3D Coordinate Transformation Based on Point-to-Line Using Quaternion and Procrustes Algorithms

3D coordinate transformation is the process of matching different three-dimensional coordinate systems equally, and is an important task in photogrammetry, computer vision, and robotics. This study proposed a method of using quaternions and Procrustes algorithms to fit different three-dimensional coordinate systems using points and straight lines. Rotational elements were calculated using quaternions by projecting the coordinates of the points in the model coordinate system onto those in the reference coordinate system. For the scale factor and three-dimensional translation, Procrustes algorithms using points and straight lines were then used. Indoor experiments using checker-boards were conducted, followed by experiments using outdoor data acquired from a terrestrial mobile mapping system. It was found that more than four point-to-line pairs are needed to perform three-dimensional transformation reliably.