/
ft_warp_apply.m
207 lines (189 loc) · 13.8 KB
/
ft_warp_apply.m
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function [output] = ft_warp_apply(M, input, method, tol)
% FT_WARP_APPLY performs a 3D linear or nonlinear transformation on the input
% coordinates, similar to those in AIR. You can find technical documentation
% on warping in general at http://air.bmap.ucla.edu/AIR5
%
% Use as
% [output] = ft_warp_apply(M, input, method, tol)
% where
% M vector or matrix with warping parameters
% input Nx3 matrix with input coordinates
% output Nx3 matrix with the transformed or warped output coordinates
% method string describing the transformation or warping method
% tol (optional) value determining the numerical precision of the
% output, to deal with numerical round-off imprecisions due to
% the warping
%
% The methods 'nonlin0', 'nonlin2' ... 'nonlin5' specify a polynomial transformation.
% The size of the transformation matrix depends on the order of the warp
% zeroth order : 1 parameter per coordinate (translation)
% first order : 4 parameters per coordinate (total 12, affine)
% second order : 10 parameters per coordinate
% third order : 20 parameters per coordinate
% fourth order : 35 parameters per coordinate
% fifth order : 56 parameters per coordinate (total 168)
% The size of M should be 3xP, where P is the number of parameters per coordinate.
% Alternatively, you can specify the method to be 'nonlinear', in which case the
% order will be determined from the size of the matrix M.
%
% If the method 'homogeneous' is selected, the input matrix M should be a 4x4
% homogenous transformation matrix.
%
% If the method 'sn2individual' or 'individual2sn' is selected, the input M should be
% a structure with the nonlinear spatial normalisation (warping) parameters created
% by SPM8 or SPM12 for alignment between an individual subject and a template brain.
% When using the 'old' method, M will have subfields like this:
% Affine: [4x4 double]
% Tr: [4-D double]
% VF: [1x1 struct]
% VG: [1x1 struct]
% flags: [1x1 struct]
% When using the 'new' or the 'mars' method, M will have subfields like this:
%
% If any other method is selected, it is assumed that it specifies the name of an
% auxiliary function that will, when given the input parameter vector M, return an
% 4x4 homogenous transformation matrix. Supplied functions are 'translate', 'rotate',
% 'scale', 'rigidbody', 'globalrescale', 'traditional', 'affine', 'perspective',
% 'quaternion'.
%
% See also FT_AFFINECOORDINATES, FT_HEADCOORDINATES, FT_WARP_OPTIM, FT_WARP_ERROR,
% MAKETFORM, AFFINE2D, AFFINE3D
% Copyright (C) 2000-2022, Robert Oostenveld
%
% This file is part of FieldTrip, see http://www.fieldtriptoolbox.org
% for the documentation and details.
%
% FieldTrip 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.
%
% FieldTrip 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 FieldTrip. If not, see <http://www.gnu.org/licenses/>.
