Homography Matrix

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Tejas Kulkarni 2012-1-15

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编辑： Matt J 2022-4-26

Can somebody please help me in understanding how to calculate an homography matrix in matlab.

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Lalit Patil 2013-1-22

I am finding homography matrix in another way and it is 3*3

So, i want to know that in image where to apply or what to do of this homography matrix.?

Why we are finding this matrix..?

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回答（2 个）

David Young 2012-1-15

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You don't say what you are starting from. If you have a set of matched input and output points, one possible method is given here. A simple implementation is below.

function v = homography_solve(pin, pout)
% HOMOGRAPHY_SOLVE finds a homography from point pairs
%   V = HOMOGRAPHY_SOLVE(PIN, POUT) takes a 2xN matrix of input vectors and
%   a 2xN matrix of output vectors, and returns the homogeneous
%   transformation matrix that maps the inputs to the outputs, to some
%   approximation if there is noise.
%
%   This uses the SVD method of
%   http://www.robots.ox.ac.uk/%7Evgg/presentations/bmvc97/criminispaper/node3.html
% David Young, University of Sussex, February 2008
if ~isequal(size(pin), size(pout))
    error('Points matrices different sizes');
end
if size(pin, 1) ~= 2
    error('Points matrices must have two rows');
end
n = size(pin, 2);
if n < 4
    error('Need at least 4 matching points');
end
% Solve equations using SVD
x = pout(1, :); y = pout(2,:); X = pin(1,:); Y = pin(2,:);
rows0 = zeros(3, n);
rowsXY = -[X; Y; ones(1,n)];
hx = [rowsXY; rows0; x.*X; x.*Y; x];
hy = [rows0; rowsXY; y.*X; y.*Y; y];
h = [hx hy];
if n == 4
    [U, ~, ~] = svd(h);
else
    [U, ~, ~] = svd(h, 'econ');
end
v = (reshape(U(:,9), 3, 3)).';
end

If your initial data is in some other form, such as camera position parameters relative to the plane, please say.

EDIT - added:

To apply the resulting matrix to a set of points, you can use the following function.

function y = homography_transform(x, v)
% HOMOGRAPHY_TRANSFORM applies homographic transform to vectors
%   Y = HOMOGRAPHY_TRANSFORM(X, V) takes a 2xN matrix, each column of which
%   gives the position of a point in a plane. It returns a 2xN matrix whose
%   columns are the input vectors transformed according to the homography
%   V, represented as a 3x3 homogeneous matrix.
q = v * [x; ones(1, size(x,2))];
p = q(3,:);
y = [q(1,:)./p; q(2,:)./p];
end