# How are the different head and MRI coordinate systems defined?

To understand the coordinate system in which data is expressed, you should consider:

• 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 millimeter?
• Is the geometry scaled to some template or atlas, or does it still match the individual’s head/brain size?

FieldTrip does not have its own coordinate system, but allows the user to use the coordinate system native to the original data. However, at the time of certain computations or visualization FieldTrip 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 geometrical 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 `xxx` pertaining to the interpretation of the geometrical 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 uses the helper-function ft_determine_units that tries to estimate the units from the range of values in the spatial data (e.g. the positions of the vertices in the boundaries that describe the volume conductor, or the positions of electrodes), assuming that the geometry corresponds to a human head that is approximately 0.25 meter, or 25 cm, or 250 mm in size.

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. This function requires some user-interaction for the specification of the origin and the orientation of the cardinal axes of the coordinate system. 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 native conventions for the coordinate systems for a number of standard atlasses, MEG systems, EEG systems, MRI systems, and for various software packages involved in processing geometrical data. Of course it might always possible that the specific user of one of these 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 commissure. Furthermore, imaging data is sometimes scaled to a specific standard 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) is the last in the volume. The voxel coordinate system however does not specify the geometrical 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 4x4 homogenous coordinate transformation matrix.

## Summary

system units orientation origin scaling notes
ACPC mm RAS anterior commissure individual brain, not normalized to a template
Allen Institute mm RAS Bregma point
Analyze mm LAS   native
BTi/4D m ALS between the ears native
CTF MRI mm ALS between the ears native voxel order can be arbitrary
CTF gradiometer cm ALS between the ears native
CapTrak mm RAS approximately between the ears
Chieti ITAB mm RAS between the ears native
DICOM mm LPS   native
FreeSurfer mm RAS center of isotropic 1 mm 256x256x256 volume
MNI mm RAS anterior commissure scaled to match averaged template
NIfTI mm RAS scanner origin (centre of gradient coil) see here, search for “Orientation information”.
Neuromag/Elekta/Megin m RAS between the ears native
Paxinos-Franklin mm RSP Bregma point
Talairach-Tournoux mm RAS anterior commissure scaled to match atlas
Yokogawa   ALS center of device

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 on the ACPC coordinate system

The ACPC coordinate system corresponds to that used in the Talairach atlas, but without the piecewise linear scaling applied to the brain, i.e. a brain in ACPC coordinates retains the individual shape and size. The landmarks used in the ACPC 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 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 (+).

## 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 by older SPM version), 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 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 digitizer or similar, a transformation from cartesian to spherical coordinates is needed.

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 towards the 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 BTi/4D coordinate system

The BTi or “4D Neuroimaging” coordinate system is expressed in meter, with the principal (X, Y, Z) axes going through fiducials placed on external anatomical landmarks. 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 CapTrak coordinate system

CapTrak is an electrode digitization system manufactured by Brain Products. CapTrak consists of a hand-held scanner featuring two cameras that track EEG electrodes on a subject’s scalp. CapTrak makes use of LEDs built into the Brain Products active electrodes and calculates the 3-D coordinates by comparing each LED position with the position of three “special LED” positions. These special LEDs form the coordinate system and are placed as fiducials onto anatomical landmarks (nasion, right and left preauricular points) on the subject’s head.

The electrode coordinates are defined in millimeters as [x,y,z] with respect to the following coordinate system:

• the X-axis goes from LPA towards (through) RPA
• the Y-axis goes orthogonally to the X-axis and towards (through) NAS
• the Z-axis goes orthogonally to the X-Y-plane upwards

If the ears are not symmetric, the origin will not be precisely between the ears; e.g., if the right ear is more to the front, the origin will be shifted to the right side of the head.

See below a visualization of the coordinate system.

## Details of the Chieti ITAB coordinate system

The ITAB coordinate system is expressed in meter, with the principal (X, Y, Z) axes going through fiducials that are placed at external landmarks. 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 CTF coordinate system

The CTF coordinate system is expressed in centimeter (except the MRI, which is expressed in millimeter), with the principal (X, Y, Z) axes going through fiducials placed on external landmarks. The fiducials are small coils that prior to the MEG measurement are placed on the landmarks. At the DCCN we usually place them on nasion and on a tube that extends from the left and right ear canal, see here for details. Although the left and right ear markers do not always correspond to the definition of the pre-auricular points (which is in front of the ear), they are commonly referred to in the CTF system as LPA and RPA. The definition of the coordinate system 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 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.

## 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

See also this frequently asked question. Note that the SPM software makes use of the MNI coordinate system.

## 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 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). See also here (search for “Orientation information”).

## 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 similarities and differences in nomenclature 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, here we will use the Bregma point as origin.

• 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 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 Talairach-Tournoux coordinate system

The Co-Planar Stereotaxic Atlas of the Human Brain (1988) by Talairach and Tournoux defines a coordinate system using the Anterior and Posterior Commissure and applies that on a post-mortem dissection of an individual human brain. Furthermore, it introduces a strategy for piece-wise linear scaling to allow other brains to be compared to the template brain that is featured in the atlas. 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, CT scan, or X-ray photo. This is in contrast to the external landmarks that are used for 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