computeHomography.asv

function H_3x3 = computeHomography(src_pts_nx2, dest_pts_nx2)
% construct linear system equations 

[rows,cols] = size (src_pts_nx2);

linearSystem = zeros (rows*2,9);
H = zeros(9,1);
solutions = zeros(9,1);
solutions(9,1) = 1;



for k = 1:rows
   
    xs=src_pts_nx2(k,1);
    ys=src_pts_nx2(k,2);
    xd= dest_pts_nx2(k,1);
    yd= dest_pts_nx2(k,2);
   linearSystem(k,1:3) = [-xs,-ys,-1];
   linearSystem(k,4:6) = 0;
   linearSystem(k,7:9) = [xs*xd,ys*xd,xd];

   linearSystem(k+1,4:6) = [-xs,-ys,-1];
   linearSystem(k+1,1:3) = 0;
   linearSystem(k+1,7:9) = [xs*yd,ys*yd,yd];
end
% solve through least square 
trans = transepose(linearSystem);
H = inv(trans*linearSystem)

H_3x3 = zeros(3,3);
H = transpose(H);
H_3x3(1,:) = H(1,1:3);
H_3x3(2,:) = H(1,4:6);
H_3x3(3,:) = H(1,7:9);