[med-svn] [python-mne] 240/376: fixing manual
Yaroslav Halchenko
debian at onerussian.com
Fri Nov 27 17:22:59 UTC 2015
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yoh pushed a commit to annotated tag v0.1
in repository python-mne.
commit a3d1ccb0029bcd961b8f8aa80bc493458241c177
Author: Emily Ruzich <emilyr at nmr.mgh.harvard.edu>
Date: Tue May 10 12:17:23 2011 -0400
fixing manual
---
doc/source/manual/forward.rst | 111 +++++++++++++++++++++---------------------
1 file changed, 55 insertions(+), 56 deletions(-)
diff --git a/doc/source/manual/forward.rst b/doc/source/manual/forward.rst
index 35860fd..71b2380 100755
--- a/doc/source/manual/forward.rst
+++ b/doc/source/manual/forward.rst
@@ -23,9 +23,9 @@ The coordinate systems used in MNE software (and FreeSurfer)
and their relationships are depicted in :ref:`CHDFFJIJ`.
Except for the *Sensor coordinates*, all of the
coordinate systems are Cartesian and have the "RAS" (Right-Anterior-Superior)
-orientation, *i.e.*, the INLINE_EQUATION axis
-points to the right, the INLINE_EQUATION axis
-to the front, and the INLINE_EQUATION axis up.
+orientation, *i.e.*, the :math:`x` axis
+points to the right, the :math:`y` axis
+to the front, and the :math:`z` axis up.
.. _CHDFFJIJ:
@@ -34,7 +34,7 @@ to the front, and the INLINE_EQUATION axis up.
MEG/EEG and MRI coordinate systems
- The coordinate transforms present in the fif files in MNE and the FreeSurfer files as well as those set to fixed values are indicated with INLINE_EQUATION, where INLINE_EQUATION identifies the transformation.
+ The coordinate transforms present in the fif files in MNE and the FreeSurfer files as well as those set to fixed values are indicated with :math:`T_x`, where :math:`x` identifies the transformation.
The coordinate systems related
to MEG/EEG data are:
@@ -52,7 +52,7 @@ to MEG/EEG data are:
This is a coordinate system tied to the MEG device. The relationship
of the Device and Head coordinates is determined during an MEG measurement
- by feeding current to INLINE_EQUATION head-position
+ by feeding current to three to five head-position
indicator (HPI) coils and by determining their locations with respect
to the MEG sensor array from the magnetic fields they generate.
@@ -112,13 +112,13 @@ to MRI data are:
further from the middle of the brain, towards the outside. The FreeSurfer
Talairach coordinates mitigate this problem by additing a an additional
transformation, defined separately for negatice and positive MNI
- Talairach INLINE_EQUATION coordinates. These two
- transformations, denoted by INLINE_EQUATION and INLINE_EQUATION in :ref:`CHDFFJIJ`, are fixed as discussed in http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach
+ Talairach :math:`z` coordinates. These two
+ transformations, denoted by :math:`T_-` and :math:`T_+` in :ref:`CHDFFJIJ`, are fixed as discussed in http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach
(*Approach 2*).
The different coordinate systems are related by coordinate
transformations depicted in :ref:`CHDFFJIJ`. The arrows and
-coordinate transformation symbols (INLINE_EQUATION)
+coordinate transformation symbols (:math:`T_x`)
indicate the transformations actually present in the FreeSurfer
files. Generally,
@@ -144,15 +144,15 @@ files. Generally,
1
\end{bmatrix}\ ,
-where INLINE_EQUATION are the location
-coordinates in two coordinate systems, INLINE_EQUATION is
+where :math:`x_k`,:math:`y_k`,and :math:`z_k` are the location
+coordinates in two coordinate systems, :math:`T_{12}` is
the coordinate transformation from coordinate system "1" to "2",
-INLINE_EQUATION is the location of the origin
-of coordinate system "1" in coordinate system"2",
-and INLINE_EQUATION are the elements of the rotation
+:math:`x_0`, :math:`y_0`,and :math:`z_0` is the location of the origin
+of coordinate system "1" in coordinate system "2",
+and :math:`R_{jk}` are the elements of the rotation
matrix relating the two coordinate systems. The coordinate transformations
are present in different files produced by FreeSurfer and MNE as
-summarized in :ref:`CHDJDEDJ`. The fixed transformations INLINE_EQUATION and INLINE_EQUATION are:
+summarized in :ref:`CHDJDEDJ`. The fixed transformations :math:`T_-` and :math:`T_+` are:
.. math:: T_{-} = \begin{bmatrix}
0.99 & 0 & 0 & 0 \\
@@ -175,18 +175,18 @@ and
.. _CHDJDEDJ:
.. tabularcolumns:: |p{0.2\linewidth}|p{0.3\linewidth}||p{0.5\linewidth}|
-.. table:: Coordinate transformations in FreeSurfer and MNE software packages. The symbols INLINE_EQUATION are defined in :ref:`CHDFFJIJ` Note: mne_make_cor_set /mne_setup_mri prior to release 2.6 did not include transformations INLINE_EQUATION, INLINE_EQUATION, INLINE_EQUATION, and INLINE_EQUATION in the fif files produced.).
