit : Maximum number of function itterations
% Options.sigma : Sigma of Gaussian smoothing of the bias field (slow
% varying non uniform illumination in CT or MRI scan).
% Options.p : Norm constant FCM objective function, must be larger than one
% defaults to 2.
% Outputs,
% B : The estimated bias field
% U : Fuzzy Partition matrix (Class membership)
%
% Example,
%
% % Compile the c-code
% mex BCFCM3D.c -v
% % Load test volume
% load MRI;
% % Convert to single
% D = single(squeeze(D))/88;
% % Class prototypes (means)
% v = [0 0.34 0.72 0.75 1.4];
% % Do the fuzzy clustering
% [B,U]=BCFCM3D(D,v,struct('maxit',5,'epsilon',1e-5,'sigma',1));
% % Show results
% figure,
% subplot(2,2,1), imshow(D(:,:,15)), title('A slice of input volume');
% subplot(2,2,2), imshow(squeeze(U(:,:,15,2:4))), title('3 classes of the partition matrix');
% subplot(2,2,3), imshow(B(:,:,15),[]), title('Estimated biasfield');
% subplot(2,2,4), imshow(D(:,:,15)-B(:,:,15)), title('Corrected slice');
%
% Function is written by D.Kroon University of Twente (November 2009)
