从几何矩 $n$-元组中获取全局对称性和正交变换
Global Symmetry and Orthogonal Transformations from Geometrical Moment $n$-tuples
AI总结：
本文提出了一种基于几何矩 $n$-元组的方法，用于检测物体的对称性和估计正交变换，通过实验验证了其在 2D 和 3D 物体中的有效性。
摘要：
检测对称性对于有效的物体抓取至关重要，原因有多个。识别物体内部的对称特征或轴有助于开发高效的抓取策略，因为沿着这些轴抓取通常会产生更稳定和平衡的抓握，从而促进成功的操作。本文利用几何矩来识别对称性并估计正交变换，包括旋转和镜像变换，用于以帧原点为中心的物体。它提供了独特的度量标准来检测对称性和估计正交变换，包括旋转、反射及其组合。开发了全面的方法来在 $n$ 维空间中获得这些函数，即矩 $n$-元组。在 2D 和 3D 物体上进行了广泛的验证测试，以确保所提出方法的鲁棒性和可靠性。所提出的方法还通过迭代优化与最先进的方法进行比较，用于检测多个对称平面。结果表明，结合我们的方法与迭代方法在检测对称平面的数量和计算时间方面取得了令人满意的结果。
英文摘要：
Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a more stable and balanced grip, thereby facilitating successful manipulation. This paper employs geometrical moments to identify symmetries and estimate orthogonal transformations, including rotations and mirror transformations, for objects centered at the frame origin. It provides distinctive metrics for detecting symmetries and estimating orthogonal transformations, encompassing rotations, reflections, and their combinations. A comprehensive methodology is developed to obtain these functions in n-dimensional space, specifically moment \( n \)-tuples. Extensive validation tests are conducted on both 2D and 3D objects to ensure the robustness and reliability of the proposed approach. The proposed method is also compared to state-of-the-art work using iterative optimization for detecting multiple planes of symmetry. The results indicate that combining our method with the iterative one yields satisfactory outcomes in terms of the number of symmetry planes detected and computation time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
