功能描述：
function [ux,uy,uz]=LK3D( image1, image2, r )
%This function estimates deformations between two subsequent 3-D images
%using Lucas-Kanade optical flow equation.
%
% Description :
%
% -image1, image2 : two subsequent images or frames
% -r : radius of the neighbourhood, default value is 2.
%
% Reference :
% Lucas, B. D., Kanade, T., 1981. An iterative image registration
% technique with an application to stereo vision. In: Proceedings of the
% 7th international joint conference on Artificial intelligence - Volume 2.
% Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, pp. 674-679.
%
% Author : Mohammad Mustafa
% By courtesy of The University of Nottingham and Mirada Medical Limited,
% Oxford, UK
%
% Published under a Creative Commons Attribution-Non-Commercial-Share Alike
% 3.0 Unported Licence http://creativecommons.org/licenses/by-nc-sa/3.0/
%
% June 2012
% Default parameter
if nargin==2
r=2;
end
[height,width,depth]=size(image1);
image1=im2double(image1);
image2=im2double(image2);
% Initializing flow vectors
ux=zeros(size(image1)); uy=ux; uz=ux;
% Computing image derivatives
[Ix,Iy,Iz,It]=imageDerivatives3D(image1,image2);
for i=(r+1):(height-r)
for j=(r+1):(width-r)
for k=(r+1):(depth-r)
blockofIx=Ix(i-r:i+r,j-r:j+r,k-r:k+r);
blockofIy=Iy(i-r:i+r,j-r:j+r,k-r:k+r);
blockofIz=Iz(i-r:i+r,j-r:j+r,k-r:k+r);
blockofIt=It(i-r:i+r,j-r:j+r,k-r:k+r);
A=zeros(3,3);
B=zeros(3,1);
A(1,1)=sum(sum(sum(blockofIx.^2)));
A(1,2)=sum(sum(sum(blockofIx.*blockofIy)));
A(1,3)=sum(sum(sum(blockofIx.*blockofIz)));
A(2,1)=sum(sum(sum(blockofIy.*blockofIx)));
A(2,2)=sum(sum(sum(blockofIy.^2)));
A(2,3)=sum(sum(sum(blockofIy.*blockofIz)));
A(3,1)=sum(sum(sum(blockofIz.*blockofIx)));
A(3,2)=sum(sum(sum(blockofIz.*blockofIy)));
A(3,3)=sum(sum(sum(blockofIz.^2)));
B(1,1)=sum(sum(sum(blockofIx.*blockofIt)));
B(2,1)=sum(sum(sum(blockofIy.*blockofIt)));
B(3,1)=sum(sum(sum(blockofIz.*blockofIt)));
invofA=pinv(A);
V=invofA*(-B);
ux(i,j,k)=V(1,1);
uy(i,j,k)=V(2,1);
uz(i,j,k)=V(3,1);
end
end
end
end
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