Space resection is the method of acquiring the exterior orientation parameters of a camera based on three ground control points（GCPs） at least and the corresponding image points. The traditional least squares method of space resection needs good initial values of exterior orientation parameters. However, good initial values are difficult to obtain in the oblique photogrammetry condition. The objective of this study is to compute accurate exterior orientation parameters automatically to provide good initial values for the least squares method of space resection. Solving the space resection problem needs three GCPs and the corresponding image points at least. This study initially starts from three GCPs and then derives a direct solution model of space resection. The three GCPs must be coplanar and the corresponding image points must also be coplanar. Thus, the homography matrix can be used to describe the geometric relationship between a set of coplanar points and another set of coplanar points. This study transforms the collinearity equation into a homography matrix model and derives two constraints based on the orthogonality of the rotation matrix. When only three GCPs exist, the space resection problem can be transformed into a set of binary quadratic equations. The binary quadratic equations have four solutions at most. An additional GCP is necessary to decide the unique solution. When three ground control points exist, the unique solution can be directly computed based on a set of linear equations, which are derived from the homography matrix model. After computing the homography matrix solution, the exterior orientation parameters can be obtained using the relationship between the homography matrix and collinearity equation. Three experiments tested the effectiveness and reliability of the proposed method. The first experiment aimed to test the performance of the proposed method when only three GCPs exist. The experimental data comprise done oblique image of the Yangjiang area and four evenly distributed GCPs. Three of the GCPs were used to compute the exterior orientation parameters, and the remaining one was used to decide the unique solution. The proposed method was compared with the traditional range and imaging equation models. In the first experiment, the proposed method showed the best back substitution accuracy, which reached as high as 9.908010E-9 pixels. However, the back substitution accuracies of the range and imaging equation models were merely 5.891172E-6 pixels and 9.285811E-4 pixels, respectively. The second experiment aimed to show the influence of the proposed method on the least squares result of space resection in different camera angle conditions. Two different datasets were used in the second experiment. The first dataset was still the oblique image of the Yangjiang area. The initial values using the proposed method were compared with the values from the traditional method and the man-made methods. In the large camera angle condition, the least squares iteration based on the traditional method was unable to converge. The accuracy of the least squares results based on the proposed method was as good as that of the man-made initial values. Both methods had back projection accuracies of 0.03592 pixels. However, the convergence rate of the proposed method was good. The second dataset was an aerial image of the Toronto area. Given that the camera angle was small, the traditional method achieved good initial values. Accordingly, the proposed method was compared with the traditional method.In the small camera angle condition, the back projection accuracy of the proposed method was as good as that of the traditional method. The accuracy of both methods was 0.02525 pixels, but the convergence rate of the proposed method is better than the traditional one. The third experiment compared the proposed method with currently popular direct solution models of space resection in the case of multiple coplanar GCPs. Camera calibration data were used in the third experiment. The accuracy of the proposed method was better than that of the coordinate transformation and polynomial models, and was as good as the accuracy of the virtual GCP model. This study proposes a new direct solution model of space resection based on the homography matrix. It transforms the space resection model into a set of binary quadratic equations and acquires the direct solution of exterior orientation parameters. When multiple coplanar GCPs exist, the proposed method is able to transform the collinearity equation into a set of linear equations. Experimental results show that the proposed method can provide good initial values for the least squares method of space resection, which can be applied in oblique photogrammetry, close-range photogrammetry, and so on. Future studies will focus on acquiring direct solutions in the case of non-coplanar GCP s to improve the universality of the proposed method.

space resection;homography matrix;closed-form solution;unit quaternions;co-planar points