Related papers: SOE: SO(3)-Equivariant 3D MRI Encoding

Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors,…

In 3D hand-object interaction (HOI) tasks, estimating precise joint poses of hands and objects from monocular RGB input remains highly challenging due to the inherent geometric ambiguity of RGB images and the severe mutual occlusions that…

In this paper, we develop SE3Set, an SE(3) equivariant hypergraph neural network architecture tailored for advanced molecular representation learning. Hypergraphs are not merely an extension of traditional graphs; they are pivotal for…

Unlike in natural images, in endoscopy there is no clear notion of an up-right camera orientation. Endoscopic videos therefore often contain large rotational motions, which require keypoint detection and description algorithms to be robust…

Neural networks that incorporate geometric relationships respecting SE(3) group transformations (e.g. rotations and translations) are increasingly important in molecular applications, such as molecular property prediction, protein structure…

Mental rotation -- the ability to compare objects seen from different viewpoints -- is a fundamental example of mental simulation and spatial world modeling in humans. Here we propose a mechanistic model of human mental rotation, leveraging…

We propose a framework to combine strong non-linear expressiveness with strict SO(3)-equivariance in prediction of the electronic-structure Hamiltonian, by exploring the mathematical relationships between SO(3)-invariant and…

Visual imitation learning with 3D point clouds has advanced robotic manipulation by providing geometry-aware, appearance-invariant observations. However, point cloud-based policies remain highly sensitive to sensor noise, pose…

Content-based image retrieval (CBIR) systems are an emerging technology that supports reading and interpreting medical images. Since 3D brain MR images are high dimensional, dimensionality reduction is necessary for CBIR using machine…

Masked Autoencoders (MAEs) have been shown to be effective in pre-training Vision Transformers (ViTs) for natural and medical image analysis problems. By reconstructing missing pixel/voxel information in visible patches, a ViT encoder can…

Rotary Positional Encodings (RoPE) have emerged as a highly effective technique for one-dimensional sequences in Natural Language Processing spurring recent progress towards generalizing RoPE to higher-dimensional data such as images and…

Discovering a new field is not usually an easy process, especially when you choose magnetic resonance imaging (MRI). MRI is one of the few non-invasive medical procedures, if not the only one, that someone can receive in modern day…

Many settings in machine learning require the selection of a rotation representation. However, choosing a suitable representation from the many available options is challenging. This paper acts as a survey and guide through rotation…

Deep learning models often need sufficient supervision (i.e. labelled data) in order to be trained effectively. By contrast, humans can swiftly learn to identify important anatomy in medical images like MRI and CT scans, with minimal…

Interpretability is a key issue when applying deep learning models to longitudinal brain MRIs. One way to address this issue is by visualizing the high-dimensional latent spaces generated by deep learning via self-organizing maps (SOM). SOM…

Image registration plays an important role in medical image analysis. Conventional optimization based methods provide an accurate estimation due to the iterative process at the cost of expensive computation. Deep learning methods such as…

Rotary Position Embedding (RoPE) is the de facto positional encoding in large language models due to its ability to encode relative positions and support length extrapolation. When adapted to vision transformers, the standard axial…

In modern medical diagnostics, magnetic resonance imaging (MRI) is an important technique that provides detailed insights into anatomical structures. In this paper, we present a comprehensive methodology focusing on streamlining the…

Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…