#ifndef _NIFTI_HEADER_
#define _NIFTI_HEADER_
/*LICENSE_START*/
/*
* Copyright (c) 2014, Washington University School of Medicine
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* NOTE: our version is somewhat modified, turning constant #defines into const int32_t, namespacing, removal of some other #defines, to try to coexist with the original header
*/
namespace cifti
{
/*****************************************************************************
** This file defines the "NIFTI-1" header format. **
** It is derived from 2 meetings at the NIH (31 Mar 2003 and **
** 02 Sep 2003) of the Data Format Working Group (DFWG), **
** chartered by the NIfTI (Neuroimaging Informatics Technology **
** Initiative) at the National Institutes of Health (NIH). **
**--------------------------------------------------------------**
** Neither the National Institutes of Health (NIH), the DFWG, **
** nor any of the members or employees of these institutions **
** imply any warranty of usefulness of this material for any **
** purpose, and do not assume any liability for damages, **
** incidental or otherwise, caused by any use of this document. **
** If these conditions are not acceptable, do not use this! **
**--------------------------------------------------------------**
** Author: Robert W Cox (NIMH, Bethesda) **
** Advisors: John Ashburner (FIL, London), **
** Stephen Smith (FMRIB, Oxford), **
** Mark Jenkinson (FMRIB, Oxford) **
******************************************************************************/
/*---------------------------------------------------------------------------*/
/* Note that the ANALYZE 7.5 file header (dbh.h) is
(c) Copyright 1986-1995
Biomedical Imaging Resource
Mayo Foundation
Incorporation of components of dbh.h are by permission of the
Mayo Foundation.
Changes from the ANALYZE 7.5 file header in this file are released to the
public domain, including the functional comments and any amusing asides.
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/*! INTRODUCTION TO NIFTI-1:
------------------------
The twin (and somewhat conflicting) goals of this modified ANALYZE 7.5
format are:
(a) To add information to the header that will be useful for functional
neuroimaging data analysis and display. These additions include:
- More basic data types.
- Two affine transformations to specify voxel coordinates.
- "Intent" codes and parameters to describe the meaning of the data.
- Affine scaling of the stored data values to their "true" values.
- Optional storage of the header and image data in one file (.nii).
(b) To maintain compatibility with non-NIFTI-aware ANALYZE 7.5 compatible
software (i.e., such a program should be able to do something useful
with a NIFTI-1 dataset -- at least, with one stored in a traditional
.img/.hdr file pair).
Most of the unused fields in the ANALYZE 7.5 header have been taken,
and some of the lesser-used fields have been co-opted for other purposes.
Notably, most of the data_history substructure has been co-opted for
other purposes, since the ANALYZE 7.5 format describes this substructure
as "not required".
NIFTI-1 FLAG (MAGIC STRINGS):
----------------------------
To flag such a struct as being conformant to the NIFTI-1 spec, the last 4
bytes of the header must be either the C String "ni1" or "n+1";
in hexadecimal, the 4 bytes
6E 69 31 00 or 6E 2B 31 00
(in any future version of this format, the '1' will be upgraded to '2',
etc.). Normally, such a "magic number" or flag goes at the start of the
file, but trying to avoid clobbering widely-used ANALYZE 7.5 fields led to
putting this marker last. However, recall that "the last shall be first"
(Matthew 20:16).
If a NIFTI-aware program reads a header file that is NOT marked with a
NIFTI magic string, then it should treat the header as an ANALYZE 7.5
structure.
NIFTI-1 FILE STORAGE:
--------------------
"ni1" means that the image data is stored in the ".img" file corresponding
to the header file (starting at file offset 0).
"n+1" means that the image data is stored in the same file as the header
information. We recommend that the combined header+data filename suffix
be ".nii". When the dataset is stored in one file, the first byte of image
data is stored at byte location (int)vox_offset in this combined file.
The minimum allowed value of vox_offset is 352; for compatibility with
some software, vox_offset should be an integral multiple of 16.
GRACE UNDER FIRE:
----------------
Most NIFTI-aware programs will only be able to handle a subset of the full
range of datasets possible with this format. All NIFTI-aware programs
should take care to check if an input dataset conforms to the program's
needs and expectations (e.g., check datatype, intent_code, etc.). If the
input dataset can't be handled by the program, the program should fail
gracefully (e.g., print a useful warning; not crash).
SAMPLE CODES:
------------
The associated files nifti1_io.h and nifti1_io.c provide a sample
implementation in C of a set of functions to read, write, and manipulate
NIFTI-1 files. The file nifti1_test.c is a sample program that uses
the nifti1_io.c functions.
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* HEADER STRUCT DECLARATION:
-------------------------
In the comments below for each field, only NIFTI-1 specific requirements
or changes from the ANALYZE 7.5 format are described. For convenience,
the 348 byte header is described as a single struct, rather than as the
ANALYZE 7.5 group of 3 substructs.
Further comments about the interpretation of various elements of this
header are after the data type definition itself. Fields that are
marked as ++UNUSED++ have no particular interpretation in this standard.
(Also see the UNUSED FIELDS comment section, far below.)
The presumption below is that the various C types have particular sizes:
sizeof(int) = sizeof(float) = 4 ; sizeof(short) = 2
-----------------------------------------------------------------------------*/
//hopefully cross-platform solution to byte padding added by some compilers
#pragma pack(push)
#pragma pack(1)
/*! \struct nifti_1_header
\brief Data structure defining the fields in the nifti1 header.
This binary header should be found at the beginning of a valid
NIFTI-1 header file.
*/
/*************************/ /************************/
struct nifti_1_header { /* NIFTI-1 usage */ /* ANALYZE 7.5 field(s) */
/*************************/ /************************/
/*--- was header_key substruct ---*/
int sizeof_hdr; /*!< MUST be 348 */ /* int sizeof_hdr; */ /* 0 */
char data_type[10]; /*!< ++UNUSED++ */ /* char data_type[10]; */ /* 4 */
char db_name[18]; /*!< ++UNUSED++ */ /* char db_name[18]; */ /* 14 */
int extents; /*!< ++UNUSED++ */ /* int extents; */ /* 32 */
short session_error; /*!< ++UNUSED++ */ /* short session_error; */ /* 36 */
char regular; /*!< ++UNUSED++ */ /* char regular; */ /* 38 */
char dim_info; /*!< MRI slice ordering. */ /* char hkey_un0; */ /* 39 */
/*--- was image_dimension substruct ---*/
short dim[8]; /*!< Data array dimensions.*/ /* short dim[8]; */ /* 40 */
float intent_p1 ; /*!< 1st intent parameter. */ /* short unused8; */ /* 56 */
/* short unused9; */
float intent_p2 ; /*!< 2nd intent parameter. */ /* short unused10; */ /* 60 */
/* short unused11; */
float intent_p3 ; /*!< 3rd intent parameter. */ /* short unused12; */ /* 64 */
/* short unused13; */
short intent_code ; /*!< NIFTI_INTENT_* code. */ /* short unused14; */ /* 68 */
short datatype; /*!< Defines data type! */ /* short datatype; */ /* 70 */
short bitpix; /*!< Number bits/voxel. */ /* short bitpix; */ /* 72 */
short slice_start; /*!< First slice index. */ /* short dim_un0; */ /* 74 */
float pixdim[8]; /*!< Grid spacings. */ /* float pixdim[8]; */ /* 76 */
float vox_offset; /*!< Offset into .nii file */ /* float vox_offset; */ /* 108 */
float scl_slope ; /*!< Data scaling: slope. */ /* float funused1; */ /* 112 */
float scl_inter ; /*!< Data scaling: offset. */ /* float funused2; */ /* 116 */
short slice_end; /*!< Last slice index. */ /* float funused3; */ /* 120 */
char slice_code ; /*!< Slice timing order. */ /* 122 */
char xyzt_units ; /*!< Units of pixdim[1..4] */ /* 123 */
float cal_max; /*!< Max display intensity */ /* float cal_max; */ /* 124 */
float cal_min; /*!< Min display intensity */ /* float cal_min; */ /* 128 */
float slice_duration;/*!< Time for 1 slice. */ /* float compressed; */ /* 132 */
float toffset; /*!< Time axis shift. */ /* float verified; */ /* 136 */
int glmax; /*!< ++UNUSED++ */ /* int glmax; */ /* 140 */
int glmin; /*!< ++UNUSED++ */ /* int glmin; */ /* 144 */
/*--- was data_history substruct ---*/
char descrip[80]; /*!< any text you like. */ /* char descrip[80]; */ /* 148 */
char aux_file[24]; /*!< auxiliary filename. */ /* char aux_file[24]; */ /* 228 */
short qform_code ; /*!< NIFTI_XFORM_* code. */ /*-- all ANALYZE 7.5 ---*/ /* 252 */
short sform_code ; /*!< NIFTI_XFORM_* code. */ /* fields below here */ /* 254 */
/* are replaced */
float quatern_b ; /*!< Quaternion b param. */ /* 256 */
float quatern_c ; /*!< Quaternion c param. */ /* 260 */
float quatern_d ; /*!< Quaternion d param. */ /* 264 */
float qoffset_x ; /*!< Quaternion x shift. */ /* 268 */
float qoffset_y ; /*!< Quaternion y shift. */ /* 272 */
float qoffset_z ; /*!< Quaternion z shift. */ /* 276 */
float srow_x[4] ; /*!< 1st row affine transform. */ /* 280 */
float srow_y[4] ; /*!< 2nd row affine transform. */ /* 296 */
float srow_z[4] ; /*!< 3rd row affine transform. */ /* 312 */
char intent_name[16];/*!< 'name' or meaning of data. */ /* 328 */
char magic[4] ; /*!< MUST be "ni1\0" or "n+1\0". */ /* 344 */
} ; /**** 348 bytes total ****/
typedef struct nifti_1_header nifti_1_header ;
/*---------------------------------------------------------------------------*/
/* HEADER EXTENSIONS:
-----------------
After the end of the 348 byte header (e.g., after the magic field),
the next 4 bytes are a char array field named "extension". By default,
all 4 bytes of this array should be set to zero. In a .nii file, these
4 bytes will always be present, since the earliest start point for
the image data is byte #352. In a separate .hdr file, these bytes may
or may not be present. If not present (i.e., if the length of the .hdr
file is 348 bytes), then a NIfTI-1 compliant program should use the
default value of extension={0,0,0,0}. The first byte (extension[0])
is the only value of this array that is specified at present. The other
3 bytes are reserved for future use.
