论文标题
探索邻接的矩阵方法的序列提取
Exploring the Adjugate Matrix Approach to Quaternion Pose Extraction
论文作者
论文摘要
四季度对于计算机图形，机器视觉和机器人技术中的各种旋转相关问题很重要。我们通过利用相关特征值问题的特征方程式的邻接矩阵来研究四元组和旋转矩阵之间关系的非平凡几何形状，从而获得四元素特征矢量空间的歧管。我们认为，通过相应的旋转矩阵参数为参数的四元素不能在机器学习任务中表达为单价值功能：相反，必须将Quathnion解决方案视为歧管的歧管，并用不同的代数解决方案对邻接矩阵代表的几个单个单个扇形中的每个扇形。我们以新的结构为结论，利用二次相邻变量重新审视几个经典的姿势估计应用：2D点云匹配，2D点对曲线到反射匹配，3D点云匹配，3D拼音孔隙曲线 - 曲线 - 突击击退匹配，以及3D Perspective Perspective Perspective Perspective Perceptive Perceptive Perceptive posspspective pospective posspective pospective pospective。我们找到了针对3D拼字法最小二乘构成提取问题的精确解决方案，并将其成功地应用于透视姿势提取问题，并改善了现有方法的结果。
Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the adjugate matrix of the characteristic equation of a related eigenvalue problem to obtain the manifold of the space of a quaternion eigenvector. We argue that quaternions parameterized by their corresponding rotation matrices cannot be expressed, for example, in machine learning tasks, as single-valued functions: the quaternion solution must instead be treated as a manifold, with different algebraic solutions for each of several single-valued sectors represented by the adjugate matrix. We conclude with novel constructions exploiting the quaternion adjugate variables to revisit several classic pose estimation applications: 2D point-cloud matching, 2D point-cloud-to-projection matching, 3D point-cloud matching, 3D orthographic point-cloud-to-projection matching, and 3D perspective point-cloud-to-projection matching. We find an exact solution to the 3D orthographic least squares pose extraction problem, and apply it successfully also to the perspective pose extraction problem with results that improve on existing methods.
