nifti1.h

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 /*! To signify that the value at each voxel is an estimate
     of some parameter, set intent_code = NIFTI_INTENT_ESTIMATE.
     The name of the parameter may be stored in intent_name.     */

#define NIFTI_INTENT_ESTIMATE  1001

 /*! To signify that the value at each voxel is an index into
     some set of labels, set intent_code = NIFTI_INTENT_LABEL.
     The filename with the labels may stored in aux_file.        */

#define NIFTI_INTENT_LABEL     1002

 /*! To signify that the value at each voxel is an index into the
     NeuroNames labels set, set intent_code = NIFTI_INTENT_NEURONAME. */

#define NIFTI_INTENT_NEURONAME 1003

 /*! To store an M x N matrix at each voxel:
       - dataset must have a 5th dimension (dim[0]=5 and dim[5]>1)
       - intent_code must be NIFTI_INTENT_GENMATRIX
       - dim[5] must be M*N
       - intent_p1 must be M (in float format)
       - intent_p2 must be N (ditto)
       - the matrix values A[i][[j] are stored in row-order:
         - A[0][0] A[0][1] ... A[0][N-1]
         - A[1][0] A[1][1] ... A[1][N-1]
         - etc., until
         - A[M-1][0] A[M-1][1] ... A[M-1][N-1]        */

#define NIFTI_INTENT_GENMATRIX 1004

 /*! To store an NxN symmetric matrix at each voxel:
       - dataset must have a 5th dimension
       - intent_code must be NIFTI_INTENT_SYMMATRIX
       - dim[5] must be N*(N+1)/2
       - intent_p1 must be N (in float format)
       - the matrix values A[i][[j] are stored in row-order:
         - A[0][0]
         - A[1][0] A[1][1]
         - A[2][0] A[2][1] A[2][2]
         - etc.: row-by-row                           */

#define NIFTI_INTENT_SYMMATRIX 1005

 /*! To signify that the vector value at each voxel is to be taken
     as a displacement field or vector:
       - dataset must have a 5th dimension
       - intent_code must be NIFTI_INTENT_DISPVECT
       - dim[5] must be the dimensionality of the displacment
         vector (e.g., 3 for spatial displacement, 2 for in-plane) */

#define NIFTI_INTENT_DISPVECT  1006   /* specifically for displacements */
#define NIFTI_INTENT_VECTOR    1007   /* for any other type of vector */

 /*! To signify that the vector value at each voxel is really a
     spatial coordinate (e.g., the vertices or nodes of a surface mesh):
       - dataset must have a 5th dimension
       - intent_code must be NIFTI_INTENT_POINTSET
       - dim[0] = 5
       - dim[1] = number of points
       - dim[2] = dim[3] = dim[4] = 1
       - dim[5] must be the dimensionality of space (e.g., 3 => 3D space).
       - intent_name may describe the object these points come from
         (e.g., "pial", "gray/white" , "EEG", "MEG").                   */

#define NIFTI_INTENT_POINTSET  1008

 /*! To signify that the vector value at each voxel is really a triple
     of indexes (e.g., forming a triangle) from a pointset dataset:
       - dataset must have a 5th dimension
       - intent_code must be NIFTI_INTENT_TRIANGLE
       - dim[0] = 5
       - dim[1] = number of triangles
       - dim[2] = dim[3] = dim[4] = 1
       - dim[5] = 3
       - datatype should be an integer type (preferably DT_INT32)
       - the data values are indexes (0,1,...) into a pointset dataset. */

#define NIFTI_INTENT_TRIANGLE  1009

 /*! To signify that the vector value at each voxel is a quaternion:
       - dataset must have a 5th dimension
       - intent_code must be NIFTI_INTENT_QUATERNION
       - dim[0] = 5
       - dim[5] = 4
       - datatype should be a floating point type     */

#define NIFTI_INTENT_QUATERNION 1010

 /*! Dimensionless value - no params - although, as in _ESTIMATE 
     the name of the parameter may be stored in intent_name.     */