If extension[0] is nonzero, it indicates that extended header information
is present in the bytes following the extension array. In a .nii file,
this extended header data is before the image data (and vox_offset
must be set correctly to allow for this). In a .hdr file, this extended
data follows extension and proceeds (potentially) to the end of the file.
The format of extended header data is weakly specified. Each extension
must be an integer multiple of 16 bytes long. The first 8 bytes of each
extension comprise 2 integers:
int esize , ecode ;
These values may need to be byte-swapped, as indicated by dim[0] for
the rest of the header.
* esize is the number of bytes that form the extended header data
+ esize must be a positive integral multiple of 16
+ this length includes the 8 bytes of esize and ecode themselves
* ecode is a non-negative integer that indicates the format of the
extended header data that follows
+ different ecode values are assigned to different developer groups
+ at present, the "registered" values for code are
= 0 = unknown private format (not recommended!)
= 2 = DICOM format (i.e., attribute tags and values)
= 4 = AFNI group (i.e., ASCII XML-ish elements)
In the interests of interoperability (a primary rationale for NIfTI),
groups developing software that uses this extension mechanism are
encouraged to document and publicize the format of their extensions.
To this end, the NIfTI DFWG will assign even numbered codes upon request
to groups submitting at least rudimentary documentation for the format
of their extension; at present, the contact is mailto:rwcox@nih.gov.
The assigned codes and documentation will be posted on the NIfTI
website. All odd values of ecode (and 0) will remain unassigned;
at least, until the even ones are used up, when we get to 2,147,483,646.
Note that the other contents of the extended header data section are
totally unspecified by the NIfTI-1 standard. In particular, if binary
data is stored in such a section, its byte order is not necessarily
the same as that given by examining dim[0]; it is incumbent on the
programs dealing with such data to determine the byte order of binary
extended header data.
Multiple extended header sections are allowed, each starting with an
esize,ecode value pair. The first esize value, as described above,
is at bytes #352-355 in the .hdr or .nii file (files start at byte #0).
If this value is positive, then the second (esize2) will be found
starting at byte #352+esize1 , the third (esize3) at byte #352+esize1+esize2,
et cetera. Of course, in a .nii file, the value of vox_offset must
be compatible with these extensions. If a malformed file indicates
that an extended header data section would run past vox_offset, then
the entire extended header section should be ignored. In a .hdr file,
if an extended header data section would run past the end-of-file,
that extended header data should also be ignored.
With the above scheme, a program can successively examine the esize
and ecode values, and skip over each extended header section if the
program doesn't know how to interpret the data within. Of course, any
program can simply ignore all extended header sections simply by jumping
straight to the image data using vox_offset.
-----------------------------------------------------------------------------*/
/*! \struct nifti1_extender
\brief This structure represents a 4-byte string that should follow the
binary nifti_1_header data in a NIFTI-1 header file. If the char
values are {1,0,0,0}, the file is expected to contain extensions,
values of {0,0,0,0} imply the file does not contain extensions.
Other sequences of values are not currently defined.
*/
struct nifti1_extender { char extension[4] ; } ;
typedef struct nifti1_extender nifti1_extender ;
/*! \struct nifti1_extension
\brief Data structure defining the fields of a header extension.
*/
struct nifti1_extension {
int esize ; /*!< size of extension, in bytes (must be multiple of 16) */
int ecode ; /*!< extension code, one of the NIFTI_ECODE_ values */
char * edata ; /*!< raw data, with no byte swapping */
} ;
typedef struct nifti1_extension nifti1_extension ;
//and restore packing behavior
#pragma pack(pop)
/*---------------------------------------------------------------------------*/
/* DATA DIMENSIONALITY (as in ANALYZE 7.5):
---------------------------------------
dim[0] = number of dimensions;
- if dim[0] is outside range 1..7, then the header information
needs to be byte swapped appropriately
- ANALYZE supports dim[0] up to 7, but NIFTI-1 reserves
dimensions 1,2,3 for space (x,y,z), 4 for time (t), and
5,6,7 for anything else needed.
dim[i] = length of dimension #i, for i=1..dim[0] (must be positive)
- also see the discussion of intent_code, far below
pixdim[i] = voxel width along dimension #i, i=1..dim[0] (positive)
- cf. ORIENTATION section below for use of pixdim[0]
- the units of pixdim can be specified with the xyzt_units
field (also described far below).
Number of bits per voxel value is in bitpix, which MUST correspond with
the datatype field. The total number of bytes in the image data is
dim[1] * ... * dim[dim[0]] * bitpix / 8
In NIFTI-1 files, dimensions 1,2,3 are for space, dimension 4 is for time,
and dimension 5 is for storing multiple values at each spatiotemporal
voxel. Some examples:
- A typical whole-brain FMRI experiment's time series:
- dim[0] = 4
- dim[1] = 64 pixdim[1] = 3.75 xyzt_units = NIFTI_UNITS_MM
- dim[2] = 64 pixdim[2] = 3.75 | NIFTI_UNITS_SEC
- dim[3] = 20 pixdim[3] = 5.0
- dim[4] = 120 pixdim[4] = 2.0
- A typical T1-weighted anatomical volume:
- dim[0] = 3
- dim[1] = 256 pixdim[1] = 1.0 xyzt_units = NIFTI_UNITS_MM
- dim[2] = 256 pixdim[2] = 1.0
- dim[3] = 128 pixdim[3] = 1.1
- A single slice EPI time series:
- dim[0] = 4
- dim[1] = 64 pixdim[1] = 3.75 xyzt_units = NIFTI_UNITS_MM
- dim[2] = 64 pixdim[2] = 3.75 | NIFTI_UNITS_SEC
- dim[3] = 1 pixdim[3] = 5.0
- dim[4] = 1200 pixdim[4] = 0.2
- A 3-vector stored at each point in a 3D volume:
- dim[0] = 5
- dim[1] = 256 pixdim[1] = 1.0 xyzt_units = NIFTI_UNITS_MM
- dim[2] = 256 pixdim[2] = 1.0
- dim[3] = 128 pixdim[3] = 1.1
- dim[4] = 1 pixdim[4] = 0.0
- dim[5] = 3 intent_code = NIFTI_INTENT_VECTOR
- A single time series with a 3x3 matrix at each point:
- dim[0] = 5
- dim[1] = 1 xyzt_units = NIFTI_UNITS_SEC
- dim[2] = 1
- dim[3] = 1
- dim[4] = 1200 pixdim[4] = 0.2
- dim[5] = 9 intent_code = NIFTI_INTENT_GENMATRIX
- intent_p1 = intent_p2 = 3.0 (indicates matrix dimensions)
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* DATA STORAGE:
------------
If the magic field is "n+1", then the voxel data is stored in the
same file as the header. In this case, the voxel data starts at offset
(int)vox_offset into the header file. Thus, vox_offset=352.0 means that
the data starts immediately after the NIFTI-1 header. If vox_offset is
greater than 352, the NIFTI-1 format does not say much about the
contents of the dataset file between the end of the header and the
start of the data.