%
% $Id$
if nargin<4
tol = [];
end
if nargin<3 && all(size(M)==4)
% no specific transformation mode has been selected
% it looks like a homogenous transformation matrix
method = 'homogeneous';
elseif nargin<3
% the default method is 'nonlinear'
method = 'nonlinear';
end
if size(input,2)==2
% convert the input points from 2D to 3D representation
input(:,3) = 0;
input3d = false;
else
input3d = true;
end
if isequal(size(input), [3 1])
% transpose the input
input = input';
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% nonlinear warping
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if any(strcmp(method, {'nonlinear', 'nonlin0', 'nonlin1', 'nonlin2', 'nonlin3', 'nonlin4', 'nonlin5'}))
x = input(:,1);
y = input(:,2);
z = input(:,3);
s = size(M);
if s(1)~=3
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin0') && s(2)~=1
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin1') && s(2)~=4
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin2') && s(2)~=10
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin3') && s(2)~=20
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin4') && s(2)~=35
ft_error('invalid size of nonlinear transformation matrix');
elseif strcmp(method, 'nonlin5') && s(2)~=56
ft_error('invalid size of nonlinear transformation matrix');
end
if s(2)==1
% this is a translation, which in a strict sense is not the 0th order nonlinear transformation
xx = M(1,1) + x;
yy = M(2,1) + y;
zz = M(3,1) + z;
elseif s(2)==4
xx = M(1,1) + M(1,2)*x + M(1,3)*y + M(1,4)*z;
yy = M(2,1) + M(2,2)*x + M(2,3)*y + M(2,4)*z;
zz = M(3,1) + M(3,2)*x + M(3,3)*y + M(3,4)*z;
elseif s(2)==10
xx = M(1,1) + M(1,2)*x + M(1,3)*y + M(1,4)*z + M(1,5)*x.*x + M(1,6)*x.*y + M(1,7)*x.*z + M(1,8)*y.*y + M(1,9)*y.*z + M(1,10)*z.*z;
yy = M(2,1) + M(2,2)*x + M(2,3)*y + M(2,4)*z + M(2,5)*x.*x + M(2,6)*x.*y + M(2,7)*x.*z + M(2,8)*y.*y + M(2,9)*y.*z + M(2,10)*z.*z;
zz = M(3,1) + M(3,2)*x + M(3,3)*y + M(3,4)*z + M(3,5)*x.*x + M(3,6)*x.*y + M(3,7)*x.*z + M(3,8)*y.*y + M(3,9)*y.*z + M(3,10)*z.*z;
elseif s(2)==20
xx = M(1,1) + M(1,2)*x + M(1,3)*y + M(1,4)*z + M(1,5)*x.*x + M(1,6)*x.*y + M(1,7)*x.*z + M(1,8)*y.*y + M(1,9)*y.*z + M(1,10)*z.*z + M(1,11)*x.*x.*x + M(1,12)*x.*x.*y + M(1,13)*x.*x.*z + M(1,14)*x.*y.*y + M(1,15)*x.*y.*z + M(1,16)*x.*z.*z + M(1,17)*y.*y.*y + M(1,18)*y.*y.*z + M(1,19)*y.*z.*z + M(1,20)*z.*z.*z;
yy = M(2,1) + M(2,2)*x + M(2,3)*y + M(2,4)*z + M(2,5)*x.*x + M(2,6)*x.*y + M(2,7)*x.*z + M(2,8)*y.*y + M(2,9)*y.*z + M(2,10)*z.*z + M(2,11)*x.*x.*x + M(2,12)*x.*x.*y + M(2,13)*x.*x.*z + M(2,14)*x.*y.*y + M(2,15)*x.*y.*z + M(2,16)*x.*z.*z + M(2,17)*y.*y.*y + M(2,18)*y.*y.*z + M(2,19)*y.*z.*z + M(2,20)*z.*z.*z;
