a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed Edge-Conv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

Point cloud registration is a key problem for computer vision applied to robotics, medical imaging, and other applications. This problem involves finding a rigid transformation from one point cloud into another so that they align. Iterative Closest Point (ICP) and its variants provide simple and easily-implemented iterative methods for this task, but these algorithms can converge to spurious local optima. To address local optima and other difficulties in the ICP pipeline, we propose a learning-based method, titled Deep Closest Point (DCP), inspired by recent techniques in computer vision and natural language processing. Our model consists of three parts: a point cloud embedding network, an attention-based module combined with a pointer generation layer, to approximate combinatorial matching, and a differentiable singular value decomposition (SVD) layer to extract the final rigid transformation. We train our model end-to-end on the ModelNet40 dataset and show in several settings that it performs better than ICP, its variants (e.g., Go-ICP, FGR), and the recently-proposed learning-based method PointNetLK. Beyond providing a state-of-the-art registration technique, we evaluate the suitability of our learned features transferred to unseen objects. We also provide preliminary analysis of our learned model to help understand whether domain-specific and/or global features facilitate rigid registration.

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Many shape and image processing tools rely on computation of correspondences between geometric domains. Efficient methods that stably extract "soft" matches in the presence of diverse geometric structures have proven to be valuable for shape retrieval and transfer of labels or semantic information. With these applications in mind, we present an algorithm for probabilistic correspondence that optimizes an entropy-regularized Gromov-Wasserstein (GW) objective. Built upon recent developments in numerical optimal transportation, our algorithm is compact, provably convergent, and applicable to any geometric domain expressible as a metric measure matrix. We provide comprehensive experiments illustrating the convergence and applicability of our algorithm to a variety of graphics tasks. Furthermore, we expand entropic GW correspondence to a framework for other matching problems, incorporating partial distance matrices, user guidance, shape exploration, symmetry detection, and joint analysis of more than two domains. These applications expand the scope of entropic GW correspondence to major shape analysis problems and are stable to distortion and noise.

Input imageFrame eld Final result Fig. 1. Given a possibly noisy grayscale bitmap image, we compute a frame field aligned with the directions on the image, superimposing multiple directions around sharp corners as well as X-and T-junctions. We then use this frame field to extract the drawing topology and create the final vectorization with the computed topology. Frame field computation (shown for a subset of pixels in the upper zoom and the full field in the lower one) is the key component of the system. The frame field disambiguates X-and T-junctions even in the noisy areas, allowing tracing to be straightforward and robust. Input images are from www.easy-drawings-and-sketches.com, ©Ivan Huska.Image tracing is a foundational component of the work ow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, modern algorithms o en fail to faithfully vectorize junctions, or points at which curves meet; this produces vector drawings with incorrect connectivity. is subtle issue undermines the practical application of vectorization tools and accounts for hesitance among artists and engineers to use automatic vectorization so ware. To address this issue, we propose a novel image vectorization method based on state-of-the-art mathematical algorithms for frame eld processing. Our algorithm is tailored speci cally to disambiguate junctions without sacri cing quality.