MINC 2.0 coordinate system

MINC 2.0, like MINC 1.0, defines both a ``voxel'' and a ``world'' spatial coordinate system. Voxel coordinates are analogous to array indices: The voxel coordinate values are nonnegative integers ranging from zero to one less than the number of data points along the axis, with the origin fixed at one corner of the image.

In contrast, the ``world'' coordinate system reflects the real world units and spatial orientation of the image. MINC world coordinates are derived from voxel coordinates using the dimension variable attributes direction_cosines, step, and start (see section 4.3.5). The direction cosine vector is a unit vector which is defined for each spatial dimension. Using the notation $c_{ij}$ to indicate the component of the $i$ axis in the $j$ direction, the cosine vector $\stackrel{\rightarrow}{c_i}$ for the axis $i$ can be written:

$$\stackrel{\rightarrow}{c_i}\:=\:(c_{ix},c_{iy},c_{iz})$$ (1)

Using $step_i$ to represent the value of the step attribute for spatial axis $i$, and defining $start_i$ similarly for the start attribute, the vector $\stackrel{\rightarrow}{v_i}$ between adjacent elements along that axis is:

$$\stackrel{\rightarrow}{v_i}\:=\:step_i * \stackrel{\rightarrow}{c_i}$$ (2)

and the origin $(0,0,0)$ in voxel coordinates is located at world coordinates $(o_x,o_y,o_z)$ as given by:

$$\left[\begin{array}{ccccccccccccc}o_x \\ o_y \\ o_z \end{arr... ...{ccccccccccccc}start_x \\ start_y \\ start_z \end{array}\right]$$ (3)

Finally, any homogeneous coordinate in voxel space $(v_x,v_y,v_z,1)$ can be transformed to its equivalent in world space using the equation:

$$\left[\begin{array}{ccccccccccccc}w_x \\ w_y \\ w_z \\ w_w \... ...n{array}{ccccccccccccc}v_x \\ v_y \\ v_z \\ 1\end{array}\right]$$ (4)

While MINC 2.0 files may store data in any orientation, MINC 2.0 follows common medical imaging practice in defining the orientation of world spatial coordinates relative to patients. The convention is that the positive $x$ axis increases from patient left to right, the positive $y$ axis increases from patient posterior to anterior, and the positive $z$ axis increases from patient inferior to superior.