#define NIFTI_INTENT_DIMLESS    1011

 /*---------- these values apply to GIFTI datasets ----------*/

 /*! To signify that the value at each location is from a time series. */

#define NIFTI_INTENT_TIME_SERIES  2001

 /*! To signify that the value at each location is a node index, from
     a complete surface dataset.                                       */

#define NIFTI_INTENT_NODE_INDEX   2002

 /*! To signify that the vector value at each location is an RGB triplet,
     of whatever type.
       - dataset must have a 5th dimension
       - dim[0] = 5
       - dim[1] = number of nodes
       - dim[2] = dim[3] = dim[4] = 1
       - dim[5] = 3
    */

#define NIFTI_INTENT_RGB_VECTOR   2003

 /*! To signify that the vector value at each location is a 4 valued RGBA
     vector, of whatever type.
       - dataset must have a 5th dimension
       - dim[0] = 5
       - dim[1] = number of nodes
       - dim[2] = dim[3] = dim[4] = 1
       - dim[5] = 4
    */

#define NIFTI_INTENT_RGBA_VECTOR  2004

 /*! To signify that the value at each location is a shape value, such
     as the curvature.  */

#define NIFTI_INTENT_SHAPE        2005

/* @} */

/*---------------------------------------------------------------------------*/
/* 3D IMAGE (VOLUME) ORIENTATION AND LOCATION IN SPACE:
   ---------------------------------------------------
   There are 3 different methods by which continuous coordinates can
   attached to voxels.  The discussion below emphasizes 3D volumes, and
   the continuous coordinates are referred to as (x,y,z).  The voxel
   index coordinates (i.e., the array indexes) are referred to as (i,j,k),
   with valid ranges:
     i = 0 .. dim[1]-1
     j = 0 .. dim[2]-1  (if dim[0] >= 2)
     k = 0 .. dim[3]-1  (if dim[0] >= 3)
   The (x,y,z) coordinates refer to the CENTER of a voxel.  In methods
   2 and 3, the (x,y,z) axes refer to a subject-based coordinate system,
   with
     +x = Right  +y = Anterior  +z = Superior.
   This is a right-handed coordinate system.  However, the exact direction
   these axes point with respect to the subject depends on qform_code
   (Method 2) and sform_code (Method 3).

   N.B.: The i index varies most rapidly, j index next, k index slowest.
    Thus, voxel (i,j,k) is stored starting at location
      (i + j*dim[1] + k*dim[1]*dim[2]) * (bitpix/8)
    into the dataset array.

   N.B.: The ANALYZE 7.5 coordinate system is
      +x = Left  +y = Anterior  +z = Superior
    which is a left-handed coordinate system.  This backwardness is
    too difficult to tolerate, so this NIFTI-1 standard specifies the
    coordinate order which is most common in functional neuroimaging.

   N.B.: The 3 methods below all give the locations of the voxel centers
    in the (x,y,z) coordinate system.  In many cases, programs will wish
    to display image data on some other grid.  In such a case, the program
    will need to convert its desired (x,y,z) values into (i,j,k) values
    in order to extract (or interpolate) the image data.  This operation
    would be done with the inverse transformation to those described below.

   N.B.: Method 2 uses a factor 'qfac' which is either -1 or 1; qfac is
    stored in the otherwise unused pixdim[0].  If pixdim[0]=0.0 (which
    should not occur), we take qfac=1.  Of course, pixdim[0] is only used
    when reading a NIFTI-1 header, not when reading an ANALYZE 7.5 header.

   N.B.: The units of (x,y,z) can be specified using the xyzt_units field.

   METHOD 1 (the "old" way, used only when qform_code = 0):
   -------------------------------------------------------
   The coordinate mapping from (i,j,k) to (x,y,z) is the ANALYZE
   7.5 way.  This is a simple scaling relationship:

     x = pixdim[1] * i
     y = pixdim[2] * j
     z = pixdim[3] * k

   No particular spatial orientation is attached to these (x,y,z)
   coordinates.  (NIFTI-1 does not have the ANALYZE 7.5 orient field,
   which is not general and is often not set properly.)  This method
   is not recommended, and is present mainly for compatibility with
   ANALYZE 7.5 files.