zz = M(3,1) + M(3,2)*x + M(3,3)*y + M(3,4)*z + M(3,5)*x.*x + M(3,6)*x.*y + M(3,7)*x.*z + M(3,8)*y.*y + M(3,9)*y.*z + M(3,10)*z.*z + M(3,11)*x.*x.*x + M(3,12)*x.*x.*y + M(3,13)*x.*x.*z + M(3,14)*x.*y.*y + M(3,15)*x.*y.*z + M(3,16)*x.*z.*z + M(3,17)*y.*y.*y + M(3,18)*y.*y.*z + M(3,19)*y.*z.*z + M(3,20)*z.*z.*z;
elseif s(2)==35
xx = M(1,1) + M(1,2)*x + M(1,3)*y + M(1,4)*z + M(1,5)*x.*x + M(1,6)*x.*y + M(1,7)*x.*z + M(1,8)*y.*y + M(1,9)*y.*z + M(1,10)*z.*z + M(1,11)*x.*x.*x + M(1,12)*x.*x.*y + M(1,13)*x.*x.*z + M(1,14)*x.*y.*y + M(1,15)*x.*y.*z + M(1,16)*x.*z.*z + M(1,17)*y.*y.*y + M(1,18)*y.*y.*z + M(1,19)*y.*z.*z + M(1,20)*z.*z.*z + M(1,21)*x.*x.*x.*x + M(1,22)*x.*x.*x.*y + M(1,23)*x.*x.*x.*z + M(1,24)*x.*x.*y.*y + M(1,25)*x.*x.*y.*z + M(1,26)*x.*x.*z.*z + M(1,27)*x.*y.*y.*y + M(1,28)*x.*y.*y.*z + M(1,29)*x.*y.*z.*z + M(1,30)*x.*z.*z.*z + M(1,31)*y.*y.*y.*y + M(1,32)*y.*y.*y.*z + M(1,33)*y.*y.*z.*z + M(1,34)*y.*z.*z.*z + M(1,35)*z.*z.*z.*z;
yy = M(2,1) + M(2,2)*x + M(2,3)*y + M(2,4)*z + M(2,5)*x.*x + M(2,6)*x.*y + M(2,7)*x.*z + M(2,8)*y.*y + M(2,9)*y.*z + M(2,10)*z.*z + M(2,11)*x.*x.*x + M(2,12)*x.*x.*y + M(2,13)*x.*x.*z + M(2,14)*x.*y.*y + M(2,15)*x.*y.*z + M(2,16)*x.*z.*z + M(2,17)*y.*y.*y + M(2,18)*y.*y.*z + M(2,19)*y.*z.*z + M(2,20)*z.*z.*z + M(2,21)*x.*x.*x.*x + M(2,22)*x.*x.*x.*y + M(2,23)*x.*x.*x.*z + M(2,24)*x.*x.*y.*y + M(2,25)*x.*x.*y.*z + M(2,26)*x.*x.*z.*z + M(2,27)*x.*y.*y.*y + M(2,28)*x.*y.*y.*z + M(2,29)*x.*y.*z.*z + M(2,30)*x.*z.*z.*z + M(2,31)*y.*y.*y.*y + M(2,32)*y.*y.*y.*z + M(2,33)*y.*y.*z.*z + M(2,34)*y.*z.*z.*z + M(2,35)*z.*z.*z.*z;
zz = M(3,1) + M(3,2)*x + M(3,3)*y + M(3,4)*z + M(3,5)*x.*x + M(3,6)*x.*y + M(3,7)*x.*z + M(3,8)*y.*y + M(3,9)*y.*z + M(3,10)*z.*z + M(3,11)*x.*x.*x + M(3,12)*x.*x.*y + M(3,13)*x.*x.*z + M(3,14)*x.*y.*y + M(3,15)*x.*y.*z + M(3,16)*x.*z.*z + M(3,17)*y.*y.*y + M(3,18)*y.*y.*z + M(3,19)*y.*z.*z + M(3,20)*z.*z.*z + M(3,21)*x.*x.*x.*x + M(3,22)*x.*x.*x.*y + M(3,23)*x.*x.*x.*z + M(3,24)*x.*x.*y.*y + M(3,25)*x.*x.*y.*z + M(3,26)*x.*x.*z.*z + M(3,27)*x.*y.*y.*y + M(3,28)*x.*y.*y.*z + M(3,29)*x.*y.*z.*z + M(3,30)*x.*z.*z.*z + M(3,31)*y.*y.*y.*y + M(3,32)*y.*y.*y.*z + M(3,33)*y.*y.*z.*z + M(3,34)*y.*z.*z.*z + M(3,35)*z.*z.*z.*z;
elseif s(2)==56
