vb_fit_3d_coord

 Transform Marker coordinate to MRI coordinate

 Usage:
 trans_mat = trans_head(marker, mri)

 --- Input
 Reference points in Marker cordinate

 marker(1,:): Left ear
 marker(2,:): Nose
 marker(3,:): Right ear

 Reference points in MRI cordinate
 mri(1,:): Left ear  in MRI
 mri(2,:): Nose      in MRI
 mri(3,:): Right ear in MRI

 --- Output
 trans_mat = Rigid Body Transformation matrix  (4 x 3)
             from Marker coordinate to MRI coordinate
 x_mri = [x_marker 1]*trans_mat
 
 Transform Marker coordinate to MRI coordinate
  by Rigid Body Transformation (Rotation + Translation)
 Three point matching (usualy Left/Right ear & Nose are used)

 Coordinate Transform by trans_mat
 x_mri = ( x_marker - org_marker )*rot + org_mri
       = x_marker*rot + (org_mri - org_marker*rot)

 trans_mat = [rot ; trans_org]        (4 x 3)
 trans_org = org_mri - org_marker*rot

 2005-06-07 made by M. Sato

 Copyright (C) 2011, ATR All Rights Reserved.
 License : New BSD License(see VBMEG_LICENSE.txt)

0001 function    [trans_mat, marker_mri] = vb_fit_3d_coord(marker, mri)
0002 % Transform Marker coordinate to MRI coordinate
0003 %
0004 % Usage:
0005 % trans_mat = trans_head(marker, mri)
0006 %
0007 % --- Input
0008 % Reference points in Marker cordinate
0009 %
0010 % marker(1,:): Left ear
0011 % marker(2,:): Nose
0012 % marker(3,:): Right ear
0013 %
0014 % Reference points in MRI cordinate
0015 % mri(1,:): Left ear  in MRI
0016 % mri(2,:): Nose      in MRI
0017 % mri(3,:): Right ear in MRI
0018 %
0019 % --- Output
0020 % trans_mat = Rigid Body Transformation matrix  (4 x 3)
0021 %             from Marker coordinate to MRI coordinate
0022 % x_mri = [x_marker 1]*trans_mat
0023 %
0024 % Transform Marker coordinate to MRI coordinate
0025 %  by Rigid Body Transformation (Rotation + Translation)
0026 % Three point matching (usualy Left/Right ear & Nose are used)
0027 %
0028 % Coordinate Transform by trans_mat
0029 % x_mri = ( x_marker - org_marker )*rot + org_mri
0030 %       = x_marker*rot + (org_mri - org_marker*rot)
0031 %
0032 % trans_mat = [rot ; trans_org]        (4 x 3)
0033 % trans_org = org_mri - org_marker*rot
0034 %
0035 % 2005-06-07 made by M. Sato
0036 %
0037 % Copyright (C) 2011, ATR All Rights Reserved.
0038 % License : New BSD License(see VBMEG_LICENSE.txt)
0039 
0040 %
0041 % XYZ-Axis of MRI cord.
0042 %
0043 
0044 % X-axis: mri(1) -> mri(3) : Left->Right ear line
0045 ex  = mri(3,:)-mri(1,:); 
0046 exx = sqrt(sum(ex.^2));
0047 ex  = ex/exx;
0048 % Z-axis: perpendicular to X & Y-axis
0049 ez  = cross(ex,mri(2,:)-mri(1,:)); 
0050 ezz = sqrt(sum(ez.^2));
0051 ez  = ez/ezz;
0052 % Y-axis: X axis -> mri(2) :perpendicular to X-axis & path through Nose
0053 ey  = cross(ez,ex); 
0054 
0055 % Unit vectors of XYZ-axis
0056 rot_mri = [ex; ey; ez]; 
0057 
0058 % Origin
0059 org_mri = sum((mri(2,:)-mri(1,:)).*ex)*ex + mri(1,:); 
0060 
0061 %
0062 % XYZ-Axis of Marker cord.
0063 %
0064 
0065 % X-axis: mri(1) -> mri(3) : Left->Right ear line
0066 ex  = marker(3,:)-marker(1,:); 
0067 exx = sqrt(sum(ex.^2));
0068 ex  = ex/exx;
0069 % Z-axis: perpendicular to X & Y-axis
0070 ez  = cross(ex,marker(2,:)-marker(1,:)); 
0071 ezz = sqrt(sum(ez.^2));
0072 ez  = ez/ezz;
0073 % Y-axis: X axis -> mri(2) :perpendicular to X-axis & path through Nose
0074 ey  = cross(ez,ex); 
0075 
0076 % Unit vectors of XYZ-axis
0077 rot_marker = [ex; ey; ez]; 
0078 
0079 % Origin
0080 org_marker = sum((marker(2,:)-marker(1,:)).*ex)*ex + marker(1,:); 
0081 
0082 % Rotation matrix from marker cord to MRI cord
0083 rot = rot_marker'*rot_mri;
0084 
0085 trans_org = org_mri - org_marker*rot;
0086 trans_mat = [rot ; trans_org];
0087 
0088 marker_mri = [marker ones(3,1)]*trans_mat;