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Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…
Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied to tasks such as predicting molecular dynamics and properties. To perform equivariant convolutional-like…
With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with $\mathsf{SO}(3)$-equivariant layers have been developed to cope with data that are samples of signals on the sphere $S^2$. One can implicitly…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
In the field of deep point cloud understanding, KPConv is a unique architecture that uses kernel points to locate convolutional weights in space, instead of relying on Multi-Layer Perceptron (MLP) encodings. While it initially achieved…
Deploying 3D graph neural networks (GNNs) that are equivariant to 3D rotations (the group SO(3)) on edge devices is challenging due to their high computational cost. This paper addresses the problem by compressing and accelerating an…
We address the problem of fitting a parametric human body model (SMPL) to point cloud data. Optimization-based methods require careful initialization and are prone to becoming trapped in local optima. Learning-based methods address this but…
To better address challenging issues of the irregularity and inhomogeneity inherently present in 3D point clouds, researchers have been shifting their focus from the design of hand-craft point feature towards the learning of 3D point…
The acquisition of inductive bias through point-level contrastive learning holds paramount significance in point cloud pre-training. However, the square growth in computational requirements with the scale of the point cloud poses a…
Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…
Equivariant diffusion models have achieved impressive performance in 3D molecule generation. These models incorporate Euclidean symmetries of 3D molecules by utilizing an SE(3)-equivariant denoising network. However, specialized equivariant…
Accurate prediction of compound-protein interactions (CPI) remains a cornerstone challenge in computational drug discovery. While existing sequence-based approaches leverage molecular fingerprints or graph representations, they critically…
Incorporating inductive bias by embedding geometric entities (such as rays) as input has proven successful in multi-view learning. However, the methods adopting this technique typically lack equivariance, which is crucial for effective 3D…
Point clouds obtained from 3D scans are typically sparse, irregular, and noisy, and required to be consolidated. In this paper, we present the first deep learning based edge-aware technique to facilitate the consolidation of point clouds.…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant…
Equivariance has gained strong interest as a desirable network property that inherently ensures robust generalization. However, when dealing with complex systems such as articulated objects or multi-object scenes, effectively capturing…
Automatic tumor or lesion segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on Convolutional Neural Networks (CNNs) have achieved the state-of-the-art performance,…