图像配准算法，可以进行精确的运动估计

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%  Name: Musawir Ali Shah
%%%  Assignment #3
%%%  Project Title: Lucas Kanade Motion Estimation Using Pyramids (Level 4)
%%%  Note: The project specification says use density of 10 in plotting
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Usage: Lucas_Kanade('1.bmp','2.bmp',10)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Lucas_Kanade(file1,file2,density);
%% Read Images %%
img1 = im2double (imread (file1));%%将图像矩阵转换为双精度类型
%% Take alternating rows and columns %%
[odd1, even1] = split (img1);
img2 = im2double (imread (file2));
[odd2, even2] = split (img2);
%% Run Lucas Kanade %%
[Dx, Dy] = Estimate (odd1, odd2);
%% Plot %%
figure; 
[maxI,maxJ]=size(Dx);
Dx=Dx(1:density:maxI,1:density:maxJ);
Dy=Dy(1:density:maxI,1:density:maxJ);
quiver(1:density:maxJ,(maxI):(-density):1,Dx,-Dy,1);%%quiver(X,Y,U,V)在指定点绘制速度向量图。参量X，Y，U，V为同维矩阵或同维向量。X,Y表示指定点坐标，U,V表示含有响应的速度分量。 
axis square;


%% Run Lucas Kanade on all levels and interpolate %%
function [Dx, Dy] = Estimate (img1, img2)

level = 4;
half_window_size=2;
[m, n] = size (img1);
G00 = img1; G10 = img2;
if (level>0)
    G01 = reduce (G00); G11 = reduce (G10);
end
if (level>1)
    G02 = reduce (G01); G12 = reduce (G11);
end
if (level>2)
    G03 = reduce (G02); G13 = reduce (G12);
end
if (level>3)
    G04 = reduce (G03); G14 = reduce (G13);
end
l = level;

for i=level:-1:0,
    if (l == level)
        switch (l)
        case 4, Dx = zeros (size (G04)); Dy = zeros (size (G04));
        case 3, Dx = zeros (size (G03)); Dy = zeros (size (G03));
        case 2, Dx = zeros (size (G02)); Dy = zeros (size (G02));
        case 1, Dx = zeros (size (G01)); Dy = zeros (size (G01));
        case 0, Dx = zeros (size (G00)); Dy = zeros (size (G00));
        end
    else
        Dx = expand (Dx); Dy = expand (Dy);
        Dx = Dx .* 2; Dy = Dy .* 2;