Detecting symmetrical properties is a fundamental task in 3D shape analysis. In the case of a 3D model with planar symmetries, each point has a corresponding mirror point w.r.t. a symmetry plane, and the correspondences remain invariant under any arbitrary Euclidean transformation. Our proposed method, E3Sym, aims to detect planar reflective symmetry in an unsupervised and end-to-end manner by leveraging E(3) invariance. E3Sym establishes robust point correspondences through the use of E(3) invariant features extracted from a lightweight neural network, from which the dense symmetry prediction is produced. We also introduce a novel and efficient clustering algorithm to aggregate the dense prediction and produce a detected symmetry set, allowing for the detection of an arbitrary number of planar symmetries while ensuring the method remains differentiable for end-to-end training. Our method also possesses the ability to infer reasonable planar symmetries from incomplete shapes, which remains challenging for existing methods. Extensive experiments demonstrate that E3Sym is both effective and robust, outperforming state-of-the-art methods.

Completing an unordered partial point cloud is a challenging task. Existing approaches that rely on decoding a latent feature to recover the complete shape, often lead to the completed point cloud being over-smoothing, losing details, and noisy. Instead of decoding a whole shape, we propose to decode and refine a low-resolution (low-res) point cloud first, and then perform a patch-wise noise-aware upsampling rather than interpolating the whole sparse point cloud at once, which tends to lose details. Regarding the possibility of lacking details of the initially decoded low-res point cloud, we propose an iterative refinement to recover the geometric details and a symmetrization process to preserve the trustworthy information from the input partial point cloud. After obtaining a sparse and complete point cloud, we propose a patch-wise upsampling strategy. Patch-based upsampling allows to recover fine details better rather than decoding a whole shape. The patch extraction approach is to generate training patch pairs between the sparse and ground-truth point clouds with an outlier removal step to suppress the noisy points from the sparse point cloud. Together with the low-res recovery, our whole pipeline can achieve high-fidelity point cloud completion. Comprehensive evaluations are provided to demonstrate the effectiveness of the proposed method and its components.