P Transforms and Mappings (Informative)

The Affine Transform Matrix is of the following form.

Equation P-1. 

This matrix requires the bottom row to be [0 0 0 1] to preserve the homogeneous coordinates.

The matrix can be of type: RIGID, RIGID_SCALE and AFFINE. These different types represent different conditions on the allowable values for the matrix elements.

For a RIGID type of Frame of Reference Transformation Matrix, the inverse is easily computed using the following formula (inverse of an orthonormal matrix):

Equation P-8. 

For RIGID_SCALE and AFFINE types of Registration Matrices, the inverse cannot be calculated using the above equation, and must be calculated using a conventional matrix inverse operation.