This is an old revision of the document!

For understanding the coordinate system, the following questions need to be addressed:
• What is the definition of the origin of the coordinate system, i.e. where is [0,0,0]?
• In which directions are the x-, y- and z-axis pointing, i.e. is +x towards the right or towards anterior?
• In what units are coordinates expressed, i.e. does the number “1” mean 1 meter, 1 centimeter or 1 milimeter?
• Is the geometry scaled to some template or atlas, or does it still match the individual's head/brain size?

FieldTrip does not have a native coordinate system, but assumes that all geometrical data which are used together (i.e. mri, headmodel, electrodes, dipoles) are expressed in the same coordinate system and with the same physical units (e.g. mm or cm). In order to be able to compare these fundamental properties across data structures, FieldTrip defines two fields in the geometrical data mentioned above. These fields pertain to the interpretation of the physical units, XXX.unit, and to the interpretation of the coordinate system in which the coordinates are expressed, XXX.coordsys.

If the unit-field is not present in the data, FieldTrip typically tries to estimate this from the magnitude and range of the values in the spatial coordinates (e.g. the position of the vertices in the boundaries that describe the volume conductor, or the positions of electrodes, assuming that a human head was used to attach the electrodes to).

The real-world interpretation of the coordinate system can typically not be determined automatically, and for this FieldTrip uses a helper-function ft_determine_coordsys, that requires some user-interaction for the specification of the orientation of the cardinal axes of the coordinate system, as well as the origin. The only thing that this function does, is to add a coordsys-field to the input data structure, specifying how the spatial coordinates in the data structure should be interpreted. Importantly, it does not change the values of the spatial coordinates that are present in the data structure.

The remainder of this page describes the external conventions for the coordinate systems for a number of EEG and MEG systems. Of course it is always possible that a specific user of one of the systems uses a different coordinate system.

The coordinate systems used in EEG and MEG measurements are usually defined in terms of anatomical landmarks on the outside of the head, such as the nasion, inion and the left and right pre-auricular points. Please see this FAQ for a discussion of the LPA and RPA.

The coordinate systems used for imaging methods such as MRI, PET and CT are usually defined in terms of internal brain structures, such as the anterior and posterior commisure. Furthermore, imaging data is sometimes scaled to a uniform brain size, e.g. based on the Talairach-Tournoux atlas or one of the templates from the Montreal Neurological Institute (MNI). An elaborate discussion on the relation between the Talairach-Tournoux atlas and the MNI templates can be found here.

Imaging methods such as MRI and CT result in 3-D volumetric representations of the data, e.g. with 256x256x256 voxels. You can think of this representation as having a “voxel” coordinate system, where voxel (1, 1, 1) is the first and (256, 256, 256) the last in the volume. The voxel coordinate system however does not specify the physical dimensions (e.g. mm or cm) and does not specify how the head (which is somewhere within the volume) relates to the voxel indices. Therefore a volumetric description of imaging data as a 3-D array has to be complemented with a description of the head coordinate system. This description is commonly implemented using a 4×4 homogenous coordinate transformation matrix, for which an excellent description is available here.

### Summary

system units orientation origin notes
CTF gradiometer cm ALS between the ears
CTF MRI mm ALS between the ears voxel order can be arbitrary
Neuromag/Elekta m RAS between the ears
4D/BTi m ALS between the ears
Yokogawa
Chieti ITAB mm RAS between the ears
DICOM mm LPS
Analyze mm LAS
Talairach-Tournoux mm RAS
MNI mm RAS
NIfTI mm RAS scanner origin (centre of gradient coil)
freesurfer mm RAS centre voxel of isotropic 256-cubic 1 mm volume
Paxinos-Franklin mm RSP Bregma point
Allen Institute mm RAS Bregma point

A/P means anterior/posterior
L/R means left/right
S/I means superior/inferior

As an example: RAS means that the first dimension orients towards Right, the second dimension orients towards Anterior, the third dimension orients towards Superior.

### Details of the CTF coordinate system

The CTF coordinate system is expressed in centimeter (except the MRI which is in mm), with the principal (X, Y, Z) axes going through external landmarks (i.e. fiducials). These external landmarks are determined using the MEG measurement by placing small coils on them, and at the FCDC we usually place them on nasion and on a tube that extends from the left and right ear canal. Although the left and right ear markers do not really correspond to pre-auricular points (which is in front of the ear), they are referred to in the CTF software as LPA and RPA. The exact definition is

• the origin is exactly between LPA and RPA
• the X-axis goes towards NAS
• the Y-axis goes approximately towards LPA, orthogonal to X and in the plane spanned by the fiducials
• the Z-axis goes approximately towards the vertex, orthogonal to X and Y

### Details of the Neuromag coordinate system

The Neuromag coordinate system is expressed in meter, with the principal (X, Y, Z) axes going through external landmarks (i.e. fiducials). The details are

• X-axis from the origin towards the RPA point (exactly through)
• Y-axis from the origin towards the nasion (exactly through)
• Z-axis from the origin upwards orthogonal to the XY-plane
• Origin: Intersection of the line through LPA and RPA and a line orthogonal to L passing through the nasion.