   METHOD 2 (used when qform_code > 0, which should be the "normal" case):
   ---------------------------------------------------------------------
   The (x,y,z) coordinates are given by the pixdim[] scales, a rotation
   matrix, and a shift.  This method is intended to represent
   "scanner-anatomical" coordinates, which are often embedded in the
   image header (e.g., DICOM fields (0020,0032), (0020,0037), (0028,0030),
   and (0018,0050)), and represent the nominal orientation and location of
   the data.  This method can also be used to represent "aligned"
   coordinates, which would typically result from some post-acquisition
   alignment of the volume to a standard orientation (e.g., the same
   subject on another day, or a rigid rotation to true anatomical
   orientation from the tilted position of the subject in the scanner).
   The formula for (x,y,z) in terms of header parameters and (i,j,k) is:

     [ x ]   [ R11 R12 R13 ] [        pixdim[1] * i ]   [ qoffset_x ]
     [ y ] = [ R21 R22 R23 ] [        pixdim[2] * j ] + [ qoffset_y ]
     [ z ]   [ R31 R32 R33 ] [ qfac * pixdim[3] * k ]   [ qoffset_z ]

   The qoffset_* shifts are in the NIFTI-1 header.  Note that the center
   of the (i,j,k)=(0,0,0) voxel (first value in the dataset array) is
   just (x,y,z)=(qoffset_x,qoffset_y,qoffset_z).

   The rotation matrix R is calculated from the quatern_* parameters.
   This calculation is described below.

   The scaling factor qfac is either 1 or -1.  The rotation matrix R
   defined by the quaternion parameters is "proper" (has determinant 1).
   This may not fit the needs of the data; for example, if the image
   grid is
     i increases from Left-to-Right
     j increases from Anterior-to-Posterior
     k increases from Inferior-to-Superior
   Then (i,j,k) is a left-handed triple.  In this example, if qfac=1,
   the R matrix would have to be

     [  1   0   0 ]
     [  0  -1   0 ]  which is "improper" (determinant = -1).
     [  0   0   1 ]

   If we set qfac=-1, then the R matrix would be

     [  1   0   0 ]
     [  0  -1   0 ]  which is proper.
     [  0   0  -1 ]

   This R matrix is represented by quaternion [a,b,c,d] = [0,1,0,0]
   (which encodes a 180 degree rotation about the x-axis).

   METHOD 3 (used when sform_code > 0):
   -----------------------------------
   The (x,y,z) coordinates are given by a general affine transformation
   of the (i,j,k) indexes:

     x = srow_x[0] * i + srow_x[1] * j + srow_x[2] * k + srow_x[3]
     y = srow_y[0] * i + srow_y[1] * j + srow_y[2] * k + srow_y[3]
     z = srow_z[0] * i + srow_z[1] * j + srow_z[2] * k + srow_z[3]

   The srow_* vectors are in the NIFTI_1 header.  Note that no use is
   made of pixdim[] in this method.

   WHY 3 METHODS?
   --------------
   Method 1 is provided only for backwards compatibility.  The intention
   is that Method 2 (qform_code > 0) represents the nominal voxel locations
   as reported by the scanner, or as rotated to some fiducial orientation and
   location.  Method 3, if present (sform_code > 0), is to be used to give
   the location of the voxels in some standard space.  The sform_code
   indicates which standard space is present.  Both methods 2 and 3 can be
   present, and be useful in different contexts (method 2 for displaying the
   data on its original grid; method 3 for displaying it on a standard grid).

   In this scheme, a dataset would originally be set up so that the
   Method 2 coordinates represent what the scanner reported.  Later,
   a registration to some standard space can be computed and inserted
   in the header.  Image display software can use either transform,
   depending on its purposes and needs.

   In Method 2, the origin of coordinates would generally be whatever
   the scanner origin is; for example, in MRI, (0,0,0) is the center
   of the gradient coil.