Medical Image Coordinate Systems

In medical imaging, there are two distinct coordinate systems: the intrinsic coordinate system and the world, or patient, coordinate system. You can access locations in medical images using the intrinsic coordinate system and the patient coordinate system.

The intrinsic coordinate system defines the voxel space, and the patient coordinate system defines the anatomical space. To understand the position and orientation of intrinsic coordinates with respect to the patient, you must transform the data into the patient coordinate system. You can use the intrinsicToWorldMapping function to obtain the transformation between the intrinsic coordinates and patient coordinates of a 3-D medical image volume stored as a medicalVolume object.

Patient Coordinate System

The patient coordinate system is made up of three orthogonal axes:

• Left (L)/Right (R) — x-axis

• Anterior (A)/Posterior (P) — y-axis

• Inferior (I)/Superior (S) — z-axis

The patient xyz-axes define the coronal, sagittal, and transverse anatomical planes. This table shows the relationship between the anatomical planes and patient axes.

Anatomical Planes and Patient Axes	Sagittal Plane	Coronal Plane	Transverse Plane
	Defined by the y- and z-axes. Divides the body into right and left segments.	Defined by the x- and z-axes. Divides the body into anterior and posterior segments.	Defined by the x- and y-axes. Divides the body into inferior and superior segments.

Note

The patient coordinate system rotates together with the physical orientation of the patient.

Mapping Patient Coordinate Axes to Anatomical Planes

Medical image files store a transformation matrix to map intrinsic coordinates (i, j, k) to patient coordinates (x, y, z), and each file format has a different convention that defines the positive direction of each axis.

For example, a DICOM file uses an LPS+ coordinate system and a NIfTI file uses an RAS+ coordinate system.

Patient Axes	DICOM	NIfTI
	x-axis values increase from right to left y-axis values increase from anterior to posterior z-axis values increase from inferior to superior	x-axis values increase from left to right y-axis values increase from posterior to anterior z-axis values increase from inferior to superior

Intrinsic Coordinate System

The intrinsic coordinate system describes the spatial dimensions of the patient coordinate system. Intrinsic coordinates are in units of voxels, while patient coordinates have real-world dimensions and are usually in units of millimeters. You can obtain pixel dimensions from the PixelSpacing property of a medicalImage object for 2-D data, and from the VoxelSpacing property of a medicalVolume object for 3-D data.

The origin of the intrinsic coordinate system is located at the center of the first pixel (2-D image) or voxel (3-D volume), represented by the black circle. The i-axis corresponds to the first dimension (rows), the j-axis corresponds to the second dimension (columns), and the k-axis corresponds to the third dimension of a medical image or volume.

This image grid shows the i-axis corresponding to the anatomical z-axis and the j-axis corresponding to the anatomical x-axis,

whereas this image grid shows the i-axis corresponding to the anatomical x-axis and the j-axis corresponding to the anatomical z-axis.

Both image grids represent a valid way a medical device might store voxels in a file. When you create a medicalVolume object for an image volume, the spatial dimensions of the patient coordinate system correspond to the values in the Voxels property of the object.

Tip

Use the intrinsicToWorldMapping function to compute the geometric transformation between the intrinsic and patient coordinate systems for a medical image volume.