xx = M(1,1) + M(1,2)*x + M(1,3)*y + M(1,4)*z + M(1,5)*x.*x + M(1,6)*x.*y + M(1,7)*x.*z + M(1,8)*y.*y + M(1,9)*y.*z + M(1,10)*z.*z + M(1,11)*x.*x.*x + M(1,12)*x.*x.*y + M(1,13)*x.*x.*z + M(1,14)*x.*y.*y + M(1,15)*x.*y.*z + M(1,16)*x.*z.*z + M(1,17)*y.*y.*y + M(1,18)*y.*y.*z + M(1,19)*y.*z.*z + M(1,20)*z.*z.*z + M(1,21)*x.*x.*x.*x + M(1,22)*x.*x.*x.*y + M(1,23)*x.*x.*x.*z + M(1,24)*x.*x.*y.*y + M(1,25)*x.*x.*y.*z + M(1,26)*x.*x.*z.*z + M(1,27)*x.*y.*y.*y + M(1,28)*x.*y.*y.*z + M(1,29)*x.*y.*z.*z + M(1,30)*x.*z.*z.*z + M(1,31)*y.*y.*y.*y + M(1,32)*y.*y.*y.*z + M(1,33)*y.*y.*z.*z + M(1,34)*y.*z.*z.*z + M(1,35)*z.*z.*z.*z + M(1,36)*x.*x.*x.*x.*x + M(1,37)*x.*x.*x.*x.*y + M(1,38)*x.*x.*x.*x.*z + M(1,39)*x.*x.*x.*y.*y + M(1,40)*x.*x.*x.*y.*z + M(1,41)*x.*x.*x.*z.*z + M(1,42)*x.*x.*y.*y.*y + M(1,43)*x.*x.*y.*y.*z + M(1,44)*x.*x.*y.*z.*z + M(1,45)*x.*x.*z.*z.*z + M(1,46)*x.*y.*y.*y.*y + M(1,47)*x.*y.*y.*y.*z + M(1,48)*x.*y.*y.*z.*z + M(1,49)*x.*y.*z.*z.*z + M(1,50)*x.*z.*z.*z.*z + M(1,51)*y.*y.*y.*y.*y + M(1,52)*y.*y.*y.*y.*z + M(1,53)*y.*y.*y.*z.*z + M(1,54)*y.*y.*z.*z.*z + M(1,55)*y.*z.*z.*z.*z + M(1,56)*z.*z.*z.*z.*z;
yy = M(2,1) + M(2,2)*x + M(2,3)*y + M(2,4)*z + M(2,5)*x.*x + M(2,6)*x.*y + M(2,7)*x.*z + M(2,8)*y.*y + M(2,9)*y.*z + M(2,10)*z.*z + M(2,11)*x.*x.*x + M(2,12)*x.*x.*y + M(2,13)*x.*x.*z + M(2,14)*x.*y.*y + M(2,15)*x.*y.*z + M(2,16)*x.*z.*z + M(2,17)*y.*y.*y + M(2,18)*y.*y.*z + M(2,19)*y.*z.*z + M(2,20)*z.*z.*z + M(2,21)*x.*x.*x.*x + M(2,22)*x.*x.*x.*y + M(2,23)*x.*x.*x.*z + M(2,24)*x.*x.*y.*y + M(2,25)*x.*x.*y.*z + M(2,26)*x.*x.*z.*z + M(2,27)*x.*y.*y.*y + M(2,28)*x.*y.*y.*z + M(2,29)*x.*y.*z.*z + M(2,30)*x.*z.*z.*z + M(2,31)*y.*y.*y.*y + M(2,32)*y.*y.*y.*z + M(2,33)*y.*y.*z.*z + M(2,34)*y.*z.*z.*z + M(2,35)*z.*z.*z.*z + M(2,36)*x.*x.*x.*x.*x + M(2,37)*x.*x.*x.*x.*y + M(2,38)*x.*x.*x.*x.*z + M(2,39)*x.*x.*x.*y.*y + M(2,40)*x.*x.*x.*y.*z + M(2,41)*x.*x.*x.*z.*z + M(2,42)*x.*x.*y.*y.*y + M(2,43)*x.*x.*y.*y.*z + M(2,44)*x.*x.*y.*z.*z + M(2,45)*x.*x.*z.*z.*z + M(2,46)*x.*y.*y.*y.*y + M(2,47)*x.*y.*y.*y.*z + M(2,48)*x.*y.*y.*z.*z + M(2,49)*x.*y.*z.*z.*z + M(2,50)*x.*z.*z.*z.*z + M(2,51)*y.*y.*y.*y.*y + M(2,52)*y.*y.*y.*y.*z + M(2,53)*y.*y.*y.*z.*z + M(2,54)*y.*y.*z.*z.*z + M(2,55)*y.*z.*z.*z.*z + M(2,56)*z.*z.*z.*z.*z;
zz = M(3,1) + M(3,2)*x + M(3,3)*y + M(3,4)*z + M(3,5)*x.*x + M(3,6)*x.*y + M(3,7)*x.*z + M(3,8)*y.*y + M(3,9)*y.*z + M(3,10)*z.*z + M(3,11)*x.*x.*x + M(3,12)*x.*x.*y + M(3,13)*x.*x.*z + M(3,14)*x.*y.*y + M(3,15)*x.*y.*z + M(3,16)*x.*z.*z + M(3,17)*y.*y.*y + M(3,18)*y.*y.*z + M(3,19)*y.*z.*z + M(3,20)*z.*z.*z + M(3,21)*x.*x.*x.*x + M(3,22)*x.*x.*x.*y + M(3,23)*x.*x.*x.*z + M(3,24)*x.