Formulation and verification to invalidation of the error evaluation for coordinate transformation by Euclidean distance between markers

Spatial markers can be used to not only complete coordinate transformation between two or more different Cartesian coordinate systems, but also to provide the error evaluation of the above transformation. On the one hand, a group of transforming markers is responsible for accurate parameters i.e. rotation matrix and translation vector; on the other hand, a group of checking markers can be used to quantify the accuracy of the results between coordinate transformation by Euclidean distance between markers. In this article, an invalidation of the error evaluation for coordinate transformation by relative Euclidean distance has been concluded and proven that the indexes are always constant because of an invariant group of checking markers, independent of the other group checking markers.