MINC coordinate system

The MINC standard defines how spatial coordinates should be oriented relative to patients. Files are free to have data stored in the desired direction, but positive world coordinates are given a definite meaning in the medical imaging context. The standard is that the positive x axis points from the patient's left to right, the positive y axis points from posterior to anterior and the positive z axis points from inferior to superior.

The conversion of element index to world coordinates is done using the dimension variable attributes MIdirection_cosines, MIstep and MIstart. If the direction cosines are ${\bf c}=(c_x, c_y, c_z)$, then the vector between adjacent elements along an axis is $step\times {\bf c}$. If $start(i)$ and ${\bf c}(i)$ are the MIstart and MIdirection_cosines attributes for dimension $i$ (one of MIxspace, MIyspace and MIzspace), then the first element of the image variable is at world coordinate $\sum_i start(i) {\bf c}(i)$.

If the direction cosines are not present, then they are assumed to be $(1,0,0)$ for MIxspace, $(0,1,0)$ for MIyspace and $(0,0,1)$ for MIzspace. Direction cosines are unit vectors and should be normalized. As well, the step attribute should carry the information about axis flipping (negative or positive) rather than the direction cosine.