Wednesday 3 September 2014
 
» The Fiber Cup » Voxel to real world coordinates
 
Voxel to real world coordinates

 

All DWI datasets have a non-zero origin, a non-unitary spacing (or voxel size) and a non-identity orientation matrix indicating how the dataset is spatially oriented. As a consequence, voxel to real world coordinates transform must take into account all of this.

  • For the 3x3x3 datasets:
    • origin is: 
\left[93, 93, -1.5\right]
    • spacing is: 
\left[3,3,3\right]
    • orientation matrix is: 
\left[
\begin{array}{ccc}
-1  &  0 & 0\\
 0  & -1  & 0\\
 0  & 0 & 1
\end{array}
\right]

Consequently, the voxel to real world coordinates transform is: 
\left[
\begin{array}{cccc}
-3  &  0 & 0 &  93\\
 0  & -3  & 0 &  93\\
 0  & 0 & 3 & -1.5\\
 0  & 0 & 0 &  1
\end{array}
\right]

or, in another form: 
Position=
\left[
\begin{array}{ccc}
-3  &  0 & 0\\
 0  & -3  & 0\\
 0  & 0 & 3
\end{array}
\right]
\times Voxel +
\left[
\begin{array}{c}
93 \\
93 \\
-1.5
\end{array}
\right]

  • For the 6x6x6 datasets:
    • origin is: 
\left[186, 186, 3\right]
    • spacing is: 
\left[6,6,6\right]
    • orientation matrix is: 
\left[
\begin{array}{ccc}
-1  &  0 & 0\\
 0  & -1  & 0\\
 0  & 0 & 1
\end{array}
\right]

Consequently, the voxel to real world coordinates transform is: 
\left[
\begin{array}{cccc}
-6  &  0 & 0 &  186\\
 0  & -6  & 0 &  186\\
 0  & 0 & 6 & 3\\
 0  & 0 & 0 &  1
\end{array}
\right]

or, in another form: 
Position=
\left[
\begin{array}{ccc}
-6  &  0 & 0\\
 0  & -6  & 0\\
 0  & 0 & 6
\end{array}
\right]
\times Voxel +
\left[
\begin{array}{c}
186 \\
186 \\
3
\end{array}
\right]

 
 
Published on Saturday 25 July 2009

 
 
 
The others articles in the same section :
 
Published on Friday 24 July 2009
Update Thursday 30 July 2009
 
Published on Saturday 25 July 2009
Update Tuesday 1 February 2011
 
Published on Thursday 26 February 2009
 
Published on Saturday 25 July 2009
Update Monday 27 July 2009
 

 
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