Detecting 3D keypoints from point clouds is important for shape reconstruction, while this work investigates the dual question: can shape reconstruction benefit 3D keypoint detection? Existing methods either seek salient features according to statistics of different orders or learn to predict keypoints that are invariant to transformation. Nevertheless, the idea of incorporating shape reconstruction into 3D keypoint detection is under-explored. We argue that this is restricted by former problem formulations. To this end, a novel unsupervised paradigm named SNAKE is proposed, which is short for shape-aware neural 3D keypoint field. Similar to recent coordinate-based radiance or distance field, our network takes 3D coordinates as inputs and predicts implicit shape indicators and keypoint saliency simultaneously, thus naturally entangling 3D keypoint detection and shape reconstruction. We achieve superior performance on various public benchmarks, including standalone object datasets ModelNet40, KeypointNet, SMPL meshes and scene-level datasets 3DMatch and Redwood. Intrinsic shape awareness brings several advantages as follows.

The budget for DGE is set to 0.5. "Resolution" refers to the side length of input images. As shown in Figure 1(a), one limitation of our work is that the acceleration ratio on GPUs (based on native PyTorch implementation) is not good when the input image size is small. We suspect that this is due to the additional modules of DGE resulting in more scheduling processes, and scheduling processes lead to static time consumption. Nevertheless, our work demonstrates the superiority of efficiency on large-size input images, which is crucial for many downstream tasks and practical scenes.

In this material, we first describe the importance of action validity prediction networks. Then, we introduce the details of the benchmarks, provide the model architecture, and present the additional experimental results, which are missing in the main article. We present the results of wall-clock time for computing the ground-truth action validity in Figure s.1. It shows that computing the action validity for a combination of 100 bricks needs more than 20 seconds. Moreover, we summarize the comparisons between possible action validation approaches as shown in Table s.1.0

In this section, we describe in detail the proposed architecture and its implementation. Our architecture is composed by an encoder and a decoder. The encoder receives as input a predefined number of learnable latent probes LP, together with the point coordinates of the target point cloud XT. Each layer of the encoder performs an operation of cross-attention between LP and XT followed by a self-attention on LP. Each attention is followed by a feed-forward layer.

In this paper, we propose a transformer-based procedure for the efficient registration of non-rigid 3D point clouds. The proposed approach is data-driven and adopts for the first time the transformer architecture in the registration task. Our method is general and applies to different settings. Given a fixed template with some desired properties (e.g.

Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the lowlevel OT, which considers the weights of all the data samples in the base class. Experiments on standard benchmarks demonstrate that our proposed plug-andplay model outperforms competing approaches and owns desired cross-domain generalization ability, proving the effectiveness of the learned adaptive weights. 1