This research develops an accurate and efficient method for the Perspective-n-Line(Pn L)problem. The developed method addresses and solves Pn L via exploiting the problem’s geometry in a non-linear least squares fash...This research develops an accurate and efficient method for the Perspective-n-Line(Pn L)problem. The developed method addresses and solves Pn L via exploiting the problem’s geometry in a non-linear least squares fashion. Specifically, by representing the rotation matrix with a novel quaternion parameterization, the Pn L problem is first decomposed into four independent subproblems. Then, each subproblem is reformulated as an unconstrained minimization problem, in which the Kronecker product is adopted to write the cost function in a more compact form. Finally, the Groobner basis technique is used to solve the polynomial system derived from the first-order optimality conditions of the cost function. Moreover, a novel strategy is presented to improve the efficiency of the algorithm. It is improved by exploiting structure information embedded in the rotation parameterization to accelerate the computing of coefficient matrix of a cost function. Experiments on synthetic data and real images show that the developed method is comparable to or better than state-of-the-art methods in accuracy, but with reduced computational requirements.展开更多
In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that t...In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that the noises(perpendicular to the line) for the two endpoints are statistically independent. However, these two noises are in fact negatively correlated when the image line segment is fitted using the least-squares technique. Therefore, we design a new error function expressed by the average integral of the distance between line segments. Three least-squares techniques that optimize both the rotation and translation simultaneously are proposed in which the new error function is exploited. In addition, Lie group formalism is utilized to describe the pose parameters, and then, the optimization problem can be solved by means of a simple iterative least squares method. To enhance the robustness to outliers existing in the match data, an M-estimation method is developed to convert the pose optimization problem into an iterative reweighted least squares problem. The proposed methods are validated through experiments using both synthetic and real-world data. The experimental results show that the proposed methods yield a clearly higher precision than the traditional methods.展开更多
基金supported in part by the National Natural Science Foundation of China(Nos.61905112 and 62073161)in part by the China Scholarship Council(Nos.201906830092)in part by the Fundamental Research Funds for the Central University(No.NZ2020005)。
文摘This research develops an accurate and efficient method for the Perspective-n-Line(Pn L)problem. The developed method addresses and solves Pn L via exploiting the problem’s geometry in a non-linear least squares fashion. Specifically, by representing the rotation matrix with a novel quaternion parameterization, the Pn L problem is first decomposed into four independent subproblems. Then, each subproblem is reformulated as an unconstrained minimization problem, in which the Kronecker product is adopted to write the cost function in a more compact form. Finally, the Groobner basis technique is used to solve the polynomial system derived from the first-order optimality conditions of the cost function. Moreover, a novel strategy is presented to improve the efficiency of the algorithm. It is improved by exploiting structure information embedded in the rotation parameterization to accelerate the computing of coefficient matrix of a cost function. Experiments on synthetic data and real images show that the developed method is comparable to or better than state-of-the-art methods in accuracy, but with reduced computational requirements.
基金supported by the National Basic Research Program of China(“973”Project)(Grant No.2013CB733100)National Natural Science Foundation of China(Grant No.11332012)
文摘In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that the noises(perpendicular to the line) for the two endpoints are statistically independent. However, these two noises are in fact negatively correlated when the image line segment is fitted using the least-squares technique. Therefore, we design a new error function expressed by the average integral of the distance between line segments. Three least-squares techniques that optimize both the rotation and translation simultaneously are proposed in which the new error function is exploited. In addition, Lie group formalism is utilized to describe the pose parameters, and then, the optimization problem can be solved by means of a simple iterative least squares method. To enhance the robustness to outliers existing in the match data, an M-estimation method is developed to convert the pose optimization problem into an iterative reweighted least squares problem. The proposed methods are validated through experiments using both synthetic and real-world data. The experimental results show that the proposed methods yield a clearly higher precision than the traditional methods.
