Related papers: AtlasD: Automatic Local Symmetry Discovery
Reasoning 3D shapes from 2D images is an essential yet challenging task, especially when only single-view images are at our disposal. While an object can have a complicated shape, individual parts are usually close to geometric primitives…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
Autonomous exploration for mapping unknown large scale environments is a fundamental challenge in robotics, with efficiency in time, stability against map corruption and computational resources being crucial. This paper presents a novel…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
Mirror symmetry of a wave system imposes corresponding even or odd parity on its eigenmodes. For a discrete system, eigenmode parity on a specific subset of sites may also originate from so-called latent symmetry. This symmetry is hidden,…
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…
Recently, it has become popular to deploy sensors such as LiDARs on the roadside to monitor the passing traffic and assist autonomous vehicle perception. Unlike autonomous vehicle systems, roadside sensors are usually affiliated with…
Self-supervised surround-view depth estimation enables dense, low-cost 3D perception with a 360{\deg} field of view from multiple minimally overlapping images. Yet, most existing methods suffer from depth estimates that are inconsistent…
Many objects are naturally symmetric, and this symmetry can be exploited to infer unseen 3D properties from a single 2D image. Recently, NeRD is proposed for accurate 3D mirror plane estimation from a single image. Despite the unprecedented…
In spite of considerable practical importance, current algorithmic fairness literature lacks technical methods to account for underlying geographic dependency while evaluating or mitigating bias issues for spatial data. We initiate the…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
Aiming at improving the performance of existing detection algorithms developed for different applications, we propose a region regression-based multi-stage class-agnostic detection pipeline, whereby the existing algorithms are employed for…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
RRT* is an efficient sampling-based motion planning algorithm. However, without taking advantages of accessible environment information, sampling-based algorithms usually result in sampling failures, generate useless nodes, and/or fail in…
We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns : the gauge symmetry Z 2 . This symmetry is present in physical problems from topological transitions to QCD, and controls the…
Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…
A staircase localization method is proposed for robots to explore urban environments autonomously. The proposed method employs a modular design in the form of a cascade pipeline consisting of three modules of stair detection, line segment…
Recent years, analysis dictionary learning (ADL) and its applications for classification have been well developed, due to its flexible projective ability and low classification complexity. With the learned analysis dictionary, test samples…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…