A Novel Absolute Orientation Method Using Local Similarities Representation

Lei Yan,Rui Chen,Jie Wan,Yanbiao Sun,Yizhen Yan,Shiyue Fan

doi:10.3390/ijgi5080135

Abstract

Absolute orientation is an important method in the field of photogrammetry. The technique is used to transform points between a local coordinate reference system and a global (geodetic) reference system. The classical transformation method uses a single set of similarity transformation parameters. However, the root mean square error (RMSE) of the classical method is large, especially for large-scale aerial photogrammetry analyses in which the points used are triangulated through free-net bundle adjustment. To improve the transformation accuracy, this study proposes a novel absolute orientation method in which the transformation uses various sets of local similarities. A Triangular Irregular Network (TIN) model is applied to divide the Ground Control Points (GCPs) into numerous triangles. Local similarities can then be computed using the three vertices of each triangle. These local similarities are combined to formulate the new transformation based on a weighting function. Both simulated and real data sets were used to assess the accuracy of the proposed method. The proposed method yields significantly improved plane and z-direction transformed point accuracies compared with the classical method. On a real data set with a mapping scale of 1:30,000 for a 53 km × 35 km study area, the plane and z RMSEs can be reduced from 1.2 m and 12.4 m to 0.4 m and 3.2 m, respectively.

Highlights

Absolute orientation is a fundamental procedure in the field of photogrammetry and plays a crucial role in the transformation of three-dimensional (3D) points from a local to a global coordinate reference system
The classical absolute orientation method accurately represents the geometric relationships between 3D points in the local and global coordinate reference systems by means of a similarity transformation, which consists of one scaling parameter, three rotation angles and three translation vector parameters [12]
For the analysis presented in this paper, the bundle adjustment (BA) method, a type of aerial triangulation, was utilized to generate such 3D points using two-dimensional (2D) image points as input to serve as the measurements for the BA non-linear optimization problem

Summary

Introduction

Absolute orientation is a fundamental procedure in the field of photogrammetry and plays a crucial role in the transformation of three-dimensional (3D) points from a local to a global (geodetic) coordinate reference system. The classical absolute orientation method accurately represents the geometric relationships between 3D points in the local and global coordinate reference systems by means of a similarity transformation, which consists of one scaling parameter, three rotation angles and three translation vector parameters [12]. The problem to be solved can be defined as a non-linear least-squares problem based on these seven unknown parameters for three or more pairs of 3D points in two coordinate reference systems. Horn et al [14] proposed a closed-form absolute orientation solution using orthonormal matrices This algorithm often produces an incorrect rotation matrix. Aurn et al [15] solved this problem by utilizing another closed-form method based on singular value decomposition (SVD) to stably determine the transformation parameters

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Conclusion