Dominant Symmetry Plane Detection for Point-Based 3D Models

In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element's area as the initial weight, a weighted PCA is performed and a plane is selected as the initial symmetry plane; and then an iterative method is used to adjust the approximate symmetry plane step by step to make it tend to perfect symmetry plane (dominant symmetry plane). In each iteration, we first update the weight of each point based on a distance metric and then use the new weights to perform a weighted PCA to determine a new symmetry plane. If the current plane of symmetry is close enough to the plane of symmetry in the previous iteration or if the number of iterations exceeds a given threshold, the iteration terminates. After the iteration is terminated, the plane of symmetry in the last iteration is taken as the dominant symmetry plane of the model. As shown in experimental results, the proposed algorithm can find the dominant symmetry plane for symmetric models and it also works well for nonperfectly symmetric models.