function [ H] = compute2DHomographyUsingDLT( p1,p2)
%B. Vandeportaele
%compute the Homography H using the DLT Algorithm for 4 2D points 
%correspondences such as : p2=H.p1
u11=p1(1,1);u12=p1(1,2);
u13=p1(1,3);u14=p1(1,4);
v11=p1(2,1);v12=p1(2,2);
v13=p1(2,3);v14=p1(2,4);

u21=p2(1,1);u22=p2(1,2);
u23=p2(1,3);u24=p2(1,4);
v21=p2(2,1);v22=p2(2,2);
v23=p2(2,3);v24=p2(2,4);

A=[ -u11, -v11, -1,    0,    0,  0, u11*u21, u21*v11;
    0,    0,  0, -u11, -v11, -1, u11*v21, v21*v11;
    -u12, -v12, -1,    0,    0,  0, u12*u22, u22*v12;
    0,    0,  0, -u12, -v12, -1, u12*v22, v22*v12;
    -u13, -v13, -1,    0,    0,  0, u13*u23, u23*v13;
    0,    0,  0, -u13, -v13, -1, u13*v23, v23*v13;
    -u14, -v14, -1,    0,    0,  0, u14*u24, u24*v14;
    0,    0,  0, -u14, -v14, -1, u14*v24, v24*v14];
B =[ -u21; -v21; -u22; -v22; -u23; -v23; -u24; -v24];
%solve A*Hv=B
Hv=inv(A)*B;
%reconstruct the homography matrix from the vector solution
H=[Hv(1:3)';Hv(4:6)';Hv(7:8)',1];
end