FILES:
-----
If the magic field is "ni1", then the voxel data is stored in the
associated ".img" file, starting at offset 0 (i.e., vox_offset is not
used in this case, and should be set to 0.0).
When storing NIFTI-1 datasets in pairs of files, it is customary to name
the files in the pattern "name.hdr" and "name.img", as in ANALYZE 7.5.
When storing in a single file ("n+1"), the file name should be in
the form "name.nii" (the ".nft" and ".nif" suffixes are already taken;
cf. http://www.icdatamaster.com/n.html ).
BYTE ORDERING:
-------------
The byte order of the data arrays is presumed to be the same as the byte
order of the header (which is determined by examining dim[0]).
Floating point types are presumed to be stored in IEEE-754 format.
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* DETAILS ABOUT vox_offset:
------------------------
In a .nii file, the vox_offset field value is interpreted as the start
location of the image data bytes in that file. In a .hdr/.img file pair,
the vox_offset field value is the start location of the image data
bytes in the .img file.
* If vox_offset is less than 352 in a .nii file, it is equivalent
to 352 (i.e., image data never starts before byte #352 in a .nii file).
* The default value for vox_offset in a .nii file is 352.
* In a .hdr file, the default value for vox_offset is 0.
* vox_offset should be an integer multiple of 16; otherwise, some
programs may not work properly (e.g., SPM). This is to allow
memory-mapped input to be properly byte-aligned.
Note that since vox_offset is an IEEE-754 32 bit float (for compatibility
with the ANALYZE-7.5 format), it effectively has a 24 bit mantissa. All
integers from 0 to 2^24 can be represented exactly in this format, but not
all larger integers are exactly storable as IEEE-754 32 bit floats. However,
unless you plan to have vox_offset be potentially larger than 16 MB, this
should not be an issue. (Actually, any integral multiple of 16 up to 2^27
can be represented exactly in this format, which allows for up to 128 MB
of random information before the image data. If that isn't enough, then
perhaps this format isn't right for you.)
In a .img file (i.e., image data stored separately from the NIfTI-1
header), data bytes between #0 and #vox_offset-1 (inclusive) are completely
undefined and unregulated by the NIfTI-1 standard. One potential use of
having vox_offset > 0 in the .hdr/.img file pair storage method is to make
the .img file be a copy of (or link to) a pre-existing image file in some
other format, such as DICOM; then vox_offset would be set to the offset of
the image data in this file. (It may not be possible to follow the
"multiple-of-16 rule" with an arbitrary external file; using the NIfTI-1
format in such a case may lead to a file that is incompatible with software
that relies on vox_offset being a multiple of 16.)
In a .nii file, data bytes between #348 and #vox_offset-1 (inclusive) may
be used to store user-defined extra information; similarly, in a .hdr file,
any data bytes after byte #347 are available for user-defined extra
information. The (very weak) regulation of this extra header data is
described elsewhere.
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* DATA SCALING:
------------
If the scl_slope field is nonzero, then each voxel value in the dataset
should be scaled as
y = scl_slope * x + scl_inter
where x = voxel value stored
y = "true" voxel value
Normally, we would expect this scaling to be used to store "true" floating
values in a smaller integer datatype, but that is not required. That is,
it is legal to use scaling even if the datatype is a float type (crazy,
perhaps, but legal).
- However, the scaling is to be ignored if datatype is DT_RGB24.
- If datatype is a complex type, then the scaling is to be
applied to both the real and imaginary parts.
The cal_min and cal_max fields (if nonzero) are used for mapping (possibly
scaled) dataset values to display colors:
- Minimum display intensity (black) corresponds to dataset value cal_min.
- Maximum display intensity (white) corresponds to dataset value cal_max.
- Dataset values below cal_min should display as black also, and values
above cal_max as white.
- Colors "black" and "white", of course, may refer to any scalar display
scheme (e.g., a color lookup table specified via aux_file).
- cal_min and cal_max only make sense when applied to scalar-valued
datasets (i.e., dim[0] < 5 or dim[5] = 1).
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* TYPE OF DATA (acceptable values for datatype field):
---------------------------------------------------
Values of datatype smaller than 256 are ANALYZE 7.5 compatible.
Larger values are NIFTI-1 additions. These are all multiples of 256, so
that no bits below position 8 are set in datatype. But there is no need
to use only powers-of-2, as the original ANALYZE 7.5 datatype codes do.
The additional codes are intended to include a complete list of basic
scalar types, including signed and unsigned integers from 8 to 64 bits,
floats from 32 to 128 bits, and complex (float pairs) from 64 to 256 bits.
Note that most programs will support only a few of these datatypes!
A NIFTI-1 program should fail gracefully (e.g., print a warning message)
when it encounters a dataset with a type it doesn't like.
