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We present a survey on 4D generation and reconstruction, a fast-evolving subfield of computer graphics whose developments have been propelled by recent advances in neural fields, geometric and motion deep learning, as well as 3D generative…
Loop closure, as one of the crucial components in SLAM, plays an essential role in correcting the accumulated errors. Traditional appearance-based methods, such as bag-of-words models, are often limited by local 2D features and the volume…
Three-dimensional gravity is a topological field theory, which can be quantized as the Ponzano-Regge state-sum model built from the $\{3nj\}$-symbols of the recoupling of the $\SU(2)$ representations, in which spins are interpreted as…
Building accurate maps is a key building block to enable reliable localization, planning, and navigation of autonomous vehicles. We propose a novel approach for building accurate maps of dynamic environments utilizing a sequence of LiDAR…
A new family of coherent states for all dimensional loop quantum gravity are proposed, which is based on the generalized twisted geometry parametrization of the phase space of $SO(D+1)$ connection theory. We prove that this family of…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
Numerical simulations of kinematic dynamo action in steady and 3-d ABC flows are presented with special focus on growth rates and multiple periods of the prescribed velocity field. It is found that the difference in growth rate is due to…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
We establish an extended version of the kinetic theory of the relativistic axionically active multi-component plasma, which is based on the inclusion of a unit time-like vector field, associated with the velocity of dynamic aether, into the…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
A bar-joint framework $(G,p)$ is the combination of a finite simple graph $G=(V,E)$ and a placement $p:V\rightarrow \mathbb{R}^d$. The framework is rigid if the only edge-length preserving continuous deformations of the vertices arise from…
We introduce a new approach for robotic manipulation tasks in human settings that necessitates understanding the 3D geometric connections between a pair of objects. Conventional end-to-end training approaches, which convert pixel…
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…
Synthesizing 3D human motion plays an important role in many graphics applications as well as understanding human activity. While many efforts have been made on generating realistic and natural human motion, most approaches neglect the…
Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely…
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…
We present a method for constructing all bounded rational motions that frame a space curve $\mathbf{r}(t)$. This means that the motion guides an orthogonal frame along the curve such that one frame axis is in direction of the curve tangent.…
State-of-the-art methods for large-scale driving-scene LiDAR semantic segmentation often project and process the point clouds in the 2D space. The projection methods includes spherical projection, bird-eye view projection, etc. Although…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
We develop a three-dimensional dynamical-systems framework for passive gliding and identify the global phase-space structures that organize its motion. Extending previous two-dimensional models of non-equilibrium gliding, we show that the…