+.. table:: Coordinate transformations in FreeSurfer and MNE software packages. The symbols :math:`T_x` are defined in :ref:`CHDFFJIJ` Note: mne_make_cor_set /mne_setup_mri prior to release 2.6 did not include transformations :math:`T_3`, :math:`T_4`, :math:`T_-`, and :math:`T_+` in the fif files produced.).
================== =============================== =======================================================================================================================================
Transformation FreeSurfer MNE
================== =============================== =======================================================================================================================================
- INLINE_EQUATION Not present Measurement data files Forward solution files (*fwd.fif) Inverse operator files (*inv.fif)
- INLINE_EQUATION Not present Channel information in files containing INLINE_EQUATION.
- INLINE_EQUATION Not present MRI description files Separate coordinate transformation files saved from mne_analyze Forward solution files Inverse operator files
- INLINE_EQUATION mri/*mgz files MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
- INLINE_EQUATION mri/transforms/talairach.xfm MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
- INLINE_EQUATION Hardcoded in software MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
- INLINE_EQUATION Hardcoded in software MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
+ :math:`T_1` Not present Measurement data files Forward solution files (*fwd.fif) Inverse operator files (*inv.fif)
+ :math:`T_{s_1} \dotso T_{s_n}` Not present Channel information in files containing :math:`T_1`.
+ :math:`T_2` Not present MRI description files Separate coordinate transformation files saved from mne_analyze Forward solution files Inverse operator files
+ :math:`T_3` mri/*mgz files MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
+ :math:`T_4` mri/transforms/talairach.xfm MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
+ :math:`T_-` Hardcoded in software MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
+ :math:`T_+` Hardcoded in software MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
================== =============================== =======================================================================================================================================
.. _BJEBIBAI:
@@ -200,28 +200,28 @@ The head and device coordinate systems
The head coordinate system
The MEG/EEG head coordinate system employed in the MNE software
-is a right-handed Cartesian coordinate system. The direction of INLINE_EQUATION axis
-is from left to right, that of INLINE_EQUATION axis
-to the front, and the INLINE_EQUATION axis thus
+is a right-handed Cartesian coordinate system. The direction of :math:`x` axis
+is from left to right, that of :math:`y` axis
+to the front, and the :math:`z` axis thus
points up.
-The INLINE_EQUATION axis of the head coordinate
+The :math:`x` axis of the head coordinate
system passes through the two periauricular or preauricular points
digitized before acquiring the data with positive direction to the
-right. The INLINE_EQUATION axis passes through
-the nasion and is normal to the INLINE_EQUATION axis.
-The INLINE_EQUATION axis points up according to
-the right-hand rule and is normal to the INLINE_EQUATION plane.
+right. The :math:`y` axis passes through
+the nasion and is normal to the :math:`x` axis.
+The :math:`z` axis points up according to
+the right-hand rule and is normal to the :math:`xy` plane.
The origin of the MEG device coordinate system is device
dependent. Its origin is located approximately at the center of
a sphere which fits the occipital section of the MEG helmet best
-with INLINE_EQUATION axis going from left to right
-and INLINE_EQUATION axis pointing front. The INLINE_EQUATION axis
-is, again normal to the INLINE_EQUATION plane
+with :math:`x` axis axis going from left to right
+and :math:`y` axis pointing front. The :math:`z` axis
+is, again, normal to the :math:`xy` plane
with positive direction up.
-.. note:: The above definition is identical to that of the Neuromag MEG/EEG (head) coordinate system. However, in 4-D Neuroimaging and CTF MEG systems the head coordinate frame definition is different. The origin of the coordinate system is at the midpoint of the left and right auricular points. The INLINE_EQUATION axis passes through the nasion and the origin with positive direction to the front. The INLINE_EQUATION axis is perpendicular to the INLINE_EQUATION axis [...]
+.. note:: The above definition is identical to that of the Neuromag MEG/EEG (head) coordinate system. However, in 4-D Neuroimaging and CTF MEG systems the head coordinate frame definition is different. The origin of the coordinate system is at the midpoint of the left and right auricular points. The :math:`x` axis passes through the nasion and the origin with positive direction to the front. The :math:`y` axis is perpendicular to the :math:`x` axis on the and lies in [...]
