Automatic Calculation of a Transformation Matrix Between Two Frames

Abstract

This paper presents a novel strategy for the automatic calculation of a homogeneous transformation matrix between two frames given a set of matched position measurements of objects as observed in both frames. The transformation matrix is calculated by applying a linear regression to matched data in two coordinate frames. This method scales linearly with the number of data points, enabling it to be used in a wide variety of applications without requiring large amounts of processing time. The automatic transformation matrix calculation is demonstrated to work in a real-world application and produce deterministic results. The error on the transformation matrix calculation was found to be low, making this an ideal method for the easy calculation of transformation matrices.