A fiducial tag invariant to rotation, translation, and perspective transformations

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.

摘要

•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.