Invariants of Space Line Element Structure Based on Projective Geometric Algebra

Based on the theory of Conformal Geometric Algebra, this paper presents a geometric constraint structure consisting of seven straight lines on three adjacent planes and its projective invariants, which can be obtained from a single frame image. Comparing with the use of multi-frame images to calculate invariants, our method is more convenient. First, this paper uses the projective property of points as an index to introduce the projective transformation properties of geometric structure of three lines on two adjacent planes. Then using it as an index, the invariant of the geometric structure of seven lines on three adjacent planes is proposed, and the invariant of the geometric structure of five lines on three adjacent planes is obtained by using the algorithm in this paper. Finally, the accuracy and stability of the invariant geometry are verified by experiments.