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). This page describes how the default coordinate system is defined 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 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

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.

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

The Yokogawa system does not have a clear and uniformly defined coordinate system that we know of. If you know the details, please share them with us here on the wiki.

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.

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.

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

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

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.

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).

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

See also this page which describes the TT and MNI space in more detail.

See also this page from the BrainStorm documentation that also explains different coordinate systems.

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 the origin is typically defined to be the centre of a 256x256x256 isotropic 1 mm volume.

See this page for more information about this.