*x.*y.*y + M(3,25)*x.*x.*y.*z + M(3,26)*x.*x.*z.*z + M(3,27)*x.*y.*y.*y + M(3,28)*x.*y.*y.*z + M(3,29)*x.*y.*z.*z + M(3,30)*x.*z.*z.*z + M(3,31)*y.*y.*y.*y + M(3,32)*y.*y.*y.*z + M(3,33)*y.*y.*z.*z + M(3,34)*y.*z.*z.*z + M(3,35)*z.*z.*z.*z + M(3,36)*x.*x.*x.*x.*x + M(3,37)*x.*x.*x.*x.*y + M(3,38)*x.*x.*x.*x.*z + M(3,39)*x.*x.*x.*y.*y + M(3,40)*x.*x.*x.*y.*z + M(3,41)*x.*x.*x.*z.*z + M(3,42)*x.*x.*y.*y.*y + M(3,43)*x.*x.*y.*y.*z + M(3,44)*x.*x.*y.*z.*z + M(3,45)*x.*x.*z.*z.*z + M(3,46)*x.*y.*y.*y.*y + M(3,47)*x.*y.*y.*y.*z + M(3,48)*x.*y.*y.*z.*z + M(3,49)*x.*y.*z.*z.*z + M(3,50)*x.*z.*z.*z.*z + M(3,51)*y.*y.*y.*y.*y + M(3,52)*y.*y.*y.*y.*z + M(3,53)*y.*y.*y.*z.*z + M(3,54)*y.*y.*z.*z.*z + M(3,55)*y.*z.*z.*z.*z + M(3,56)*z.*z.*z.*z.*z;
else
ft_error('invalid size of nonlinear transformation matrix');
end
output = [xx yy zz];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% linear warping using homogenous coordinate transformation matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
elseif strcmp(method, 'homogenous') || strcmp(method, 'homogeneous')
if all(size(M)==3)
% convert the 3x3 homogenous transformation matrix (corresponding with 2D)
% into a 4x4 homogenous transformation matrix (corresponding with 3D)
M = [
M(1,1) M(1,2) 0 M(1,3)
M(2,1) M(2,2) 0 M(2,3)
0 0 0 0
M(3,1) M(3,2) 0 M(3,3)
];
end
%warped = M * [input'; ones(1, size(input, 1))];
%warped = warped(1:3,:)';
% below achieves the same as lines 154-155
output = [input ones(size(input, 1),1)]*M(1:3,:)';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% using external function that returns a homogeneous transformation matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
elseif exist(method, 'file') && ~isa(M, 'struct')
% get the homogenous transformation matrix
H = feval(method, M);
output = ft_warp_apply(H, input, 'homogeneous');
elseif strcmp(method, 'sn2individual') && isa(M, 'struct')
% use SPM structure with parameters for an inverse warp
% from normalized space to individual, can be non-linear
output = sn2individual(M, input);
elseif strcmp(method, 'individual2sn') && isa(M, 'struct')
% use SPM structure with parameters for a warp from
% individual space to normalized space, can be non-linear
%error('individual2sn is not yet implemented');
output = individual2sn(M, input);
else
ft_error('unrecognized transformation method');
end
if ~input3d
% convert from 3D back to 2D representation
output = output(:,1:2);
end
if ~isempty(tol)
if tol>0
output = fix(output./tol)*tol;
end
end