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1. 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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2. On the Convergence of IRLS and Its Variants in Outlier-Robust Estimation

   https://doi.org/10.1109/CVPR52729.2023.01708  

   Peng, Liangzu; Kümmerle, Christian; Vidal, René (June 2023, IEEE)

   Outlier-robust estimation involves estimating some parameters (e.g., 3D rotations) from data samples in the presence of outliers, and is typically formulated as a non-convex and non-smooth problem. For this problem, the classical method called iteratively reweighted least-squares (IRLS) and its variants have shown impressive performance. This paper makes several contributions towards understanding why these algorithms work so well. First, we incorporate majorization and graduated non-convexity (GNC) into the IRLS framework and prove that the resulting IRLS variant is a convergent method for outlier-robust estimation. Moreover, in the robust regression context with a constant fraction of outliers, we prove this IRLS variant converges to the ground truth at a global linear and local quadratic rate for a random Gaussian feature matrix with high probability. Experiments corroborate our theory and show that the proposed IRLS variant converges within 5-10 iterations for typical problem instances of outlier-robust estimation, while state-of-the-art methods need at least 30 iterations. A basic implementation of our method is provided: https: //github.com/liangzu/IRLS-CVPR2023 

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3. 3D-UCaps: 3D Capsules Unet for Volumetric Image Segmentation

   https://doi.org/10.1007/978-3-030-87193-2_52  

   Le, Thi Hoang (September 2021, Lecture notes in computer science)

   Medical image segmentation has been so far achieving promising results with Convolutional Neural Networks (CNNs). However, it is arguable that in traditional CNNs, its pooling layer tends to discard important information such as positions. Moreover, CNNs are sensitive to rotation and ane transformation. Capsule network is a data-ecient network design proposed to overcome such limitations by replacing pooling layers with dynamic routing and convolutional strides, which aims to preserve the part-whole relationships. Capsule network has shown a great performance in image recognition and natural language processing, but applications for medical image segmentation, particularly volumetric image segmentation, has been limited. In this work, we propose 3D-UCaps, a 3D voxel-based Capsule network for medical volumetric image segmentation. We build the concept of capsules into a CNN by designing a network with two pathways: the rst pathway is encoded by 3D Capsule blocks, whereas the second pathway is decoded by 3D CNNs blocks. 3D-UCaps, therefore inherits the merits from both Capsule network to preserve the spatial relationship and CNNs to learn visual representation. We conducted experiments on various datasets to demonstrate the robustness of 3D-UCaps including iSeg-2017, LUNA16, Hippocampus, and Cardiac, where our method outperforms previous Capsule networks and 3D-Unets. 

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4. CAPTRA: CAtegory-level Pose Tracking for Rigid and Articulated Objects from Point Clouds

   https://doi.org/10.1109/ICCV48922.2021.01296  

   Weng, Yijia; Wang, He; Zhou, Qiang; Qin, Yuzhe; Duan, Yueqi; Fan, Qingnan; Chen, Baoquan; Su, Hao; Guibas, Leonidas J. (October 2021, 2021 IEEE/CVF International Conference on Computer Vision (ICCV))

   In this work, we tackle the problem of category-level online pose tracking of objects from point cloud sequences. For the first time, we propose a unified framework that can handle 9DoF pose tracking for novel rigid object instances as well as per-part pose tracking for articulated objects from known categories. Here the 9DoF pose, comprising 6D pose and 3D size, is equivalent to a 3D amodal bounding box representation with free 6D pose. Given the depth point cloud at the current frame and the estimated pose from the last frame, our novel end-to-end pipeline learns to accurately update the pose. Our pipeline is composed of three modules: 1) a pose canonicalization module that normalizes the pose of the input depth point cloud; 2) RotationNet, a module that directly regresses small interframe delta rotations; and 3) CoordinateNet, a module that predicts the normalized coordinates and segmentation, enabling analytical computation of the 3D size and translation. Leveraging the small pose regime in the pose-canonicalized point clouds, our method integrates the best of both worlds by combining dense coordinate prediction and direct rotation regression, thus yielding an end-to-end differentiable pipeline optimized for 9DoF pose accuracy (without using non-differentiable RANSAC). Our extensive experiments demonstrate that our method achieves new state-of-the-art performance on category-level rigid object pose (NOCSREAL275 [29]) and articulated object pose benchmarks (SAPIEN [34], BMVC [18]) at the fastest FPS ∼ 12. 

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5. On Greedy Routing in Dynamic UAV Networks

   https://doi.org/10.1109/SECONW.2018.8396354  

   Khaledi, Mehrdad; Rovira-Sugranes, Arnau; Afghah, Fatemeh; Razi, Abolfazl (June 2018, IEEE International Conference on Sensing, Communication and Networking (SECON Workshops))

   Unmanned aerial vehicles (UAVs), commonly known as drones, are becoming increasingly popular for various applications. Freely flying drones create highly dynamic environments, where conventional routing algorithms which rely on stationary network contact graphs fail to perform efficiently. Also, link establishment through exploring optimal paths using hello messages (as is used in AODV algorithm) deems extremely inefficient and costly for rapidly changing network topologies. In this paper, we present a distance-based greedy routing algorithm for UAV networks solely based on UAVs' local observations of their surrounding subnetwork. Thereby, neither a central decision maker nor a time consuming route setup and maintenance mechanism is required. To evaluate the proposed method, we derive an analytical bound for the expected number of hops that a packet traverses. Also, we find the expected end-to-end distance traveled by each packet as well as the probability of successful delivery. The simulation results verify the accuracy of the developed analytical expressions and show considerable improvement compared to centralized shortest path routing algorithms. 

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