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Compared with perfect global symmetry, partial intrinsic symmetry region is more common in three-dimensional and high-dimensional data sets. In this paper, point clouds are used as input, and K-Isomap algorithm is employed to construct the graph and calculate edge weights. According to the constraint of geodesic distance and election strategies, we obtain the sets of support point pairs reflecting locally implied symmetric regions. Aiming to achieve the more precise symmetrical region represented by the sets of point pairs, Symmetrical Weighting Degree is defined based on the distances between the pair of points in the sets, and we propose two methods for calculating the Symmetrical Weighting Degree for different dimensions. Then, two algorithms for obtaining potential skeleton points are introduced in view of the set of points on the shortest path between points pair. The potential skeleton points are voted on …