-----------------------------------------------------------------------------*/
#undef DT_UNKNOWN /* defined in dirent.h on some Unix systems */
#include<stdint.h>
/*! \defgroup NIFTI1_DATATYPES
\brief nifti1 datatype codes
@{
*/
/*--- the original ANALYZE 7.5 type codes ---*/
const int32_t DT_NONE =0;
const int32_t DT_UNKNOWN =0; /* what it says, dude */
const int32_t DT_BINARY =1; /* binary (1 bit/voxel) */
const int32_t DT_UNSIGNED_CHAR =2; /* unsigned char (8 bits/voxel) */
const int32_t DT_SIGNED_SHORT =4; /* signed short (16 bits/voxel) */
const int32_t DT_SIGNED_INT =8; /* signed int (32 bits/voxel) */
const int32_t DT_FLOAT =16; /* float (32 bits/voxel) */
const int32_t DT_COMPLEX =32; /* complex (64 bits/voxel) */
const int32_t DT_DOUBLE =64; /* double (64 bits/voxel) */
const int32_t DT_RGB =128; /* RGB triple (24 bits/voxel) */
const int32_t DT_ALL =255; /* not very useful (?) */
/*----- another set of names for the same ---*/
const int32_t DT_UINT8 =2;
const int32_t DT_INT16 =4;
const int32_t DT_INT32 =8;
const int32_t DT_FLOAT32 =16;
const int32_t DT_COMPLEX64 =32;
const int32_t DT_FLOAT64 =64;
const int32_t DT_RGB24 =128;
/*------------------- new codes for NIFTI ---*/
const int32_t DT_INT8 =256; /* signed char (8 bits) */
const int32_t DT_UINT16 =512; /* unsigned short (16 bits) */
const int32_t DT_UINT32 =768; /* unsigned int (32 bits) */
const int32_t DT_INT64 =1024; /* long long (64 bits) */
const int32_t DT_UINT64 =1280; /* unsigned long long (64 bits) */
const int32_t DT_FLOAT128 =1536; /* long double (128 bits) */
const int32_t DT_COMPLEX128 =1792; /* double pair (128 bits) */
const int32_t DT_COMPLEX256 =2048; /* long double pair (256 bits) */
/* @} */
/*------- aliases for all the above codes ---*/
/*! \defgroup NIFTI1_DATATYPE_ALIASES
\brief aliases for the nifti1 datatype codes
@{
*/
/*! unsigned char. */
const int32_t NIFTI_TYPE_UINT8 =2;
/*! signed short. */
const int32_t NIFTI_TYPE_INT16 =4;
/*! signed int. */
const int32_t NIFTI_TYPE_INT32 =8;
/*! 32 bit float. */
const int32_t NIFTI_TYPE_FLOAT32 =16;
/*! 64 bit complex = 2 32 bit floats. */
const int32_t NIFTI_TYPE_COMPLEX64 =32;
/*! 64 bit float = double. */
const int32_t NIFTI_TYPE_FLOAT64 =64;
/*! 3 8 bit bytes. */
const int32_t NIFTI_TYPE_RGB24 =128;
/*! signed char. */
const int32_t NIFTI_TYPE_INT8 =256;
/*! unsigned short. */
const int32_t NIFTI_TYPE_UINT16 =512;
/*! unsigned int. */
const int32_t NIFTI_TYPE_UINT32 =768;
/*! signed long long. */
const int32_t NIFTI_TYPE_INT64 =1024;
/*! unsigned long long. */
const int32_t NIFTI_TYPE_UINT64 =1280;
/*! 128 bit float = long double. */
const int32_t NIFTI_TYPE_FLOAT128 =1536;
/*! 128 bit complex = 2 64 bit floats. */
const int32_t NIFTI_TYPE_COMPLEX128 =1792;
/*! 256 bit complex = 2 128 bit floats */
const int32_t NIFTI_TYPE_COMPLEX256 =2048;
/* @} */
/*-------- sample typedefs for complicated types ---*/
#if 0
typedef struct { float r,i; } complex_float ;
typedef struct { double r,i; } complex_double ;
typedef struct { long double r,i; } complex_longdouble ;
typedef struct { unsigned char r,g,b; } rgb_byte ;
#endif
/*---------------------------------------------------------------------------*/
/* INTERPRETATION OF VOXEL DATA:
----------------------------
The intent_code field can be used to indicate that the voxel data has
some particular meaning. In particular, a large number of codes is
given to indicate that the the voxel data should be interpreted as
being drawn from a given probability distribution.
VECTOR-VALUED DATASETS:
----------------------
The 5th dimension of the dataset, if present (i.e., dim[0]=5 and
dim[5] > 1), contains multiple values (e.g., a vector) to be stored
at each spatiotemporal location. For example, the header values
- dim[0] = 5
- dim[1] = 64
- dim[2] = 64
- dim[3] = 20
- dim[4] = 1 (indicates no time axis)
- dim[5] = 3
- datatype = DT_FLOAT
- intent_code = NIFTI_INTENT_VECTOR
mean that this dataset should be interpreted as a 3D volume (64x64x20),
with a 3-vector of floats defined at each point in the 3D grid.
A program reading a dataset with a 5th dimension may want to reformat
the image data to store each voxels' set of values together in a struct
or array. This programming detail, however, is beyond the scope of the
NIFTI-1 file specification! Uses of dimensions 6 and 7 are also not
specified here.
STATISTICAL PARAMETRIC DATASETS (i.e., SPMs):
--------------------------------------------
Values of intent_code from NIFTI_FIRST_STATCODE to NIFTI_LAST_STATCODE
(inclusive) indicate that the numbers in the dataset should be interpreted
as being drawn from a given distribution. Most such distributions have
auxiliary parameters (e.g., NIFTI_INTENT_TTEST has 1 DOF parameter).
If the dataset DOES NOT have a 5th dimension, then the auxiliary parameters
are the same for each voxel, and are given in header fields intent_p1,
intent_p2, and intent_p3.
If the dataset DOES have a 5th dimension, then the auxiliary parameters
are different for each voxel. For example, the header values
- dim[0] = 5
- dim[1] = 128
- dim[2] = 128
- dim[3] = 1 (indicates a single slice)
- dim[4] = 1 (indicates no time axis)
- dim[5] = 2
- datatype = DT_FLOAT
- intent_code = NIFTI_INTENT_TTEST
mean that this is a 2D dataset (128x128) of t-statistics, with the
t-statistic being in the first "plane" of data and the degrees-of-freedom
parameter being in the second "plane" of data.
If the dataset 5th dimension is used to store the voxel-wise statistical
parameters, then dim[5] must be 1 plus the number of parameters required
by that distribution (e.g., intent_code=NIFTI_INTENT_TTEST implies dim[5]
must be 2, as in the example just above).
Note: intent_code values 2..10 are compatible with AFNI 1.5x (which is
why there is no code with value=1, which is obsolescent in AFNI).
OTHER INTENTIONS:
----------------
The purpose of the intent_* fields is to help interpret the values
stored in the dataset. Some non-statistical values for intent_code
and conventions are provided for storing other complex data types.
The intent_name field provides space for a 15 character (plus 0 byte)
'name' string for the type of data stored. Examples:
- intent_code = NIFTI_INTENT_ESTIMATE; intent_name = "T1";
could be used to signify that the voxel values are estimates of the
NMR parameter T1.
- intent_code = NIFTI_INTENT_TTEST; intent_name = "House";
could be used to signify that the voxel values are t-statistics
for the significance of 'activation' response to a House stimulus.
- intent_code = NIFTI_INTENT_DISPVECT; intent_name = "ToMNI152";
could be used to signify that the voxel values are a displacement
vector that transforms each voxel (x,y,z) location to the
corresponding location in the MNI152 standard brain.
- intent_code = NIFTI_INTENT_SYMMATRIX; intent_name = "DTI";
could be used to signify that the voxel values comprise a diffusion
tensor image.
If no data name is implied or needed, intent_name[0] should be set to 0.
-----------------------------------------------------------------------------*/
/*! default: no intention is indicated in the header. */
const int32_t NIFTI_INTENT_NONE =0;
/*-------- These codes are for probability distributions ---------------*/
/* Most distributions have a number of parameters,
below denoted by p1, p2, and p3, and stored in
- intent_p1, intent_p2, intent_p3 if dataset doesn't have 5th dimension
- image data array if dataset does have 5th dimension
Functions to compute with many of the distributions below can be found
in the CDF library from U Texas.
Formulas for and discussions of these distributions can be found in the
following books:
[U] Univariate Discrete Distributions,
NL Johnson, S Kotz, AW Kemp.
[C1] Continuous Univariate Distributions, vol. 1,
NL Johnson, S Kotz, N Balakrishnan.
[C2] Continuous Univariate Distributions, vol. 2,
NL Johnson, S Kotz, N Balakrishnan. */
/*----------------------------------------------------------------------*/
/*! [C2, chap 32] Correlation coefficient R (1 param):
p1 = degrees of freedom
R/sqrt(1-R*R) is t-distributed with p1 DOF. */
/*! \defgroup NIFTI1_INTENT_CODES
\brief nifti1 intent codes, to describe intended meaning of dataset contents
@{
*/
const int32_t NIFTI_INTENT_CORREL =2;
/*! [C2, chap 28] Student t statistic (1 param): p1 = DOF. */
const int32_t NIFTI_INTENT_TTEST =3;
/*! [C2, chap 27] Fisher F statistic (2 params):
p1 = numerator DOF, p2 = denominator DOF. */
const int32_t NIFTI_INTENT_FTEST =4;
/*! [C1, chap 13] Standard normal (0 params): Density = N(0,1). */
const int32_t NIFTI_INTENT_ZSCORE =5;
/*! [C1, chap 18] Chi-squared (1 param): p1 = DOF.
Density(x) proportional to exp(-x/2) * x^(p1/2-1). */
const int32_t NIFTI_INTENT_CHISQ =6;
/*! [C2, chap 25] Beta distribution (2 params): p1=a, p2=b.
Density(x) proportional to x^(a-1) * (1-x)^(b-1). */
const int32_t NIFTI_INTENT_BETA =7;
/*! [U, chap 3] Binomial distribution (2 params):
p1 = number of trials, p2 = probability per trial.
