A minimal solution for plane motion and structure from two perspective views

Plane motion and structure is a classical problem in photogrammetry and computer vision communities. While the methods based on the Singular Value Decomposition of the plane-induced homography matrix have been largely successful, they are subject to the special assumption about the bottom right entry or the determinant sign of the homography matrix. This paper proposes firstly an explicit closed-form solution for the homography using the normalized barycentric coordinates from four image point correspondences in general position. Then we use algebraic method to propose a minimal solution for the plane motion and structure problem. Further, we derive a concise closed-form relation between two solutions of the plane motion and structure. The performance and practicability of our method are validated by testing on synthetic and real data. (C) 2019 Elsevier B.V. All rights reserved.