Quantification of Projective Distortion for Fiducial Markers

Abstract

The aim of this study is to quantify the projective distortion of candidate quadrilaterals found in a square-framed fiducial marker detection algorithm. Based on the quantified value, candidates can be eliminated in such a way that only the quadrilaterals that may be a projective transformation of a square remain. In the first part of the study, it is shown that under a projective transform, the line at infinity of a plane corresponds to a line that is not at infinity. Two methods to find the equation of the corresponding line are proposed. The first method uses the homography matrix that represents a particular projective transformation. The correspondant of the line at infinity can be found using this homography matrix. The second method is a direct algorithm that utilizes the parallelism of the opposing edges of the square frame. At the last section, the obtained line is used to quantify the projective distortion and an elimination is performed on this basis.