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Efficiency and robustness are increasingly needed for applications on 3D point clouds, with the ubiquitous use of edge devices in scenarios like autonomous driving and robotics, which often demand real-time and reliable responses. The paper…

Point clouds provide a compact and efficient representation of 3D shapes. While deep neural networks have achieved impressive results on point cloud learning tasks, they require massive amounts of manually labeled data, which can be costly…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…

Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…

Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…

We propose an octree guided neural network architecture and spherical convolutional kernel for machine learning from arbitrary 3D point clouds. The network architecture capitalizes on the sparse nature of irregular point clouds, and…

Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations. As panoramas are defined on the sphere, they naturally transform under the action of $SO(3)$, rendering conventional planar representations…

This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The main challenge when designing equivariant models for point…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…

We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the…

We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…

Panoramic semantic segmentation models are typically trained under a strict gravity-aligned assumption. However, real-world captures often deviate from this canonical orientation due to unconstrained camera motions, such as the rotational…

Learning to predict reliable characteristic orientations of 3D point clouds is an important yet challenging problem, as different point clouds of the same class may have largely varying appearances. In this work, we introduce a novel method…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

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…

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…