.. _BEHCGJDD:
@@ -285,9 +285,9 @@ The command-line options are:
of triangles increases by a factor of four in each subdivision,
starting from 20 triangles in an icosahedron and 8 triangles in
an octahedron. Since the number of vertices on a closed surface
- is INLINE_EQUATION, the number of vertices in
- the *k*th subdivision of an icosahedron and an
- octahedron are INLINE_EQUATION and INLINE_EQUATION,
+ is :math:`n_{vert} = (n_{tri} + 4) / 2`, the number of vertices in
+ the *k* th subdivision of an icosahedron and an
+ octahedron are :math:`10 \cdot 4^k +2` and :math:`4_{k + 1} + 2`,
respectively. The recommended values for <*number*> and
the corresponding number of source space locations are listed in Table 3.1.
@@ -301,7 +301,7 @@ The command-line options are:
**\---src <*name*>**
- Output file name. Use a name * <*dir*>/ <*name*>*-src.fif
+ Output file name. Use a name <*dir*>/<*name*>-src.fif
.. note:: If both ``--ico`` and ``--spacing`` options are present the later one on the command line takes precedence.
@@ -572,24 +572,24 @@ topology checks are performed:
- The completeness of each surface is
confirmed by calculating the total solid angle subtended by all
triangles from a point inside the triangulation. The result should
- be very close to INLINE_EQUATION. If the result
- is INLINE_EQUATION instead, it is conceivable
+ be very close to :math:`4 \pi`. If the result
+ is :math:`-4 \pi` instead, it is conceivable
that the ordering of the triangle vertices is incorrect and the
``--swap`` option should be specified.
- The correct ordering of the surfaces is verified by checking
that the surfaces are inside each other as expected. This is accomplished
by checking that the sum solid angles subtended by triangles of
- a surface INLINE_EQUATION at all vertices of another
- surface INLINE_EQUATION which is supposed to be
- inside it equals INLINE_EQUATION. Naturally, this
+ a surface :math:`S_k` at all vertices of another
+ surface :math:`S_p` which is supposed to be
+ inside it equals :math:`4 \pi`. Naturally, this
check is applied only if the model has more than one surface. Since
the surface relations are transitive, it is enough to check that
the outer skull surface is inside the skin surface and that the
inner skull surface is inside the outer skull one.
- The extent of each of the triangulated volumes is checked.
- If the extent is smaller than 50 mm, an error is reported. This
+ If the extent is smaller than 50mm, an error is reported. This
may indicate that the vertex coordinates have been specified in
meters instead of millimeters.
@@ -660,15 +660,14 @@ was used. Optionally, the MNE software forward calculation applies
another coordinate transformation to the head-coordinate data to
bring the coil locations and orientations to the MRI coordinate system.
-If INLINE_EQUATION is a row vector for
-the origin of the local sensor coordinate system and INLINE_EQUATION, INLINE_EQUATION,
-and INLINE_EQUATION are the row vectors for the
+If :math:`r_0` is a row vector for
+the origin of the local sensor coordinate system and :math:`e_x`, :math:`e_y`, and :math:`e_z` are the row vectors for the
three orthogonal unit vectors, all given in device coordinates,
-a location of a point INLINE_EQUATION in sensor coordinates
-is transformed to device coordinates (INLINE_EQUATION)
+a location of a point :math:`r_C` in sensor coordinates
+is transformed to device coordinates (:math:`r_D`)
by
-.. math:: [r_D 1] = [r_c 1] T_{CD}\ ,
+.. math:: [r_D 1] = [r_C 1] T_{CD}\ ,
where
@@ -693,18 +692,18 @@ The output of each SQUID sensor is a weighted sum of the
magnetic fluxes threading the loops comprising the detection coil.
Since the flux threading a coil loop is an integral of the magnetic
field component normal to the coil plane, the output of the *k*th
-MEG channel, INLINE_EQUATION, can be approximated
+MEG channel, :math:`b_k`, can be approximated
by:
.. math:: b_k = \sum_{p = 1}^{N_k} {w_{kp} B(r_{kp}) \cdot n_{kp}}
-where INLINE_EQUATION are a set of INLINE_EQUATION integration
-points covering the pickup coil loops of the sensor, INLINE_EQUATION is
-the magnetic field due to the current sources calculated at INLINE_EQUATION, INLINE_EQUATION are
-the coil normal directions at these points, and INLINE_EQUATION are
+where :math:`r_{kp}` are a set of :math:`N_k` integration
+points covering the pickup coil loops of the sensor, :math:`B(r_{kp})` is
+the magnetic field due to the current sources calculated at :math:`r_{kp}`, :math:`n_{kp}` are
+the coil normal directions at these points, and :math:`w_{kp}` are
the weights associated to the integration points. This formula essentially
presents numerical integration of the magnetic field over the pickup
-loops of sensor INLINE_EQUATION.
+loops of sensor :math:`k`.
There are three accuracy levels for the numerical integration
expressed above. The *simple* accuracy means
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