Prob(x) = (p1 choose x) * p2^x * (1-p2)^(p1-x), for x=0,1,...,p1. */
const int32_t NIFTI_INTENT_BINOM =8;
/*! [C1, chap 17] Gamma distribution (2 params):
p1 = shape, p2 = scale.
Density(x) proportional to x^(p1-1) * exp(-p2*x). */
const int32_t NIFTI_INTENT_GAMMA =9;
/*! [U, chap 4] Poisson distribution (1 param): p1 = mean.
Prob(x) = exp(-p1) * p1^x / x! , for x=0,1,2,.... */
const int32_t NIFTI_INTENT_POISSON =10;
/*! [C1, chap 13] Normal distribution (2 params):
p1 = mean, p2 = standard deviation. */
const int32_t NIFTI_INTENT_NORMAL =11;
/*! [C2, chap 30] Noncentral F statistic (3 params):
p1 = numerator DOF, p2 = denominator DOF,
p3 = numerator noncentrality parameter. */
const int32_t NIFTI_INTENT_FTEST_NONC=12;
/*! [C2, chap 29] Noncentral chi-squared statistic (2 params):
p1 = DOF, p2 = noncentrality parameter. */
const int32_t NIFTI_INTENT_CHISQ_NONC=13;
/*! [C2, chap 23] Logistic distribution (2 params):
p1 = location, p2 = scale.
Density(x) proportional to sech^2((x-p1)/(2*p2)). */
const int32_t NIFTI_INTENT_LOGISTIC =14;
/*! [C2, chap 24] Laplace distribution (2 params):
p1 = location, p2 = scale.
Density(x) proportional to exp(-abs(x-p1)/p2). */
const int32_t NIFTI_INTENT_LAPLACE =15;
/*! [C2, chap 26] Uniform distribution: p1 = lower end, p2 = upper end. */
const int32_t NIFTI_INTENT_UNIFORM =16;
/*! [C2, chap 31] Noncentral t statistic (2 params):
p1 = DOF, p2 = noncentrality parameter. */
const int32_t NIFTI_INTENT_TTEST_NONC=17;
/*! [C1, chap 21] Weibull distribution (3 params):
p1 = location, p2 = scale, p3 = power.
Density(x) proportional to
((x-p1)/p2)^(p3-1) * exp(-((x-p1)/p2)^p3) for x > p1. */
const int32_t NIFTI_INTENT_WEIBULL =18;
/*! [C1, chap 18] Chi distribution (1 param): p1 = DOF.
Density(x) proportional to x^(p1-1) * exp(-x^2/2) for x > 0.
p1 = 1 = 'half normal' distribution
p1 = 2 = Rayleigh distribution
p1 = 3 = Maxwell-Boltzmann distribution. */
const int32_t NIFTI_INTENT_CHI =19;
/*! [C1, chap 15] Inverse Gaussian (2 params):
p1 = mu, p2 = lambda
Density(x) proportional to
exp(-p2*(x-p1)^2/(2*p1^2*x)) / x^3 for x > 0. */
const int32_t NIFTI_INTENT_INVGAUSS =20;
/*! [C2, chap 22] Extreme value type I (2 params):
p1 = location, p2 = scale
cdf(x) = exp(-exp(-(x-p1)/p2)). */
const int32_t NIFTI_INTENT_EXTVAL =21;
/*! Data is a 'p-value' (no params). */
const int32_t NIFTI_INTENT_PVAL =22;
/*! Data is ln(p-value) (no params).
To be safe, a program should compute p = exp(-abs(this_value)).
The nifti_stats.c library returns this_value
as positive, so that this_value = -log(p). */
const int32_t NIFTI_INTENT_LOGPVAL =23;
/*! Data is log10(p-value) (no params).
To be safe, a program should compute p = pow(10.,-abs(this_value)).
The nifti_stats.c library returns this_value
as positive, so that this_value = -log10(p). */
const int32_t NIFTI_INTENT_LOG10PVAL =24;
/*! Smallest intent_code that indicates a statistic. */
const int32_t NIFTI_FIRST_STATCODE =2;
/*! Largest intent_code that indicates a statistic. */
const int32_t NIFTI_LAST_STATCODE =24;
/*---------- these values for intent_code aren't for statistics ----------*/
/*! To signify that the value at each voxel is an estimate
of some parameter, set intent_code = NIFTI_INTENT_ESTIMATE.
The name of the parameter may be stored in intent_name. */
const int32_t NIFTI_INTENT_ESTIMATE =1001;
/*! To signify that the value at each voxel is an index into
some set of labels, set intent_code = NIFTI_INTENT_LABEL.
The filename with the labels may stored in aux_file. */
const int32_t NIFTI_INTENT_LABEL =1002;
/*! To signify that the value at each voxel is an index into the
NeuroNames labels set, set intent_code = NIFTI_INTENT_NEURONAME. */
const int32_t NIFTI_INTENT_NEURONAME=1003;
/*! To store an M x N matrix at each voxel:
- dataset must have a 5th dimension (dim[0]=5 and dim[5]>1)
- intent_code must be NIFTI_INTENT_GENMATRIX
- dim[5] must be M*N
- intent_p1 must be M (in float format)
- intent_p2 must be N (ditto)
- the matrix values A[i][[j] are stored in row-order:
- A[0][0] A[0][1] ... A[0][N-1]
- A[1][0] A[1][1] ... A[1][N-1]
- etc., until
- A[M-1][0] A[M-1][1] ... A[M-1][N-1] */
const int32_t NIFTI_INTENT_GENMATRIX=1004;
/*! To store an NxN symmetric matrix at each voxel:
- dataset must have a 5th dimension
- intent_code must be NIFTI_INTENT_SYMMATRIX
- dim[5] must be N*(N+1)/2
- intent_p1 must be N (in float format)
- the matrix values A[i][[j] are stored in row-order:
- A[0][0]
- A[1][0] A[1][1]
- A[2][0] A[2][1] A[2][2]
- etc.: row-by-row */
const int32_t NIFTI_INTENT_SYMMATRIX=1005;
/*! To signify that the vector value at each voxel is to be taken
as a displacement field or vector:
- dataset must have a 5th dimension
- intent_code must be NIFTI_INTENT_DISPVECT
- dim[5] must be the dimensionality of the displacment
vector (e.g., 3 for spatial displacement, 2 for in-plane) */
const int32_t NIFTI_INTENT_DISPVECT =1006; /* specifically for displacements */
const int32_t NIFTI_INTENT_VECTOR =1007; /* for any other type of vector */
/*! To signify that the vector value at each voxel is really a
spatial coordinate (e.g., the vertices or nodes of a surface mesh):
- dataset must have a 5th dimension
- intent_code must be NIFTI_INTENT_POINTSET
- dim[0] = 5
- dim[1] = number of points
- dim[2] = dim[3] = dim[4] = 1
- dim[5] must be the dimensionality of space (e.g., 3 => 3D space).
- intent_name may describe the object these points come from
(e.g., "pial", "gray/white" , "EEG", "MEG"). */
const int32_t NIFTI_INTENT_POINTSET =1008;
/*! To signify that the vector value at each voxel is really a triple
of indexes (e.g., forming a triangle) from a pointset dataset:
- dataset must have a 5th dimension
- intent_code must be NIFTI_INTENT_TRIANGLE
- dim[0] = 5
- dim[1] = number of triangles
- dim[2] = dim[3] = dim[4] = 1
- dim[5] = 3
- datatype should be an integer type (preferably DT_INT32)
- the data values are indexes (0,1,...) into a pointset dataset. */
const int32_t NIFTI_INTENT_TRIANGLE =1009;
/*! To signify that the vector value at each voxel is a quaternion:
- dataset must have a 5th dimension
- intent_code must be NIFTI_INTENT_QUATERNION
- dim[0] = 5
- dim[5] = 4
- datatype should be a floating point type */
const int32_t NIFTI_INTENT_QUATERNION=1010;
/*! Dimensionless value - no params - although, as in _ESTIMATE
the name of the parameter may be stored in intent_name. */
const int32_t NIFTI_INTENT_DIMLESS =1011;
/* @} */
/*---------------------------------------------------------------------------*/
/* 3D IMAGE (VOLUME) ORIENTATION AND LOCATION IN SPACE:
---------------------------------------------------
There are 3 different methods by which continuous coordinates can
attached to voxels. The discussion below emphasizes 3D volumes, and
the continuous coordinates are referred to as (x,y,z). The voxel
index coordinates (i.e., the array indexes) are referred to as (i,j,k),
with valid ranges:
i = 0 .. dim[1]-1
j = 0 .. dim[2]-1 (if dim[0] >= 2)
k = 0 .. dim[3]-1 (if dim[0] >= 3)
The (x,y,z) coordinates refer to the CENTER of a voxel. In methods
2 and 3, the (x,y,z) axes refer to a subject-based coordinate system,
with
+x = Right +y = Anterior +z = Superior.
