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# 3D to 2D calibration matrix matlab

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Camera calibration involves finding the geometric relationship between 3D world
coordinates and their 2D projected positions in the image.
i need to write a code that can do the above in MATLAB, there is a tool in matlab that does this, but can't use it, need to code the function.
picking up 3d coordinates from the image and then picking up 2d coordinates and calibrating them to ensure the function ran correctly.
Task 2 involves transformation of the image using DLT algorithm.
i cant copy the code available online due to plagiarism issues.

##### Additional Instructions:

% CLAB3
%
I = imread('stereo2012a.jpg');
imshow(I);
display('click mouse for 6 features...')
uv = ginput(6); % Graphical user interface to get 6 points
display(uv);
function C = calibrate(im, XYZ, uv)
%% TASK 1: CALIBRATE
%
% Function to perform camera calibration
%
% Usage: K = calibrate(image, XYZ, uv)
%
% Where: image - is the image of the calibration target.
% XYZ - is a N x 3 array of XYZ coordinates
% of the calibration target points.
% uv - is a N x 2 array of the image coordinates
% of the calibration target points.
% K - is the 3 x 4 camera calibration matrix.
% The variable N should be an integer greater than or equal to 6.
%
% This function plots the uv coordinates onto the image of the calibration
% target.
%
% It also projects the XYZ coordinates back into image coordinates using
% the calibration matrix and plots these points too as
% a visual check on the accuracy of the calibration process.
%
% Lines from the origin to the vanishing points in the X, Y and Z
% directions are overlaid on the image.
%
% The mean squared error between the positions of the uv coordinates
% and the projected XYZ coordinates is also reported.
%
% The function should also report the error in satisfying the
% camera calibration matrix constraints.
end
function H = homography(u2Trans, v2Trans, uBase, vBase)
%% TASK 2:
% Computes the homography H applying the Direct Linear Transformation
% The transformation is such that
% p = H p' , i.e.,:
% (uBase, vBase, 1)'=H*(u2Trans , v2Trans, 1)'
%
% INPUTS:
% u2Trans, v2Trans - vectors with coordinates u and v of the transformed image point (p')
% uBase, vBase - vectors with coordinates u and v of the original base image point p
%
% OUTPUT
% H - a 3x3 Homography matrix
%
% your name, date
end
function [R,Q] = rq(A)
%% RQ factorisation
[q,r]=qr(A'); % Matlab has QR decomposition but not RQ decomposition
% with Q: orthonormal and R: upper triangle. Apply QR
% for the A-transpose, then A = (qr)^T = r^T*q^T = RQ
R=r';
Q=q';
end

%VGG_KR_FROM_P Extract K, R from camera matrix.
%
% [K,R,t] = VGG_KR_FROM_P(P [,noscale]) finds K, R, t such that P = K*R*[eye(3) -t].
% It is det(R)==1.
% K is scaled so that K(3,3)==1 and K(1,1)>0. Optional parameter noscale prevents this.
%
% Works also generally for any P of size N-by-(N+1).
% Works also for P of size N-by-N, then t is not computed.
% Author: Andrew Fitzgibbon
% Modified by werner.
% Date: 15 May 98
function [K, R, t] = vgg_KR_from_P(P, noscale)
N = size(P,1);
H = P(:,1:N);
[K,R] = vgg_rq(H);
if nargin < 2
K = K / K(N,N);
if K(1,1) < 0
D = diag([-1 -1 ones(1,N-2)]);
K = K * D;
R = D * R;
% test = K*R;
% vgg_assert0(test/test(1,1) - H/H(1,1), 1e-07)
end
end
if nargout > 2
t = -P(:,1:N)\P(:,end);
end
return

% [R,Q] = vgg_rq(S) Just like qr but the other way around.
%
% If [R,Q] = vgg_rq(X), then R is upper-triangular, Q is orthogonal, and X==R*Q.
% Moreover, if S is a real matrix, then det(Q)>0.
% By awf
function [U,Q] = rq(S)
S = S';
[Q,U] = qr(S(end:-1:1,end:-1:1));
Q = Q';
Q = Q(end:-1:1,end:-1:1);
U = U';
U = U(end:-1:1,end:-1:1);
if det(Q)

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