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1. Geometry-complete perceptron networks for 3D molecular graphs

   https://doi.org/10.1093/bioinformatics/btae087  

   Morehead, Alex; Cheng, Jianlin (February 2024, Bioinformatics)

   Valencia, Alfonso (Ed.)

   Abstract MotivationThe field of geometric deep learning has recently had a profound impact on several scientific domains such as protein structure prediction and design, leading to methodological advancements within and outside of the realm of traditional machine learning. Within this spirit, in this work, we introduce GCPNet, a new chirality-aware SE(3)-equivariant graph neural network designed for representation learning of 3D biomolecular graphs. We show that GCPNet, unlike previous representation learning methods for 3D biomolecules, is widely applicable to a variety of invariant or equivariant node-level, edge-level, and graph-level tasks on biomolecular structures while being able to (1) learn important chiral properties of 3D molecules and (2) detect external force fields. ResultsAcross four distinct molecular-geometric tasks, we demonstrate that GCPNet’s predictions (1) for protein–ligand binding affinity achieve a statistically significant correlation of 0.608, more than 5%, greater than current state-of-the-art methods; (2) for protein structure ranking achieve statistically significant target-local and dataset-global correlations of 0.616 and 0.871, respectively; (3) for Newtownian many-body systems modeling achieve a task-averaged mean squared error less than 0.01, more than 15% better than current methods; and (4) for molecular chirality recognition achieve a state-of-the-art prediction accuracy of 98.7%, better than any other machine learning method to date. Availability and implementationThe source code, data, and instructions to train new models or reproduce our results are freely available at https://github.com/BioinfoMachineLearning/GCPNet. 

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2. Polylidar3D-Fast Polygon Extraction from 3D Data

   https://doi.org/10.3390/s20174819  

   Castagno, Jeremy; Atkins, Ella (September 2020, Sensors)

   null (Ed.)

   Flat surfaces captured by 3D point clouds are often used for localization, mapping, and modeling. Dense point cloud processing has high computation and memory costs making low-dimensional representations of flat surfaces such as polygons desirable. We present Polylidar3D, a non-convex polygon extraction algorithm which takes as input unorganized 3D point clouds (e.g., LiDAR data), organized point clouds (e.g., range images), or user-provided meshes. Non-convex polygons represent flat surfaces in an environment with interior cutouts representing obstacles or holes. The Polylidar3D front-end transforms input data into a half-edge triangular mesh. This representation provides a common level of abstraction for subsequent back-end processing. The Polylidar3D back-end is composed of four core algorithms: mesh smoothing, dominant plane normal estimation, planar segment extraction, and finally polygon extraction. Polylidar3D is shown to be quite fast, making use of CPU multi-threading and GPU acceleration when available. We demonstrate Polylidar3D’s versatility and speed with real-world datasets including aerial LiDAR point clouds for rooftop mapping, autonomous driving LiDAR point clouds for road surface detection, and RGBD cameras for indoor floor/wall detection. We also evaluate Polylidar3D on a challenging planar segmentation benchmark dataset. Results consistently show excellent speed and accuracy. 

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3. Image to Icosahedral Projection for SO(3) Object Reasoning from Single-View Images

   Klee, David; Biza, Ondrej; Platt, Robert; Walters, Robin (December 2022, Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations)

   Reasoning about 3D objects based on 2D images is challenging due to variations in appearance caused by viewing the object from different orientations. Tasks such as object classification are invariant to 3D rotations and other such as pose estimation are equivariant. However, imposing equivariance as a model constraint is typically not possible with 2D image input because we do not have an a priori model of how the image changes under out-of-plane object rotations. The only SO(3)-equivariant models that currently exist require point cloud or voxel input rather than 2D images. In this paper, we propose a novel architecture based on icosahedral group convolutions that reasons in SO(3) by learning a projection of the input image onto an icosahedron. The resulting model is approximately equivariant to rotation in SO(3). We apply this model to object pose estimation and shape classification tasks and find that it outperforms reasonable baselines. 

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4. Quaternion Equivariant Capsule Networks for 3D Point Clouds

   https://doi.org/10.1007/978-3-030-58452-8_1  

   Zhao, Yongheng; Birdal, Tolga; Lenssen, Jan Eric; Menegatti, Emanuele; Guibas, Leonidas; Tombari, Federico (November 2020, European Conference on Computer Vision)

   null (Ed.)

   We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end transformation equivariance through a novel dynamic routing procedure on quaternions. Further, we theoretically connect dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving iterative re-weighted least squares (IRLS) problems with provable convergence properties. It is shown that such group dynamic routing can be interpreted as robust IRLS rotation averaging on capsule votes, where information is routed based on the final inlier scores. Based on our operator, we build a capsule network that disentangles geometry from pose, paving the way for more informative descriptors and a structured latent space. Our architecture allows joint object classification and orientation estimation without explicit supervision of rotations. We validate our algorithm empirically on common benchmark datasets. 

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5. Quaternion Equivariant Capsule Networks for 3D Point Clouds

   Zhao, Yongheng; Birdal, Tolga; Lenssen, Jan Eric; Menegatti, Emanuele; Guibas, Leonidas; Tombari, Federico (November 2020, European Conference on Computer Vision)

   null (Ed.)

   We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end transformation equivariance through a novel dynamic routing procedure on quaternions. Further, we theoretically connect dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving iterative re-weighted least squares (IRLS) problems with provable convergence properties. It is shown that such group dynamic routing can be interpreted as robust IRLS rotation averaging on capsule votes, where information is routed based on the final inlier scores. Based on our operator, we build a capsule network that disentangles geometry from pose, paving the way for more informative descriptors and a structured latent space. Our architecture allows joint object classification and orientation estimation without explicit supervision of rotations. We validate our algorithm empirically on common benchmark datasets. 

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