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grassmannianRepresentationSingle.m
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grassmannianRepresentationSingle.m
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%
% {GrassGraph Algorithm, used to perform affine invariant feature matching.}
% Copyright (C) {2016} {Mark Moyou}
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
%
% mmoyou@my.fit.edu
% Information Characterization and Exploitation (ICE) Lab
% ------------------------------------------------------------------------------
function UX = grassmannianRepresentationSingle(X)
% [UX, UY] = grassmannianRepresentation(X, Y)
% The number of points in X and Y are equal in this version of the
% GrassGraphs algorithm, so npX = npY.
[npX, nDim] = size(X); % Number of points in X.
% Add homogeneous representation to X and Y.
hX = [X ones(npX,1)];
% Compute the svd of hX and hY.
[UX, ~, ~] = svd(hX);
% Choose the first D+1 columns of U.
UX = UX(:,1:nDim + 1);