A fiducial tag invariant to rotation, translation, and perspective transformations. (September 2018) - Cruz-Hernández, Heriberto; de la Fraga, Luis Gerardo
Highlights: We test experimentally the use of the Computational Geometry construction called order type for auto-identification of a fiducial tag. We describe a procedure for detecting the fiducial tag from an image and the algorithms for computing an identification number from them. We do extensively tests to show that the proposed construction is invariant to translation, rotation, and perspective transformations. We analyze which is the maximum noise in point positions for all points within a set that allows to compute correctly the order type in that set of points. As the proposed new tags are invariant to perspective transformation, it is not necessary to remove in the tag image this distortion in order to recover its associated identification number. With a tag of 21  ×  21 cm and images of size 640  ×  480 pixels, our results show that the tag and its associated ID can be recovered if the tag is tilt less than 81°, including perspective distortion, and at a distance less than 91 cm. Also, up to 3472 of such IDs are available. Abstract: This work introduces a novel visual fiducial tag appropriate for applications of automatic identification. The proposed tag is based in Order Type, a construction defined in Computational Geometry, which is invariant to 3D translation, rotation, and projective transformations. Three main contributions are presented: first we describe the design of the proposed tags, the procedures for detecting them from an image, and the algorithms for computing an identifier from them. Second, we analyze the feasibility of the proposal in three different conditions of tag's rotation, distance to the tag, and the effect of noise in point positions for the recognition process. Third, we show the applicability of the proposed tags with simulated images. The conducted experiments indicate that the tags are very robust to the image generation process, suitable for automatic identification up to 3472 different tags, and also for the pose estimation in Computer Vision applications.