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Reflectional symmetry is a ubiquitous pattern in nature. Previous works usually solve this problem by voting or sampling, suffering from high computational cost and randomness. In this paper, we propose a learning-based approach to intrinsic reflectional symmetry detection. Instead of directly finding symmetric point pairs, we parametrize this self-isometry using a functional map matrix, which can be easily computed given the signs of Laplacian eigenfunctions under the symmetric mapping. Therefore, we manually label the eigenfunction signs for a variety of shapes and train a novel neural network to predict the sign of each eigenfunction under symmetry. Our network aims at learning the global property of functions and consequently converts the problem defined on the manifold to the functional domain. By disentangling the prediction of the matrix into separated bases, our method generalizes well to new shapes and is invariant under perturbation of eigenfunctions. Through extensive experiments, we demonstrate the robustness of our method in challenging cases, including different topology and incomplete shapes with holes. By avoiding random sampling, our learning-based algorithm is over 20 times faster than state-of-the-art methods, and meanwhile, is more robust, achieving higher correspondence accuracy in commonly used metrics.

3D models are commonly used in computer vision and graphics. With the wider availability of mesh data, an efficient and intrinsic deep learning approach to processing 3D meshes is in great need. Unlike images, 3D meshes have irregular connectivity, requiring careful design to capture relations in the data. To utilize the topology information while staying robust under different triangulations, we propose to encode mesh connectivity using Laplacian spectral analysis, along with mesh feature aggregation blocks (MFABs) that can split the surface domain into local pooling patches and aggregate global information amongst them. We build a mesh hierarchy from fine to coarse using Laplacian spectral clustering, which is flexible under isometric transformations. Inside the MFABs there are pooling layers to collect local information and multi-layer perceptrons to compute vertex features of increasing complexity. To obtain the relationships among different clusters, we introduce a Correlation Net to compute a correlation matrix, which can aggregate the features globally by matrix multiplication with cluster features. Our network architecture is flexible enough to be used on meshes with different numbers of vertices. We conduct several experiments including shape segmentation and classification, and our method outperforms state-of-the-art algorithms for these tasks on the ShapeNet and COSEG datasets.

We present a modified velocity-obstacle (VO) algorithm that uses probabilistic partial observations of the environment to compute velocities and navigate a robot to a target. Our system uses commodity visual sensors, including a mono-camera and a 2D Lidar, to explicitly predict the velocities and positions of surrounding obstacles through optical flow estimation, object detection, and sensor fusion. A key aspect of our work is coupling the perception (OF: optical flow) and planning (VO) components for reliable navigation. Overall, our OF-VO algorithm using learning-based perception and model-based planning methods offers better performance than prior algorithms in terms of navigation time and success rate of collision avoidance. Our method also provides bounds on the probabilistic collision avoidance algorithm. We highlight the realtime performance of OF-VO on a Turtlebot navigating among pedestrians in both simulated and real-world scenes. A demo video is available at https://gamma.umd.edu/ofvo/, 10 pages