FieldTrip does not have a native coordinate system, but assumes that all geometrical data (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 points to the right ear
• Y-axis points to the nose
• Z-axis points upwards

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 carthesian coordinates (x, y, z). If you have measured electrode positions with a Polhemus 3-D tracker, you also need this transformation. In the BESA carthesian 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 the electromagnetic 3-D trackers, and usually the trackers are sold to you by an EEG company. The EEG company bundles the tracker with a software program. 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 use a coordinate system that is linked to the external landmarks (i.e. fiducials) on the head and usually the left and right pre-auricular points and the nasion are used. The most common definition of the 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

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 radioligical conventions.

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 the different coordinate systems.