### Details of the 4D/BTi coordinate system

The 4D Neuroimaging (also known as BTi) coordinate system is expressed in meter, with the principal (X, Y, Z) axes going through external landmarks (i.e. fiducials). The details are

• the origin is exactly between LPA and RPA
• the X-axis goes towards NAS
• the Y-axis goes approximately towards LPA, orthogonal to X and in the plane spanned by the fiducials
• the Z-axis goes approximately towards the vertex, orthogonal to X and Y

### Details of the Yokogawa coordinate system

Unlike other systems, the Yokogawa system software does not automatically analyze its sensorlocations relative to fiducial coils. Instead the positions of the fiducial points are saved in an external textfile - in the helmet's own coordinate system - using the property menu of the YOKOGAWA MEG-VISION software. The details are

• the origin is at the center of the helmet
• the X-axis goes towards the nose
• the Y-axis goes towards the left
• the Z-axis goes towards the top of the head

### Details of the Chieti ITAB coordinate system

The ITAB coordinate system is expressed in meter, with the principal (X, Y, Z) axes going through external landmarks (i.e. fiducials). The details are

• X-axis from the origin towards the RPA point (exactly through)
• Y-axis from the origin towards the nasion (exactly through)
• Z-axis from the origin upwards orthogonal to the XY-plane
• Origin: Intersection of the line through LPA and RPA and a line orthogonal to L passing through the nasion.

### Details of BESA coordinate system

The BESA native coordinate system is expressed in spherical coordinates. If you want to express the location of a dipole in 3-D space, it is more convenient to translate from spherical coordinates (phi, theta, r) to cartesian coordinates (x, y, z). If you have measured electrode positions with a Polhemus 3-D tracker, you also need this transformation. In the BESA cartesian coordinate system, the principal (x, y, z) axes are defined as

• the x-axis passes through LPA and RPA. Positive x is right.
• the y-axis passes through the nasion and is orthogonal to the x-axis. Positive y is anterior
• the z-axis is orthogonal to x and y. Positive z is superior.

If you prefer to consider the center of the sphere to coincide with the origin of the coordinate system, the principal axes will not go exactly through the external landmarks (i.e. fiducials). The reason for the shift in the negative z-direction of LPA, RPA and Nasion is that, after the shift, the electrodes better fit on the spherical head model. I.e. the nose and ears are not in the middle of the sphere, but are lower.

### Details of the Polhemus coordinate system

The Polhemus coordinate system as such does not exist. Polhemus is the company that manufactures electromagnetic 3-D trackers for a large variety of applications, and usually the trackers are sold to you by an EEG company. The EEG company bundles the tracker with specific software for recording the position of the electrodes. The software program communicates with the tracker, and presents the measured electrode locations on the computer screen and writes them to an ascii file. Therefore, the software determines the coordinate system that is used. It is common to require the user first to record external anatomical landmarks (i.e. fiducials) on the head: usually the left and right pre-auricular points and the nasion. Using there fiducials, the software can convert all subsequent electrode positions into a head coordinate system.

The most common definition of the head coordinate system used by the software that accompanies the Polhemus tracker is

• the origin is exactly between LPA and RPA
• the X-axis goes towards NAS
• the Y-axis goes approximately towards LPA, orthogonal to X and in the plane spanned by the fiducials
• the Z-axis goes approximately towards the vertex, orthogonal to X and Y

### Details of the DICOM coordinate system

DICOM is a standard for handling digital imaging in medicine, and as such uses a radiological coordinate system, defined as

• x increases from right to left
• y increases from anterior to posterior
• z increases from inferior to superior

### Details of the Analyze coordinate system

The Analyze coordinate system is defined by and used in the Analyze software developed by the Mayo Clinic (see also this pdf). The orientation is according to radiological conventions, and uses a left-handed coordinate system. The definition of the Analyze coordinate system is

• the x-axis goes from right to left
• the y-axis goes from posterior to anterior
• the z-axis goes from inferior to superior

Note that the Analyze *.img/*.hdr file format is also being used by other software (notably SPM), but the conventions of the coordinate systems may be different. Typically, fMRI specific software will use neurological conventions instead of radiological conventions.

