LÁVIČKA MiroslavReconstructing Symmetries in 3D Point Clouds Using DecompositionSymmetry simplifies complex problems by revealing patterns, making it a central concept in mathematics and geometry. While mathematicians study exact symmetries of analytic objects, computer scientists focus on detecting symmetries in discrete point sets—vital for applications in graphics, vision, and pattern recognition. This talk presents a decomposition-based method to recover the full symmetry group of 3D point clouds by breaking them into simpler parts with identifiable symmetries. We also propose a technique for detecting rotational symmetries using the covariance matrix and, when needed, higher-order tensors. The approach, though designed for exact data, can be adapted to handle noise, making it suitable for real-world use. |