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.

翻译：检测对称性对于实现有效的物体抓取至关重要，原因如下：识别物体内部的对称特征或对称轴有助于制定高效的抓取策略，因为沿这些轴线进行抓取通常能获得更稳定、更平衡的握持，从而促进成功的操作。本文采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），适用于以坐标系原点为中心的物体。该方法提供了用于检测对称性和估计正交变换（涵盖旋转、反射及其组合）的独特度量指标。研究建立了在n维空间中获取这些函数的完整方法学，具体表现为矩$n$元组。通过对二维和三维物体进行大量验证测试，确保了所提方法的鲁棒性和可靠性。本文还将所提方法与基于迭代优化检测多对称平面的前沿工作进行了对比。结果表明，将我们的方法与迭代方法相结合，在检测到的对称平面数量和计算时间方面均能获得令人满意的结果。