/usr/share/octave/site/m/vlfeat/toolbox/imop/vl_tps.m is in octave-vlfeat 0.9.17+dfsg0-6build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | function [phi,S] = vl_tps(x1,x2,Y)
% VL_TPS Compute the thin-plate spline basis
% PHI=VL_TPS(X1,X2,Y) returns the basis PHI of a thin-plate spline
% (TPS) defined on the domain X1,X2 with control points Y.
%
% X1 and X2 are MxN matrices specifying the grid vertices. When
% warping images, these usually correspond to image pixels.
%
% Y is a 2xK matrix specifying the control points, one per
% column. Ofthen Y is a subset of the domain X1,X2, but this is not
% required.
%
% PHI is a (K+3)xNxM matrix, with one layer per basis element. Each
% basis element is a function of the domain X1,X2.
%
% [PHI,S] = VL_TPS(X1,X2,Y) additionally returns the stiffness matrix S
% of the TPS.
%
% See also: VL_WTPS(), VL_HELP().
% Copyright (C) 2007-12 Andrea Vedaldi and Brian Fulkerson.
% All rights reserved.
%
% This file is part of the VLFeat library and is made available under
% the terms of the BSD license (see the COPYING file).
X = [x1(:)';x2(:)'] ;
K = size(Y,2) ;
Q = size(X,2) ;
U = vl_tpsu(Y,Y) ;
L = [[ones(1,K); Y], zeros(3) ; U, ones(K,1), Y'] ;
invL = inv(L) ;
tmp = vl_tpsu(Y,X) ;
phi = invL * [ ones(1,Q) ; X(1,:) ; X(2,:) ; tmp ] ;
[M,N] = size(x1) ;
phi = reshape(phi,K+3,M,N) ;
if nargout > 1
% See Bookstein; note that here the terms are re-arranged a bit
invLn = invL(1:K, end-K+1:end) ;
S = invLn * U * invLn ;
end
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