Reconstruct Dynamic Scene for Spike Camera Based on 3D Space Time Similarity

A two-dimensional (2D) space-time (ST) delay operator D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ST</sup> [·] and a novel discrete-space-continuous-time (DSCT) CMOS VLSI implementation at radio frequency (RF) is proposed. The proposed delay operator is able to delay 2D ST antenna array signals along space and time and can be used as a building block in 2D ST array processing algorithms. A 2D non-separable DSCT transfer function (TF), Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">App</sub> (z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> , s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ct</sub> ) is used to approximate the ideal 2D ST delay represented by the 2D TF equation. A passive frequency planar transformation followed by bilinear transform along spatial dimension is used to derive Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">App</sub> (z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> , s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ct</sub> ) starting from a 1D passive all-pass prototype. The 2D delay D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ST</sup> [·] is proposed to be realized using an array of identical analog modules (AMs). A CMOS VLSI circuit operating at RF is proposed for each AM. Magnitude and phase frequency responses of a single AM operating at 1 GHz is obtained using 65 nm TSMC CMOS simulations in Cadence and compared with the theoretical responses. The 2D phase frequency response of D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ST</sup> [·] is obtained using the CMOS simulated response of a single AM.

The initial assumption of theories with extra dimension is based on the efforts to yield a geometrical interpretation of the gravitation field. In this paper, using an infinitesimal parallel transportation of a vector, we generalize the obtained results in four dimensions to five-dimensional space–time. For this purpose, we first consider the effect of the geometrical structure of 4D space–time on a vector in a round trip of a closed path, which is basically quoted from chapter three of Ref. [5] . If the vector field is a gravitational field, then the required round trip will lead us to an equation which is dynamically governed by the Riemann tensor. We extend this idea to five-dimensional space–time and derive an improved version of Bianchi's identity. By doing tensor contraction on this identity, we obtain field equations in 5D space–time that are compatible with Einstein's field equations in 4D space–time. As an interesting result, we find that when one generalizes the results to 5D space–time, the new field equations imply a constraint on Ricci scalar equations, which might be containing a new physical insight.

View invariant action recognition using generalized 4D features

Visual Simultaneous Localization and Mapping (VSLAM) estimates the robot’s pose in three-dimensional space by analyzing the depth variations of inter-frame feature points. Inter-frame feature point mismatches can lead to tracking failure, impacting the accuracy of the mobile robot’s self-localization and mapping. This paper proposes a method for removing mismatches of image features in dynamic scenes in visual SLAM. First, the Grid-based Motion Statistics (GMS) method was introduced for fast coarse screening of mismatched image features. Second, an Adaptive Error Threshold RANSAC (ATRANSAC) method, determined by the internal matching rate, was proposed to improve the accuracy of removing mismatched image features in dynamic and static scenes. Third, the GMS-ATRANSAC method was tested for removing mismatched image features, and experimental results showed that GMS-ATRANSAC can remove mismatches of image features on moving objects. It achieved an average error reduction of 29.4% and 32.9% compared to RANSAC and GMS-RANSAC, with a corresponding reduction in error variance of 63.9% and 58.0%, respectively. The processing time was reduced by 78.3% and 38%, respectively. Finally, the effectiveness of inter-frame feature mismatch removal in the initialization thread of ORB-SLAM2 and the tracking thread of ORB-SLAM3 was verified for the proposed algorithm.

Three-dimensional (3D) displays provides valuable tools for many fields, such as scientific experiment, education, information transmission, medical imaging and physical simulation. Ground based 360° 3D display with dynamic and controllable scene can find some special applications, such as design and construction of buildings, aeronautics, military sand table and so on. It can be utilized to evaluate and visualize the dynamic scene of the battlefield, surgical operation and the 3D canvas of art. In order to achieve the ground based 3D display, the public focus plane should be parallel to the camera’s imaging planes, and optical axes should be offset to the center of public focus plane in both vertical and horizontal directions. Virtual cameras are used to display 3D dynamic scene with Unity 3D engine. Parameters of virtual cameras for capturing scene are designed and analyzed, and locations of virtual cameras are determined by the observer’s eye positions in the observing space world. An interactive dynamic 3D scene for ground based 360° 3D display is demonstrated, which provides high-immersion 3D visualization.