This is a right-handed coordinate system. However, the exact direction
these axes point with respect to the subject depends on qform_code
(Method 2) and sform_code (Method 3).
N.B.: The i index varies most rapidly, j index next, k index slowest.
Thus, voxel (i,j,k) is stored starting at location
(i + j*dim[1] + k*dim[1]*dim[2]) * (bitpix/8)
into the dataset array.
N.B.: The ANALYZE 7.5 coordinate system is
+x = Left +y = Anterior +z = Superior
which is a left-handed coordinate system. This backwardness is
too difficult to tolerate, so this NIFTI-1 standard specifies the
coordinate order which is most common in functional neuroimaging.
N.B.: The 3 methods below all give the locations of the voxel centers
in the (x,y,z) coordinate system. In many cases, programs will wish
to display image data on some other grid. In such a case, the program
will need to convert its desired (x,y,z) values into (i,j,k) values
in order to extract (or interpolate) the image data. This operation
would be done with the inverse transformation to those described below.
N.B.: Method 2 uses a factor 'qfac' which is either -1 or 1; qfac is
stored in the otherwise unused pixdim[0]. If pixdim[0]=0.0 (which
should not occur), we take qfac=1. Of course, pixdim[0] is only used
when reading a NIFTI-1 header, not when reading an ANALYZE 7.5 header.
N.B.: The units of (x,y,z) can be specified using the xyzt_units field.
METHOD 1 (the "old" way, used only when qform_code = 0):
-------------------------------------------------------
The coordinate mapping from (i,j,k) to (x,y,z) is the ANALYZE
7.5 way. This is a simple scaling relationship:
x = pixdim[1] * i
y = pixdim[2] * j
z = pixdim[3] * k
No particular spatial orientation is attached to these (x,y,z)
coordinates. (NIFTI-1 does not have the ANALYZE 7.5 orient field,
which is not general and is often not set properly.) This method
is not recommended, and is present mainly for compatibility with
ANALYZE 7.5 files.
METHOD 2 (used when qform_code > 0, which should be the "normal" case):
---------------------------------------------------------------------
The (x,y,z) coordinates are given by the pixdim[] scales, a rotation
matrix, and a shift. This method is intended to represent
"scanner-anatomical" coordinates, which are often embedded in the
image header (e.g., DICOM fields (0020,0032), (0020,0037), (0028,0030),
and (0018,0050)), and represent the nominal orientation and location of
the data. This method can also be used to represent "aligned"
coordinates, which would typically result from some post-acquisition
alignment of the volume to a standard orientation (e.g., the same
subject on another day, or a rigid rotation to true anatomical
orientation from the tilted position of the subject in the scanner).
The formula for (x,y,z) in terms of header parameters and (i,j,k) is:
[ x ] [ R11 R12 R13 ] [ pixdim[1] * i ] [ qoffset_x ]
[ y ] = [ R21 R22 R23 ] [ pixdim[2] * j ] + [ qoffset_y ]
[ z ] [ R31 R32 R33 ] [ qfac * pixdim[3] * k ] [ qoffset_z ]
The qoffset_* shifts are in the NIFTI-1 header. Note that the center
of the (i,j,k)=(0,0,0) voxel (first value in the dataset array) is
just (x,y,z)=(qoffset_x,qoffset_y,qoffset_z).
The rotation matrix R is calculated from the quatern_* parameters.
This calculation is described below.
The scaling factor qfac is either 1 or -1. The rotation matrix R
defined by the quaternion parameters is "proper" (has determinant 1).
This may not fit the needs of the data; for example, if the image
grid is
i increases from Left-to-Right
j increases from Anterior-to-Posterior
k increases from Inferior-to-Superior
Then (i,j,k) is a left-handed triple. In this example, if qfac=1,
the R matrix would have to be
[ 1 0 0 ]
[ 0 -1 0 ] which is "improper" (determinant = -1).
[ 0 0 1 ]
If we set qfac=-1, then the R matrix would be
[ 1 0 0 ]
[ 0 -1 0 ] which is proper.
[ 0 0 -1 ]
This R matrix is represented by quaternion [a,b,c,d] = [0,1,0,0]
(which encodes a 180 degree rotation about the x-axis).
METHOD 3 (used when sform_code > 0):
-----------------------------------
The (x,y,z) coordinates are given by a general affine transformation
of the (i,j,k) indexes:
x = srow_x[0] * i + srow_x[1] * j + srow_x[2] * k + srow_x[3]
y = srow_y[0] * i + srow_y[1] * j + srow_y[2] * k + srow_y[3]
z = srow_z[0] * i + srow_z[1] * j + srow_z[2] * k + srow_z[3]
The srow_* vectors are in the NIFTI_1 header. Note that no use is
made of pixdim[] in this method.
WHY 3 METHODS?
--------------
Method 1 is provided only for backwards compatibility. The intention
is that Method 2 (qform_code > 0) represents the nominal voxel locations
as reported by the scanner, or as rotated to some fiducial orientation and
location. Method 3, if present (sform_code > 0), is to be used to give
the location of the voxels in some standard space. The sform_code
indicates which standard space is present. Both methods 2 and 3 can be
present, and be useful in different contexts (method 2 for displaying the
data on its original grid; method 3 for displaying it on a standard grid).
In this scheme, a dataset would originally be set up so that the
Method 2 coordinates represent what the scanner reported. Later,
a registration to some standard space can be computed and inserted
in the header. Image display software can use either transform,
depending on its purposes and needs.
In Method 2, the origin of coordinates would generally be whatever
the scanner origin is; for example, in MRI, (0,0,0) is the center
of the gradient coil.
In Method 3, the origin of coordinates would depend on the value
of sform_code; for example, for the Talairach coordinate system,
(0,0,0) corresponds to the Anterior Commissure.
QUATERNION REPRESENTATION OF ROTATION MATRIX (METHOD 2)
-------------------------------------------------------
The orientation of the (x,y,z) axes relative to the (i,j,k) axes
in 3D space is specified using a unit quaternion [a,b,c,d], where
a*a+b*b+c*c+d*d=1. The (b,c,d) values are all that is needed, since
we require that a = sqrt(1.0-(b*b+c*c+d*d)) be nonnegative. The (b,c,d)
values are stored in the (quatern_b,quatern_c,quatern_d) fields.
The quaternion representation is chosen for its compactness in
representing rotations. The (proper) 3x3 rotation matrix that
corresponds to [a,b,c,d] is
[ a*a+b*b-c*c-d*d 2*b*c-2*a*d 2*b*d+2*a*c ]
R = [ 2*b*c+2*a*d a*a+c*c-b*b-d*d 2*c*d-2*a*b ]
[ 2*b*d-2*a*c 2*c*d+2*a*b a*a+d*d-c*c-b*b ]
[ R11 R12 R13 ]
= [ R21 R22 R23 ]
[ R31 R32 R33 ]
If (p,q,r) is a unit 3-vector, then rotation of angle h about that
direction is represented by the quaternion
[a,b,c,d] = [cos(h/2), p*sin(h/2), q*sin(h/2), r*sin(h/2)].
Requiring a >= 0 is equivalent to requiring -Pi <= h <= Pi. (Note that
[-a,-b,-c,-d] represents the same rotation as [a,b,c,d]; there are 2
quaternions that can be used to represent a given rotation matrix R.)