### Details of the NIfTI coordinate system

NIfTI is adapted from the Analyze 7.5 format (see this page for more information). It allows two coordinate systems: one related to the scanner coordinate system (qform) and one related to a standard coordinate system (sform) such as MNI or Talairach-Tournoux (see below). The default scanner coordinate system is defined as

• The origin is generally the scanner origin, for example the center of the gradient coil
• The x-axis increases from left to right
• The y-axis increases from posterior to anterior
• The z-axis increases from inferior to superior

Note that this coordinate system applies when images are not registered to a standard space; if they are, the coordinate system of the relevant standard space applies (e.g. MNI or Talairach-Tournoux).

### Details of the Talairach-Tournoux coordinate system

The Talairach-Tournoux coordinate system is comparable to, but not exactly the same as the MNI coordinate system. It is defined using landmarks inside the brain and therefore can only be determined from an MRI scan, in contrast to the external landmarks that are used during an EEG/MEG recording. The landmarks used in the TT coordinate system are the anterior and posterior commisura (AC and PC) and the coordinate axes are defined according to

• the origin of the TT coordinate system is in the AC
• the y-axis goes towards the front of the brain, along the line connecting PC and AC
• the z-axis goes towards the top of the brain
• the x-axis goes towards the right side of the brain

### Details of the MNI coordinate system

The Montreal Neurological Institute coordinate system is comparable to, but not exactly the same as the Talairach-Tournoux coordinate system. Rather than being based on a single specimen, it is the result from spatially transforming and averaging MRI scans of many subjects.

• The origin of the MNI coordinate system is the anterior commissure
• The X-axis extends from the left side of the brain to the right side
• The Y-axis points from posterior to anterior
• The Z-axis points from inferior to superior

The SPM software also makes use of the MNI coordinate system.

### Details of the FreeSurfer coordinate system

FreeSurfer is a software package that can be used to process anatomical MRIs, to obtain segmentations, cortical meshes, and inflated surfaces. The orientation of the coordinate system is RAS, and for volumetric (i.e. anatomical MRI) data the origin is defined to be the centre of a 256x256x256 isotropic 1 mm volume. Note that if the head is not centered in the volume, the origin of the coordinate system will not coincide with the center of the head.

For surface based data FreeSurfer uses the tkrRAS coordinate system.

### Details on the Paxinos-Franklin mouse coordinate system

The Paxinos-Franklin atlas The Mouse Brain in Stereotaxic Coordinate (2001) defines a commonly used coordinate system for the mouse brain anatomy. Note however, that other coordinate system definitions are also being used.

For the mouse coordinate system it is relevant to understand the nomenclature differences similarities and differences between the human anatomy and that of most other animals. A nice explanation is provided on wikipedia and here.

The Paxinos-Franklin atlas specifies two points of reference: the Bregma point and the midpoint of the intra-aural line. Both are indicated as [0, 0, 0] in the atlas, we will make use of the Bregma point.

• The origin of the coordinate system is at the Bregma point.
• The X-axis extends along the Medial-Lateral direction, with positive towards the right (see below).
• The Y-axis points from Dorsal to Ventral, i.e. towards the top of the head.
• The Z-axis points from Cranial to Caudal, or Anterior to Posterior, i.e. towards the tail of the animal. The Z-axis extends from the Bregma point to the Lambda point

The Paxinos-Franklin atlas is not explicit about the positive and negative x-direction. We observe that the y-axis is from Inferior to Superior and the z-axis from Anterior to Posterior, which means that we obtain a right-handed coordinate system by defining the x-axis from Medial to the Right Lateral side.

Although we define the origin at the Bregma point, the Paxinos-Franklin atlas also refers to the interaural point as a possible origin. The interaural point is a logical choice if a stereotact is used with pins in both ear canals. Converting from interaural to Bregma as origin of the coordinate system involves a translation which can be described in the following homogenous transformation matrix

``` interaural2bregma = [
1 0 0 Tx
0 1 0 Ty
0 0 1 Tz
0 0 0 1
];```

Converting from Bregma to interaural as origin of the coordinate system involves a translation which can be described in the following homogenous transformation matrix

``` bregma2interaural = [
1 0 0 Tx
0 1 0 Ty
0 0 1 Tz
0 0 0 1
];```

### Details on the Allen Institute mouse coordinate system

The Allen Institute has created a scalable mouse brain atlas (ABA12). In this atlas, the coordinate system is defined as

• The origin of the coordinate system is at the Bregma point.
• The X-axis points from left (-) to right (+).
• The Y-axis points from posterior (-) to anterior (+).
• The Z-axis points from inferior (-) to superior (+).