Pose estimation based on the constraints of inner angles and areas of triangles

This paper presents an iterative pose estimation method on the basis of point correspondences, which are composed of 3D coordinates of feature points under object reference frame and their 2D projective coordinates under image reference frame. The proposed method decomposes the pose estimation into two steps. Firstly, the 3D coordinates of the feature points under camera reference frame are estimated iteratively by Gauss-Newton method. In this process, the variables are defined by the lengths of the vectors from the focus point of camera to the feature points; meanwhile, several novel constraints are constructed by a set of error functions built out of the inner angles and areas of the triangles formed by three arbitrary non-collinear feature points, because they can describe the shape of object uniquely and completely. Secondly, by using Gauss-Newton method again, the rotation angles (i.e., pitch, yaw, and roll) and 3D translation of the object are estimated from the 3D coordinates of the feature points under camera reference frame obtained in the first step. Experiments involving synthetic data as well as real data indicate that the proposed method is more accurate and no less fast than the previous method.