metric_rect1.m

function H = metric_rect(Iin,out_string)
%=========================================================================%
% The funtion performs Metric rectification on a given image and then 
% outputs the resulting image.
% Specs: H = Required Projective transformation for metric rectification
% Iin = imread of the image to be input
% out_string = desired filename of the output image
%=========================================================================%

%==========================Step 1========================================%
% to locate the pair of orthogonal lines on the world plane....
figure(1)
imshow(Iin)
title('Select 2 pairs of orthogonal lines from the image below by using mouse')
xlabel('Press enter once done')
[x,y] = getpts;
close Figure 1
% assigning variables...
l11 = x(1)
l12 = y(1)
l21 = x(3)
l22 = y(3)
m11 = x(2)
m12 = y(2)
m21 = x(4)
m22 = y(4)
%==========================Step 2========================================%
% Defining variables to find S
M = [l11*m11 (l11*m12 + l12*m11) ; l21*m21 (l21*m22 + l22*m21)]
b = [-l12*m12;-l22*m22 ]
% solving for the linear constraint on 2 × 2 matrix S...
x = linsolve(M,b)
% defining S....
S = eye(2)
S(1,1) = x(1)
S(1,2) = x(2)
S(2,1) = x(2)
%==========================Step 3========================================%
% obtaining a suitable rectifying homography....
[U,D,V] = svd(S)
sqrtD = sqrt(D)
U_T = transpose(U)
A = U_T*sqrtD
A = A*V
H2 = eye(3)
H2(1,1) = A(1,1)
H2(1,2) = A(1,2)
H2(2,1) = A(2,1)
H2(2,2) = A(2,2)
if H2(1,1) < 0
    H2(1,1) = -H2(1,1)

elseif H2(2,2) < 0
    H2(2,2) = -H2(2,2)
end
H = H2'
%==========================Step 4========================================%

temp = maketform('projective',H)
Iout = imtransform(Iin, temp);
myout = imshow(Iout) % required metric rectified image...
saveas(myout,out_string)
end