7 
an empty line ('\n' alone). Some header lines give perarray 
an empty line ('\n' alone). Some header lines give perarray 
8 
information, some give peraxis information. 
information, some give peraxis information. 
9 


10 

Note that the distinction between scalar and nonscalar images is 
11 

given by the peraxis "kinds" field, so that is where further 
12 

information is given about the constraints associated iwth nonscalar 
13 

image data. 
14 


15 
============================================================ 
============================================================ 
16 
The basic fields that should be there are: 
The basic fields that should be there are: 
96 
The "space" kind is for a typical axis of the image, with samples that 
The "space" kind is for a typical axis of the image, with samples that 
97 
subtend some region of the spatial domain of the image. All the other 
subtend some region of the spatial domain of the image. All the other 
98 
kinds are the sequence of scalar values that compose a nonscalar 
kinds are the sequence of scalar values that compose a nonscalar 
99 
image value (vectors and tensors). We are currently not allowing the 
image value (vectors and tensors). 
100 
"measurement frame" field that identifies the coordinate system in 

101 
which these are measured relative to the image orientation, so nothing 
We currently allow there to be *at* *most* *one* axis with a 
102 
should be assumed about the space in which these coefficients are 
non"space" kind. We can have nonscalar image values, but we don't 
103 
measured: 
have cartesian products of nonscalar image values. The non"space" 
104 

kind can be anywhere in the axis ordering. If all the axis kinds are 
105 

"space", then then image data is for scalars, else it is for 
106 

nonscalar data. 
107 


108 

In scalar data, the image "dimension" must equal the "space dimension". 
109 

In nonscalar data, the image "dimension" must equal *one* plus 
110 

the "space dimension". That is, the spatial axes have to form a 
111 

basis, not necessarily orthonormal, for world space (the vectors 
112 

are defined by the "space directions" field, below). Thus, a 
113 

3D scalar image can't reside in a 2D or 4D world space, nor can 
114 

a 3D vector image reside in a 3D or 5D world space. 
115 


116 

We are currently not allowing the "measurement frame" field that 
117 

identifies the coordinate system in which these are measured relative 
118 

to the image orientation, so nothing should be assumed about the space 
119 

in which these coefficients are measured. The order of coefficients 
120 

for these nonscalar kinds is: 
121 


122 
2Dsymmetricmatrix: Mxx Mxy Myy 
2Dsymmetricmatrix: Mxx Mxy Myy 
123 
2Dmatrix: Mxx Mxy Myx Myy 
2Dmatrix: Mxx Mxy Myx Myy 
124 
3Dsymmetricmatrix: Mxx Mxy Mxz Myy Myz Mzz 
3Dsymmetricmatrix: Mxx Mxy Mxz Myy Myz Mzz 
125 
3Dmatrix: Mxx Mxy Mxz Myx Myy Myz Mzx Mzy Mzz 
3Dmatrix: Mxx Mxy Mxz Myx Myy Myz Mzx Mzy Mzz 
126 



We currently allow there to be *at* *most* *one* axis with a 


non"space" kind. We can have nonscalar image values, but we don't 


have cartesian products of nonscalar image values. The non"space" 


kind can be anywhere in the axis ordering. 




127 
 
 
128 
space directions: (<x1>,<x2>,...,<xN>) (<x1>,<x2>,...,<xN>) ... 
space directions: (<x1>,<x2>,...,<xN>) (<x1>,<x2>,...,<xN>) ... 
129 
(and at most one of these vectors is actually "none") 
(and at most one of these vectors is actually "none") 