Definition of commonly used coordinate systems

In Plus the following coordinate systems are used commonly:

Reference frame name	Origin	Unit	Axes directions
Tracker	Origin of the tracking system (position of the field generator, camera, etc.)	mm	as defined by the tracking system manufacturer
Stylus	Origin of the marker that is attached to the pointer tool	mm	as defined by the tracking system / marker manufacturer
Probe	Origin of the marker that is attached to the ultrasound probe (transducer)	mm	as defined by the tracking system / marker manufacturer
Reference	Origin of the marker attached to the object of interest (phantom, cadaver, patient, etc.)	mm	as defined by the tracking system / marker manufacturer
StylusTip	Tip of the stylus	mm	X axis: aligned with the Stylus coordinate system’s X axis (unless StylusTip Z axis is parallel with the StylusTip Z axis - in this case the StylusTip Y axis is aligned with the Stylus X axis). Y axis: chosen to be the cross product of the Z and X axes. Z axis: the axis that points from the Stylus coordinate system origin towards StylusTip coordinate syste origin.
Image	Position of the pixel that is in the origin of the MF oriented image	pixel	X axis: towards the marked side of the transducer Y axis: towards the direction that points away (far) from the transducer Z axis: cross product of X and Y
Transducer	Center of the transducer crystal array	mm	X axis: towards the marked side of the transducer Y axis: towards the direction that points away (far) from the transducer Z axis: cross product of X and Y

Coordinate systems overview sketch (3D Slicer compatible interactive 3D model of the figure below is available here):