To rotate a 3-vector (x,y,z) using quaternions, we compute the
quaternion product
[0,x',y',z'] = [a,b,c,d] * [0,x,y,z] * [a,-b,-c,-d]
which is equivalent to the matrix-vector multiply
[ x' ] [ x ]
[ y' ] = R [ y ] (equivalence depends on a*a+b*b+c*c+d*d=1)
[ z' ] [ z ]
Multiplication of 2 quaternions is defined by the following:
[a,b,c,d] = a*1 + b*I + c*J + d*K
where
I*I = J*J = K*K = -1 (I,J,K are square roots of -1)
I*J = K J*K = I K*I = J
J*I = -K K*J = -I I*K = -J (not commutative!)
For example
[a,b,0,0] * [0,0,0,1] = [0,0,-b,a]
since this expands to
(a+b*I)*(K) = (a*K+b*I*K) = (a*K-b*J).
The above formula shows how to go from quaternion (b,c,d) to
rotation matrix and direction cosines. Conversely, given R,
we can compute the fields for the NIFTI-1 header by
a = 0.5 * sqrt(1+R11+R22+R33) (not stored)
b = 0.25 * (R32-R23) / a => quatern_b
c = 0.25 * (R13-R31) / a => quatern_c
d = 0.25 * (R21-R12) / a => quatern_d
If a=0 (a 180 degree rotation), alternative formulas are needed.
See the nifti1_io.c function mat44_to_quatern() for an implementation
of the various cases in converting R to [a,b,c,d].
Note that R-transpose (= R-inverse) would lead to the quaternion
[a,-b,-c,-d].
The choice to specify the qoffset_x (etc.) values in the final
coordinate system is partly to make it easy to convert DICOM images to
this format. The DICOM attribute "Image Position (Patient)" (0020,0032)
stores the (Xd,Yd,Zd) coordinates of the center of the first voxel.
Here, (Xd,Yd,Zd) refer to DICOM coordinates, and Xd=-x, Yd=-y, Zd=z,
where (x,y,z) refers to the NIFTI coordinate system discussed above.
(i.e., DICOM +Xd is Left, +Yd is Posterior, +Zd is Superior,
whereas +x is Right, +y is Anterior , +z is Superior. )
Thus, if the (0020,0032) DICOM attribute is extracted into (px,py,pz), then
qoffset_x = -px qoffset_y = -py qoffset_z = pz
is a reasonable setting when qform_code=NIFTI_XFORM_SCANNER_ANAT.
That is, DICOM's coordinate system is 180 degrees rotated about the z-axis
from the neuroscience/NIFTI coordinate system. To transform between DICOM
and NIFTI, you just have to negate the x- and y-coordinates.
The DICOM attribute (0020,0037) "Image Orientation (Patient)" gives the
orientation of the x- and y-axes of the image data in terms of 2 3-vectors.
The first vector is a unit vector along the x-axis, and the second is
along the y-axis. If the (0020,0037) attribute is extracted into the
value (xa,xb,xc,ya,yb,yc), then the first two columns of the R matrix
would be
[ -xa -ya ]
[ -xb -yb ]
[ xc yc ]
The negations are because DICOM's x- and y-axes are reversed relative
to NIFTI's. The third column of the R matrix gives the direction of
displacement (relative to the subject) along the slice-wise direction.
This orientation is not encoded in the DICOM standard in a simple way;
DICOM is mostly concerned with 2D images. The third column of R will be
either the cross-product of the first 2 columns or its negative. It is
possible to infer the sign of the 3rd column by examining the coordinates
in DICOM attribute (0020,0032) "Image Position (Patient)" for successive
slices. However, this method occasionally fails for reasons that I
(RW Cox) do not understand.
-----------------------------------------------------------------------------*/
/* [qs]form_code value: */ /* x,y,z coordinate system refers to: */
/*-----------------------*/ /*---------------------------------------*/
/*! \defgroup NIFTI1_XFORM_CODES
\brief nifti1 xform codes to describe the "standard" coordinate system
@{
*/
/*! Arbitrary coordinates (Method 1). */
const int32_t NIFTI_XFORM_UNKNOWN =0;
/*! Scanner-based anatomical coordinates */
const int32_t NIFTI_XFORM_SCANNER_ANAT=1;
/*! Coordinates aligned to another file's,
or to anatomical "truth". */
const int32_t NIFTI_XFORM_ALIGNED_ANAT=2;
/*! Coordinates aligned to Talairach-
Tournoux Atlas; (0,0,0)=AC, etc. */
const int32_t NIFTI_XFORM_TALAIRACH =3;
/*! MNI 152 normalized coordinates. */
const int32_t NIFTI_XFORM_MNI_152 =4;
/* @} */
/*---------------------------------------------------------------------------*/
/* UNITS OF SPATIAL AND TEMPORAL DIMENSIONS:
----------------------------------------
The codes below can be used in xyzt_units to indicate the units of pixdim.
As noted earlier, dimensions 1,2,3 are for x,y,z; dimension 4 is for
time (t).
- If dim[4]=1 or dim[0] < 4, there is no time axis.
- A single time series (no space) would be specified with
- dim[0] = 4 (for scalar data) or dim[0] = 5 (for vector data)
- dim[1] = dim[2] = dim[3] = 1
- dim[4] = number of time points
- pixdim[4] = time step
- xyzt_units indicates units of pixdim[4]
- dim[5] = number of values stored at each time point
Bits 0..2 of xyzt_units specify the units of pixdim[1..3]
(e.g., spatial units are values 1..7).
Bits 3..5 of xyzt_units specify the units of pixdim[4]
(e.g., temporal units are multiples of 8).
This compression of 2 distinct concepts into 1 byte is due to the
limited space available in the 348 byte ANALYZE 7.5 header. The
macros XYZT_TO_SPACE and XYZT_TO_TIME can be used to mask off the
undesired bits from the xyzt_units fields, leaving "pure" space
and time codes. Inversely, the macro SPACE_TIME_TO_XYZT can be
used to assemble a space code (0,1,2,...,7) with a time code
(0,8,16,32,...,56) into the combined value for xyzt_units.
Note that codes are provided to indicate the "time" axis units are
actually frequency in Hertz (_HZ), in part-per-million (_PPM)
or in radians-per-second (_RADS).
The toffset field can be used to indicate a nonzero start point for
the time axis. That is, time point #m is at t=toffset+m*pixdim[4]
for m=0..dim[4]-1.
-----------------------------------------------------------------------------*/
/*! \defgroup NIFTI1_UNITS
\brief nifti1 units codes to describe the unit of measurement for
each dimension of the dataset
@{
*/
/*! NIFTI code for unspecified units. */
const int32_t NIFTI_UNITS_UNKNOWN=0;
/** Space codes are multiples of 1. **/
/*! NIFTI code for meters. */
const int32_t NIFTI_UNITS_METER =1;
/*! NIFTI code for millimeters. */
const int32_t NIFTI_UNITS_MM =2;
/*! NIFTI code for micrometers. */
const int32_t NIFTI_UNITS_MICRON =3;
/** Time codes are multiples of 8. **/
/*! NIFTI code for seconds. */
const int32_t NIFTI_UNITS_SEC =8;
/*! NIFTI code for milliseconds. */
const int32_t NIFTI_UNITS_MSEC =16;
/*! NIFTI code for microseconds. */
const int32_t NIFTI_UNITS_USEC =24;
/*** These units are for spectral data: ***/
/*! NIFTI code for Hertz. */
const int32_t NIFTI_UNITS_HZ =32;
/*! NIFTI code for ppm. */
const int32_t NIFTI_UNITS_PPM =40;
/*! NIFTI code for radians per second. */
const int32_t NIFTI_UNITS_RADS =48;
/* @} */
#undef XYZT_TO_SPACE
#undef XYZT_TO_TIME
#define XYZT_TO_SPACE(xyzt) ( (xyzt) & 0x07 )
#define XYZT_TO_TIME(xyzt) ( (xyzt) & 0x38 )
#undef SPACE_TIME_TO_XYZT
#define SPACE_TIME_TO_XYZT(ss,tt) ( (((char)(ss)) & 0x07) \
| (((char)(tt)) & 0x38) )
/*---------------------------------------------------------------------------*/
/* MRI-SPECIFIC SPATIAL AND TEMPORAL INFORMATION:
---------------------------------------------
A few fields are provided to store some extra information
that is sometimes important when storing the image data
from an FMRI time series experiment. (After processing such
data into statistical images, these fields are not likely
to be useful.)
