3D multi-person motion prediction is a highly complex task, primarily due to the dependencies on both individual past movements and the interactions between agents. Moreover, effectively modeling these interactions often incurs substantial computational costs. In this work, we propose a computationally efficient model for multi-person motion prediction by simplifying spatial and temporal interactions. Our approach begins with the design of lightweight dual branches that learn local and global representations for individual and multiple persons separately. Additionally, we introduce a novel cross-level interaction block to integrate the spatial and temporal representations from both branches. To further enhance interaction modeling, we explicitly incorporate the spatial inter-person distance embedding. With above efficient temporal and spatial design, we achieve state-of-the-art performance for multiple metrics on standard datasets of CMU-Mocap, MuPoTS-3D, and 3DPW, while significantly reducing the computational cost. Code is available at https://github.com/Yuanhong-Zheng/EMPMP.

We propose a novel two-stage framework, Coarse-to-Fine Part Assembly (CFPA), for 3D shape assembly from basic parts. Effective part assembly demands precise local geometric reasoning for accurate component assembly, as well as global structural understanding to ensure semantic coherence and plausible configurations. CFPA addresses this challenge by integrating semantic abstraction and symmetry-aware reasoning into a unified pose prediction process. In the first stage, semantic super-parts are constructed via an optimal transport formulation to capture high-level object structure, which is then propagated to individual parts through a dual-range feature propagation mechanism. The second stage refines part poses via cross-stage feature interaction and instance-level geometric encoding, improving spatial precision and coherence. To enable diverse yet valid assemblies, we introduce a symmetry-aware loss that jointly models both self-symmetry and inter-part geometric similarity, allowing for diverse but structurally consistent assemblies. Extensive experiments on the PartNet benchmark demonstrate that CFPA achieves state-of-the-art performance in assembly accuracy, structural consistency, and diversity across multiple categories.

Predicting 3D point trajectory is a fundamental learning task which commonly should be equivariant under Eu-clidean transformation, e.g., SE(3). The existing equivari-ant models are commonly based on the group equivariant convolution, equivariant message passing, vector neuron, frame averaging, etc. In this paper, we propose a novel pose-transformed equivariant network, in which the points are firstly uniquely normalized and then transformed by the learned pose transformations, upon which the points after motion are predicted and aggregated. Under each trans-formed pose, we design the point position predictor consisting of multiple Pose- Transformed Points Prediction blocks, in which the global and local motions are estimated and aggregated. This framework can be proven to be equiv-ariant to SE(3) transformation over 3D points. We eval-uate the pose-transformed equivariant network on exten-sive datasets including human motion capture, molecular dynamics modeling and dynamics simulation. Extensive experimental comparisons demonstrated our SOTA performance compared with the existing equivariant networks for 3D point trajectory prediction.

Implicit neural representation gains popularity in modeling the continuous 3D surface for 3D representation and reconstruction. In this work, we are motivated by the fact that the local 3D patches repeatedly appear on 3D shapes/surfaces if the factor of poses is removed. Based on this observation, we propose the 3D patch-level equivariant implicit function (PEIF) based on the 3D patch-level pose-invariant representation, allowing us to reconstruct 3D surfaces by estimating equivariant displacement vector fields for query points. Specifically, our model is based on the pose-normalized query/patch pairs and enhanced by the proposed intrinsic patch geometry representation, modeling the intrinsic 3D patch geometry feature by learnable multi-head memory banks. Extensive experiments show that our model achieves state-of-the-art performance on multiple surface reconstruction datasets, and also exhibits better generalization to crossdataset shapes and robustness to arbitrary rotations. Our code will be available at https://github.com/mathXin112/PEIF.git.

