%B. Vandeportaele
%script to achieve symbolic computation of the jacobian
% du2/dHij
% dv2/dHij
% Hij being the coefficients of the homography such as
% w.u2       u1
% w.v2 = H . v1
%   w.        1
clear all

param=1

h11=sym('h11','real');h12=sym('h12','real');h13=sym('h13','real');
h21=sym('h21','real');h22=sym('h22','real');h23=sym('h23','real');
h31=sym('h31','real');h32=sym('h32','real');h33=sym('h33','real');
%possibly use 2 parameterization for the homography, h33 may be set to 1
if param==0
    H=[h11 h12 h13; h21 h22 h23;h31 h32 h33]
else
    H=[h11 h12 h13; h21 h22 h23;h31 h32 1]
end

u1=sym('u1','real');
v1=sym('v1','real');

P1=[u1;v1;1];
%apply the homography
P2=H*P1
%deshomogeneization
u2=P2(1,:)/P2(3,:)
v2=P2(2,:)/P2(3,:)
%compute the jacobians
if param==0
    J=jacobian ([u2, v2], [h11, h12, h13, h21, h22, h23, h31, h32, h33])
else
    J=jacobian ([u2, v2], [h11, h12, h13, h21, h22, h23, h31, h32])
end