{ freq_dim } = These fields encode which spatial dimension (1,2, or 3)
{ phase_dim } = corresponds to which acquisition dimension for MRI data.
{ slice_dim } =
Examples:
Rectangular scan multi-slice EPI:
freq_dim = 1 phase_dim = 2 slice_dim = 3 (or some permutation)
Spiral scan multi-slice EPI:
freq_dim = phase_dim = 0 slice_dim = 3
since the concepts of frequency- and phase-encoding directions
don't apply to spiral scan
slice_duration = If this is positive, AND if slice_dim is nonzero,
indicates the amount of time used to acquire 1 slice.
slice_duration*dim[slice_dim] can be less than pixdim[4]
with a clustered acquisition method, for example.
slice_code = If this is nonzero, AND if slice_dim is nonzero, AND
if slice_duration is positive, indicates the timing
pattern of the slice acquisition. The following codes
are defined:
NIFTI_SLICE_SEQ_INC == sequential increasing
NIFTI_SLICE_SEQ_DEC == sequential decreasing
NIFTI_SLICE_ALT_INC == alternating increasing
NIFTI_SLICE_ALT_DEC == alternating decreasing
NIFTI_SLICE_ALT_INC2 == alternating increasing #2
NIFTI_SLICE_ALT_DEC2 == alternating decreasing #2
{ slice_start } = Indicates the start and end of the slice acquisition
{ slice_end } = pattern, when slice_code is nonzero. These values
are present to allow for the possible addition of
"padded" slices at either end of the volume, which
don't fit into the slice timing pattern. If there
are no padding slices, then slice_start=0 and
slice_end=dim[slice_dim]-1 are the correct values.
For these values to be meaningful, slice_start must
be non-negative and slice_end must be greater than
slice_start. Otherwise, they should be ignored.
The following table indicates the slice timing pattern, relative to
time=0 for the first slice acquired, for some sample cases. Here,
dim[slice_dim]=7 (there are 7 slices, labeled 0..6), slice_duration=0.1,
and slice_start=1, slice_end=5 (1 padded slice on each end).
slice
index SEQ_INC SEQ_DEC ALT_INC ALT_DEC ALT_INC2 ALT_DEC2
6 : n/a n/a n/a n/a n/a n/a n/a = not applicable
5 : 0.4 0.0 0.2 0.0 0.4 0.2 (slice time offset
4 : 0.3 0.1 0.4 0.3 0.1 0.0 doesn't apply to
3 : 0.2 0.2 0.1 0.1 0.3 0.3 slices outside
2 : 0.1 0.3 0.3 0.4 0.0 0.1 the range
1 : 0.0 0.4 0.0 0.2 0.2 0.4 slice_start ..
0 : n/a n/a n/a n/a n/a n/a slice_end)
The SEQ slice_codes are sequential ordering (uncommon but not unknown),
either increasing in slice number or decreasing (INC or DEC), as
illustrated above.
The ALT slice codes are alternating ordering. The 'standard' way for
these to operate (without the '2' on the end) is for the slice timing
to start at the edge of the slice_start .. slice_end group (at slice_start
for INC and at slice_end for DEC). For the 'ALT_*2' slice_codes, the
slice timing instead starts at the first slice in from the edge (at
slice_start+1 for INC2 and at slice_end-1 for DEC2). This latter
acquisition scheme is found on some Siemens scanners.
The fields freq_dim, phase_dim, slice_dim are all squished into the single
byte field dim_info (2 bits each, since the values for each field are
limited to the range 0..3). This unpleasantness is due to lack of space
in the 348 byte allowance.
The macros DIM_INFO_TO_FREQ_DIM, DIM_INFO_TO_PHASE_DIM, and
DIM_INFO_TO_SLICE_DIM can be used to extract these values from the
dim_info byte.
The macro FPS_INTO_DIM_INFO can be used to put these 3 values
into the dim_info byte.
-----------------------------------------------------------------------------*/
#undef DIM_INFO_TO_FREQ_DIM
#undef DIM_INFO_TO_PHASE_DIM
#undef DIM_INFO_TO_SLICE_DIM
#define DIM_INFO_TO_FREQ_DIM(di) ( ((di) ) & 0x03 )
#define DIM_INFO_TO_PHASE_DIM(di) ( ((di) >> 2) & 0x03 )
#define DIM_INFO_TO_SLICE_DIM(di) ( ((di) >> 4) & 0x03 )
#undef FPS_INTO_DIM_INFO
#define FPS_INTO_DIM_INFO(fd,pd,sd) ( ( ( ((char)(fd)) & 0x03) ) | \
( ( ((char)(pd)) & 0x03) << 2 ) | \
( ( ((char)(sd)) & 0x03) << 4 ) )
/*! \defgroup NIFTI1_SLICE_ORDER
\brief nifti1 slice order codes, describing the acquisition order
of the slices
@{
*/
const int32_t NIFTI_SLICE_UNKNOWN =0;
const int32_t NIFTI_SLICE_SEQ_INC =1;
const int32_t NIFTI_SLICE_SEQ_DEC =2;
const int32_t NIFTI_SLICE_ALT_INC =3;
const int32_t NIFTI_SLICE_ALT_DEC =4;
const int32_t NIFTI_SLICE_ALT_INC2 =5; /* 05 May 2005: RWCox */
const int32_t NIFTI_SLICE_ALT_DEC2 =6; /* 05 May 2005: RWCox */
/* @} */
/*---------------------------------------------------------------------------*/
/* UNUSED FIELDS:
-------------
Some of the ANALYZE 7.5 fields marked as ++UNUSED++ may need to be set
to particular values for compatibility with other programs. The issue
of interoperability of ANALYZE 7.5 files is a murky one -- not all
programs require exactly the same set of fields. (Unobscuring this
murkiness is a principal motivation behind NIFTI-1.)
Some of the fields that may need to be set for other (non-NIFTI aware)
software to be happy are:
extents dbh.h says this should be 16384
regular dbh.h says this should be the character 'r'
glmin, } dbh.h says these values should be the min and max voxel
glmax } values for the entire dataset
It is best to initialize ALL fields in the NIFTI-1 header to 0
(e.g., with calloc()), then fill in what is needed.
-----------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* MISCELLANEOUS C MACROS
-----------------------------------------------------------------------------*/
/*.................*/
/*! Given a nifti_1_header struct, check if it has a good magic number.
Returns NIFTI version number (1..9) if magic is good, 0 if it is not. */
/*#define NIFTI_VERSION(h) \
( ( (h).magic[0]=='n' && (h).magic[3]=='\0' && \
( (h).magic[1]=='i' || (h).magic[1]=='+' ) && \
( (h).magic[2]>='1' && (h).magic[2]<='9' ) ) \
? (h).magic[2]-'0' : 0 )
//*/
/*.................*/
/*! Check if a nifti_1_header struct says if the data is stored in the
same file or in a separate file. Returns 1 if the data is in the same
file as the header, 0 if it is not. */
//#define NIFTI_ONEFILE(h) ( (h).magic[1] == '+' )
/*.................*/
/*! Check if a nifti_1_header struct needs to be byte swapped.
Returns 1 if it needs to be swapped, 0 if it does not. */
//#define NIFTI_NEEDS_SWAP(h) ( (h).dim[0] < 0 || (h).dim[0] > 7 )
/*.................*/
/*! Check if a nifti_1_header struct contains a 5th (vector) dimension.
Returns size of 5th dimension if > 1, returns 0 otherwise. */
//#define NIFTI_5TH_DIM(h) ( ((h).dim[0]>4 && (h).dim[5]>1) ? (h).dim[5] : 0 )
/*****************************************************************************/
}//namespace
#endif /* _NIFTI_HEADER_ */