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iCAPs_v2/packages/cbiNifti/cbiHomogeneousToQuaternion.m
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cbiHomogeneousToQuaternion.m
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function [quatern, qfac, pixdim]=cbiHomogeneousToQuaternion( R )
% Calculates quaternion parameters from a 4x4 matrix
% [quatern, qfac, pixdim]=cbiHomogeneousToQuaternion( M44 )
%
% - OR - (using a 3x3 rotation matrix)
% [quatern, qfac, pixdim]=cbiHomogeneousToQuaternion( R )
%
% Modified from nifti_io.c
% check args
if (nargin~=1)
error('Wrong number of input arguments!');
end
if (size(R)==[4,4] | size(R)==[3,3])
R=R(1:3,1:3);
else
error('Input argument must be a homogeneous 4x4 matrix or 3x3 rotation matrix');
end
if (nargout~=3)
error('Wrong number of output arguments!');
end
[quatern,qfac, pixdim]=calcQuatFromRotMat(R);
return
function [quatern,qfac,pixdim]=calcQuatFromRotMat(R)
% BEGIN calc
% assume R set
% /* compute lengths of each column; these determine grid spacings */
xd = sqrt( sum(R(:,1).^2) );
yd = sqrt( sum(R(:,2).^2) );
zd = sqrt( sum(R(:,3).^2) );
% $$$ /* if a column length is zero, patch the trouble */
if ( xd == 0 )
R(1,1) = 1 ; R(2,1) = 0; R(3,1) = 0 ; xd = 1 ;
end
if ( yd == 0 )
R(2,2) = 1 ; R(1,2) = 0; R(3,2) = 0 ; yd = 1 ;
end
if ( zd == 0 )
R(3,3) = 1 ; R(1,3) = 0; R(2,3) = 0 ; zd = 1 ;
end
pixdim=[xd yd zd];
% $$$ /* normalize the columns */
R(:,1)=R(:,1)./xd;
R(:,2)=R(:,2)./yd;
R(:,3)=R(:,3)./zd;
R=polarDecomp33(R);
zd=det(R);
if (zd>0)
qfac=1;
else
qfac=-1;
R(:,3)=-R(:,3);
end
a=R(1,1)+R(2,2)+R(3,3)+1;
if (a>0.5)
a = 0.5 * sqrt(a) ;
b = 0.25 * (R(3,2)-R(2,3)) / a ;
c = 0.25 * (R(1,3)-R(3,1)) / a ;
d = 0.25 * (R(2,1)-R(1,2)) / a ;
else
xd = 1.0 + R(1,1) - (R(2,2)+R(3,3)) ;
yd = 1.0 + R(2,2) - (R(1,1)+R(3,3)) ;
zd = 1.0 + R(3,3) - (R(1,1)+R(2,2)) ;
if( xd > 1.0 )
b = 0.5 * sqrt(xd) ;
c = 0.25* (R(1,2)+R(2,1)) / b ;
d = 0.25* (R(1,3)+R(3,1)) / b ;
a = 0.25* (R(3,2)-R(2,3)) / b ;
elseif ( yd > 1.0 )
c = 0.5 * sqrt(yd) ;
b = 0.25* (R(1,2)+R(2,1)) / c ;
d = 0.25* (R(2,3)+R(3,2)) / c ;
a = 0.25* (R(1,3)-R(3,1)) / c ;
else
d = 0.5 * sqrt(zd) ;
b = 0.25* (R(1,3)+R(3,1)) / d ;
c = 0.25* (R(2,3)+R(3,2)) / d ;
a = 0.25* (R(2,1)-R(1,2)) / d ;
end
if( a < 0.0 )
b=-b; c=-c; d=-d; a=-a;
end
end
quatern=[b c d];
return;
function OM=polarDecomp33( M );
X = M;
gam = det(X) ;
while ( gam == 0.0 )
gam = 0.00001 * ( 0.001 + norm(X,'inf'));
X(1,1)=X(1,1)+gam;
X(2,2)=X(2,2)+gam;
X(3,3)=X(3,3)+gam;
gam = det(X);
end
dif=1;
k=0;
while (1)
Y = inv(X);
if( dif > 0.3 )
alp = sqrt( norm(X,'inf') * norm(X','inf'));
bet = sqrt( norm(Y,'inf') * norm(Y','inf'));
gam = sqrt( bet / alp ) ;
gmi = 1.0 / gam ;
else
gam = 1.0;
gmi = 1.0 ;
end
Z(1,1) = 0.5 * ( gam*X(1,1) + gmi*Y(1,1) ) ;
Z(1,2) = 0.5 * ( gam*X(1,2) + gmi*Y(2,1) ) ;
Z(1,3) = 0.5 * ( gam*X(1,3) + gmi*Y(3,1) ) ;
Z(2,1) = 0.5 * ( gam*X(2,1) + gmi*Y(1,2) ) ;
Z(2,2) = 0.5 * ( gam*X(2,2) + gmi*Y(2,2) ) ;
Z(2,3) = 0.5 * ( gam*X(2,3) + gmi*Y(3,2) ) ;
Z(3,1) = 0.5 * ( gam*X(3,1) + gmi*Y(1,3) ) ;
Z(3,2) = 0.5 * ( gam*X(3,2) + gmi*Y(2,3) ) ;
Z(3,3) = 0.5 * ( gam*X(3,3) + gmi*Y(3,3) ) ;
dif = abs(Z(1,1)-X(1,1))+abs(Z(1,2)-X(1,2)) ...
+abs(Z(1,3)-X(1,3))+abs(Z(2,1)-X(2,1)) ...
+abs(Z(2,2)-X(2,2))+abs(Z(2,3)-X(2,3)) ...
+abs(Z(3,1)-X(3,1))+abs(Z(3,2)-X(3,2)) ...
+abs(Z(3,3)-X(3,3));
k = k+1 ;
if ( k > 100 | dif < 3.e-6 )
break ;
end
X = Z ;
end
OM=Z;
return
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