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为了减小正交迭代法用于跟踪相机位姿的累积误差,提出基于流形优化方法的估计相机位姿新颖算法.算法利用共线性误差模型将位姿估计转化为流形上实值函数最小化问题,然后运用微分几何的结论进行目标优化.优化过程包括搜索更新向量和收缩映射:在流形仿射切空间内对目标函数进行泰勒展开以搜索函数的零切向量场;用收缩映射将偏离流形的点重新映射到流形表面.比较了流形优化法与正交迭代法位姿估计的性能,并给出了新算法在增强现实中的实际应用.结果表明:流行优化算法的性能优于正交迭代,在综合数据试验中噪声方差为1时,前者的旋转轴、旋转角的相对误差为0.5%和0.25%,仅为后者相对误差的1/5和1/2.
In order to reduce the cumulative error of the orthogonal iteration method to track the pose of the camera, a novel algorithm based on the manifold optimization method is proposed to estimate the pose of the camera. The algorithm uses the colinearity error model to convert the pose estimation to the minimum And then use the conclusion of differential geometry to optimize the target.The optimization process includes searching for update vectors and contracting mappings: performing Taylor expansion on the objective function to search the zero-cut vector field of the function in the manifold affine cut space; The points that deviate from the manifold are remapped to the manifold surface.The performance of the manifold optimization method and the orthogonality iteration method are compared, and the practical application of the new algorithm in augmented reality is given.The results show that: The performance is better than orthogonal iteration. When the noise variance is 1 in the comprehensive data experiment, the relative errors of the former rotation axis and rotation angle are 0.5% and 0.25%, respectively, only 1/5 and 1/2 of the latter relative error.