View-based approach that recognizes 3D shape through its projected 2D images has achieved state-of-the-art results for 3D shape recognition. The major challenges are how to aggregate multi-view features and deal with 3D shapes in arbitrary poses. We propose two versions of a novel view-based Graph Convolutional Network, dubbed view-GCN and view-GCN++, to recognize 3D shape based on graph representation of multiple views. We first construct view-graph with multiple views as graph nodes, then design two graph convolutional networks over the view-graph to hierarchically learn discriminative shape descriptor considering relations of multiple views. Specifically, view-GCN is a hierarchical network based on two pivotal operations, i.e., feature transform based on local positional and non-local graph convolution, and graph coarsening based on a selective view-sampling operation. To deal with rotation sensitivity, we further propose view-GCN++ with local attentional graph convolution operation and rotation robust view-sampling operation for graph coarsening. By these designs, view-GCN++ achieves invariance to transformations under the finite subgroup of rotation group SO(3). Extensive experiments on benchmark datasets (i.e., ModelNet40, ScanObjectNN, RGBD and ShapeNet Core55) show that view-GCN and view-GCN++ achieve state-of-the-art results for 3D shape classification and retrieval tasks under aligned and rotated settings.

3D object recognition is one of the most important tasks in 3D data processing, and has been extensively studied recently. Researchers have proposed various 3D recognition methods based on deep learning, among which a class of view-based approaches is a typical one. However, in the view-based methods, the commonly used view pooling layer to fuse multi-view features causes a loss of visual information. To alleviate this problem, in this paper, we construct a novel layer called Dynamic Routing Layer (DRL) by modifying the dynamic routing algorithm of capsule network, to more effectively fuse the features of each view. Concretely, in DRL, we use rearrangement and affine transformation to convert features, then leverage the modified dynamic routing algorithm to adaptively choose the converted features, instead of ignoring all but the most active feature in view pooling layer. We also illustrate that the view pooling layer is a special case of our DRL. In addition, based on DRL, we further present a Dynamic Routing Convolutional Neural Network (DRCNN) for multi-view 3D object recognition. Our experiments on three 3D benchmark datasets show that our proposed DRCNN outperforms many state-of-the-arts, which demonstrates the efficacy of our method.

View-based approach that recognizes 3D shape through its projected 2D images has achieved state-of-the-art results for 3D shape recognition. The major challenge for view-based approach is how to aggregate multi-view features to be a global shape descriptor. In this work, we propose a novel view-based Graph Convolutional Neural Network, dubbed as view-GCN, to recognize 3D shape based on graph representation of multiple views in flexible view configurations. We first construct view-graph with multiple views as graph nodes, then design a graph convolutional neural network over view-graph to hierarchically learn discriminative shape descriptor considering relations of multiple views. The view-GCN is a hierarchical network based on local and non-local graph convolution for feature transform, and selective view-sampling for graph coarsening. Extensive experiments on benchmark datasets show that view-GCN achieves state-of-the-art results for 3D shape classification and retrieval.

In this paper, we propose a novel network block, dubbed as second-order spectral transform block, for 3D shape retrieval and classification. This network block generalizes the second-order pooling to 3D surface by designing a learnable non-linear transform on the spectrum of the pooled descriptor. The proposed block consists of following two components. First, the second-order average (SO-Avr) and max-pooling (SOMax) operations are designed on 3D surface to aggregate local descriptors, which are shown to be more discriminative than the popular average-pooling or max-pooling. Second, a learnable spectral transform parameterized by mixture of power function is proposed to perform non-linear feature mapping in the space of pooled descriptors, i.e., manifold of symmetric positive definite matrix for SO-Avr, and space of symmetric matrix for SOMax. The proposed block can be plugged into existing network architectures to aggregate local shape descriptors for boosting their performance. We apply it to a shallow network for nonrigid 3D shape analysis and to existing networks for rigid shape analysis, where it improves the first-tier retrieval accuracy by 7.2% on SHREC'14 Real dataset and achieves state-of-the-art classification accuracy on ModelNet40. As an extension, we apply our block to 2D image classification, showing its superiority compared with traditional second-order pooling methods. We also provide theoretical and experimental analysis on stability of the proposed second-order spectral transform block.