When aligning preoperative MRI data with intraoperative ultrasound, what is the mathematical process used to transform the two datasets into the same coordinate system?

Aligning preoperative MRI data with intraoperative ultrasound is a process called image registration, which mathematically determines the spatial transformation required to map the coordinates of one image into the coordinate space of the other. The process begins by defining a coordinate system for each dataset, where every pixel or voxel has a unique position represented by numerical values. A transformation matrix is then calculated to relate these systems, typically using a rigid-body t....