# Voxels Space Orientation and Coordinate Conventions¶

## Images¶

It is important to note that SCT Images, which are derived from NIFTI images, have their contents indexed in “Fortran order”, meaning that in an image of shape $$(N_a, N_b, N_c)$$, where we consider the a axis to be the first, two consecutive (in the sense of storage location) elements are in the a dimension, the first. This is by opposition to the C ordering which is more widely used in most software, and where the fastest varying element is indexed last.

## Reference Spaces¶

As in many other tools, SCT follows a standard nomenclature for reference spaces in which the world or local coordinates are expressed.

The string is formed from character label among (relative to a human subject):

• L / R: left-right

• P / A: posterior-anterior

• I / S: inferior-superior

The character position corresponds to the axis index.

SCT uses the “from” convention, which for clarity we postfix by a dash.

The reference space for physical coordinates is LPI- (which is coming from nibabel and NIFTI).

An “image orientation” corresponds to the orientation of the surface/volume with regard to the reference orientation. It is encoded in the (NIFTI) file header.

For example, a RAS image orientation corresponds to a 3D image with:

• X axis oriented L towards R;

• Y axis oriented P towards A;

• Z axis oriented I towards S.

Notes:

• nibabel, BIDS are using the “towards” convention, ie. SCT’s LPI(-) is their RAS(+).

## Coordinate Conventions¶

### Local/Voxel Coordinates¶

When voxel coordinates are integers, coordinates are indices. Indices are expressed starting from 0 and up to N-1 where N is the number of voxels in the considered dimension.

When voxel coordinates are real numbers, we are using an integer voxel center convention (consistent with nibabel and NIFTI).

This means that a coordinate such as (i,j,k) == np.round((i,j,k)) expresses the center of a voxel.

NB: Voxel coordinates are called $$(i,j,k)$$ in the NIFTI documentation.

### Global/Physical Coordinates¶

Physical coordinates are always expressed as real numbers. They are defined from the relation expressed by the transform and unit system expressed in a image header.

Physical coordinates are expressed relative to the LPI- frame, considering the voxel dimensions, affine transform between voxel coordinates and world coordinates, and the physical dimension unit, all of which is encoded in the NIFTI file header.

NB: Voxel coordinates are called $$(x,y,z)$$ in the NIFTI documentation.