Related papers: AtlasD: Automatic Local Symmetry Discovery
Place recognition is an important capability for autonomously navigating vehicles operating in complex environments and under changing conditions. It is a key component for tasks such as loop closing in SLAM or global localization. In this…
Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…
In the last decade many works has been done on the Internet topology at router or autonomous system (AS) level. As routers is the essential composition of ASes while ASes dominate the behavior of their routers. It is no doubt that…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
Local feature matching remains a fundamental challenge in computer vision. Recent Area to Point Matching (A2PM) methods have improved matching accuracy. However, existing research based on this framework relies on inefficient pixel-level…
Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance,…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
LiDAR is an important method for autonomous driving systems to sense the environment. The point clouds obtained by LiDAR typically exhibit sparse and irregular distribution, thus posing great challenges to the detection of 3D objects,…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
Anomaly detection on attributed graphs is a crucial topic for its practical application. Existing methods suffer from semantic mixture and imbalance issue because they mainly focus on anomaly discrimination, ignoring representation…
Real-world geometry and 3D vision tasks are replete with challenging symmetries that defy tractable analytical expression. In this paper, we introduce Neural Isometries, an autoencoder framework which learns to map the observation space to…
Place recognition is an important task within autonomous navigation, involving the re-identification of previously visited locations from an initial traverse. Unlike visual place recognition (VPR), LiDAR place recognition (LPR) is tolerant…
Time series anomaly detection plays a crucial role in a wide range of real-world applications. Given that time series data can exhibit different patterns at different sampling granularities, multi-scale modeling has proven beneficial for…
We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates.…
We present an algorithm for the determination of the local symmetry group for arbitrary k-points in 3D Brillouin zones. First, we test our implementation against tabulated results available for standard high-symmetry points (given by…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…