ijk2xyz {AnalyzeFMRI}R Documentation

ijk2xyz

Description

This function maps from data coordinates (e.g. column i, row j, slice k), into some real world (x,y,z) positions in space. These positions could relate to Talairach-Tournoux (T&T) space, MNI space, or patient-based scanner coordinates.

Usage

ijk2xyz(ijk=c(1,1,1),method=2,L)

Arguments

ijk

matrix. Each column of ijk should contain a voxel index coordinates (i,j,k) to be mapped to its (x,y,z) real coordinates in some other space

method

1 (qform.code=sform.code=0),2 (qform.code>0, rigid transformation) or 3 (sform.code>0, affine transformation).

L

header list of a NIFTI file

Details

The NIfTI format allows storage on disk to be in either a left- or right-handed coordinate system. However, the format includes an implicit spatial transformation into a RIGHT-HANDED coordinate system. This transform maps from data coordinates (e.g. column i, row j, slice k), into some real world (x,y,z) positions in space. These positions could relate to Talairach-Tournoux (T&T) space, MNI space, or patient-based scanner coordinates. For T&T, and MNI coordinates, x increases from left to right, y increases from posterior to anterior, and z increases in the inferior to superior direction. Directions in the scanner coordinate system are similar. MRI data is usually exported as DICOM format, which encodes the positions and orientations of the slices. When data are converted from DICOM to NIfTI-1 format, the relevant information can be determined from the Pixel Spacing, Image Orientation (Patient) and Image Position (Patient) fields of the DICOM files. NIfTI-1 also allows the space of one image to be mapped to that of another (via a rigid or affine transform). This is to enable on-the-fly resampling of registered images. This would allow intra-subject images, collected with lots of different orientations or resolutions, to be treated as if they are all in register.

Neurological and radiological conventions only relate to visualization of axial images. They are unrelated to how the data are stored on disk, or even how the real-world coordinates are represented. It is more appropriate to consider whether the real-world coordinate system is left- or right-handed (see below). Talairach and Tournoux use a right-handed system, whereas the storage convention of ANALYZE files is usually considered as left-handed. These coordinate systems are mirror images of each other (if you are a psychologist, try explaining why mirror images appear to be left-right flipped, rather than flipped up-down, or back-front). Transforming between left- and right-handed coordinate systems involves flipping, and can not be done by rotations alone.

x=thumb, y=index finger (forefinger), z=left (resp. right) hand's middle finger for left-handed persons (resp. right-handed persons).

Volume orientation is given by a transformation that maps voxel indices (i,j,k) to spatial coordinates (x,y,z), typically anatomical coordinates assigned by the scanner. This transformation (Method 2 in the ‘nifti1.h’ documentation) is generated using the voxel dimensions, a quaternion encoding a rotation matrix, and a 3D shift, all stored in the NIfTI-1 header; details can be found in the ‘nifti1.h’ comments. The NIfTI-1 header also provides for a general affine transformation, separate from that described by Method 2. This transformation (Method 3) also maps voxel indices (i,j,k) to (x,y,z), which in this case are typically coordinates in a standard space such as the Talairach space. The elements of this transformation matrix are stored in the NIfTI-1 header. For example, the Method 2 transformation can be constructed from the attributes from a set of DICOM files; the Method 3 transform can be computed offline and inserted into the header later. The exact "meaning" of the coordinates given by the Method 2 and Method 3 transformations is recorded in header fields qform.code and sform.code, respectively. Code values can indicate if the (x,y,z) axes are

It is possible that neither transformation is specified (i.e., qform.code=sform.code=0), in which case we are left with the voxel size in pixdim[], and no orientation is given or assumed. This use (Method 1) is discouraged.

The basic idea behind having two coordinate systems is to allow the image to store information about (1) the scanner coordinate system used in the acquisition of the volume (in the qform) and (2) the relationship to a standard coordinate system - e.g. MNI coordinates (in the sform). The qform allows orientation information to be kept for alignment purposes without losing volumetric information, since the qform only stores a rigid-body transformation which preserves volume. On the other hand, the sform stores a general affine transformation which can map the image coordinates into a standard coordinate system, like Talairach or MNI, without the need to resample the image. By having both coordinate systems, it is possible to keep the original data (without resampling), along with information on how it was acquired (qform) and how it relates to other images via a standard space (sform). This ability is advantageous for many analysis pipelines, and has previously required storing additional files along with the image files. By using NIfTI-1 this extra information can be kept in the image files themselves.
Note: the qform and sform also store information on whether the coordinate system is left-handed or right-handed (see Q15) and so when both are set they must be consistent, otherwise the handedness of the coordinate system (often used to distinguish left-right order) is unknown and the results of applying operations to such an image are unspecified.

There are 3 different methods by which continuous coordinates can be 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:

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*\code{dim[1]} + k*\code{dim[1]}*\code{dim[2]}) * (\code{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.

Value

A list containing the matrix xyz of the positions of the points specified in ijk.

See Also

xyz2ijk Q2R R2Q

Examples

L <- f.read.header(system.file("example-nifti.hdr",
package="AnalyzeFMRI"))
ijk <- matrix(c(1,1,1,2,3,7),byrow=FALSE,nrow=3)
ijk2xyz(ijk=ijk,method=2,L)

[Package AnalyzeFMRI version 1.1-23 Index]