The Similarity Transformation

First, two control points and are chosen. These two points are mapped precisely onto the database by the similarity transformation . A similarity transformation is by definition composed of rotation, scaling, and translation, so the transformation is given by

where and are found by solving . Here denotes the coordinates of the point in the database and denotes the coordinates of the point in the measurement.

The Mathematica implementation is straightforward.

The numbers and are found by the following.