Space-time (ST) wave packets are pulsed beams endowed with tight spatio-temporal spectral correlations, whereby each spatial frequency is associated with a single wavelength resulting in propagation invariance at an arbitrary group velocity. Previously, our group introduced an experimental methodology to synthesize 2D ST wave packets, i.e. light sheets, based on 2D pulse shaper. Here, we demonstrate a new experimental method to synthesize ST wave packets localized in all dimensions, including 3D space and 1D time. We show that 3D ST wave packets propagate longer distances without spreading compared with traditional Bessel beams, and propagate at subluminal and superluminal group velocities.

Surface And Hypersurface Meshing Techniques for Space–Time Finite Element Methods

Region Connectivity Calculus (RCC) can be used to define the formal grammar describing the relationship between image regions. While RCC provides a possible framework for representation of object part constellations leading to object recognition, little has been done in the direction of RCC for 3D images. Almost all prior RCC representations, such as RCC5/ RCC8/ RCC23/RCC62 are oriented towards 2D projections. While the recently introduced RCC-3D does address this limitation to a certain extent, it heavily depends on other 2D RCC frameworks and as such is limited -- it provides no representation for orthogonally aligned or staggered object parts. It also does not provide convenient representations for shape related pose information (such as "horizontally aligned along principal axis" or "vertically aligned" etc.). While it is possible to use oriented matroids for projected 3D representations using cocircuits and chirotopes, these are again sub-optimal given that there is considerable information loss (through dimensionality reduction) and multiple object models map to the same structures. In this paper, we introduce a new hierarchical graph based 3D Region/ Surface/ Object/ Part Connectivity Calculus (OCC/PCC), given the domain of affordance based equivalence recognition. We call our PCC -- 4D Space Time Mereo-topo-geometry (4D-STMTG) and the equivalent OCC as 4D Space Time Joint Topo-geometry (4D-STJTG). The modeling of simple objects using the calculus is demonstrated in practical scenarios. Comparisons of the proposed calculus with respect to the state-of-art RCC-3D is also presented, demonstrating the flexibility, suitability and superiority of 4D-STMTG.

The phenomenon of fermion production in a 5D FRW space–time with a warped extra dimension is studied by considering the canonical method based on Bogoliubov transformation connecting the "in" with the "out" states. For an exactly solvable model, two sets of exact solution are expressed in terms of Bessel functions. Studying the semiclassical Hamilton–Jacobi equation, the "in" and "out" states are identified. The pair creation probability and the mean number of created particles are calculated from the Bogoliubov coefficients. It is shown that the particle creation probability and the number density of created particles depend on the ratio of the scale factors associated with the ordinary space {x} and the extra dimension. It is also shown that the contraction of the extra dimension induces particle creation like the ordinary space expansion.

A five-dimensional perspective on the Klein–Gordon equation

Motivated by string-theoretic swampland conjectures, the existence of a dark fifth dimension, whose size is roughly 1–10 microns, has been proposed. A great deal of supporting evidence has been presented, and definitive experimental tests are likely to be carried out. The basic idea is that the four-dimensional space–time that we observe is confined to a brane that is localized in the dark dimension. This short note points out that there are two distinct ways to realize such a scenario in string theory/M-theory. In the one considered previously, the dark dimension is topologically a circle and our observable 4d space–time is confined to a brane that is localized in a GUT-scale region of the circle. An alternative possibility is that the dark dimension is a line interval with “end-of-the-world-branes” at each end. The latter option would imply the existence of a parallel 4d space–time, with the same gravitational forces as ours, but otherwise its own physical laws, microns away from us!

In the last hundred years mankind has fully absorbed the idea of multi-dimensional space, starting with 4D space time. Due to the increase in computational power, scientists can now manipulate molecules in 4D (3D vibrating molecules in VR) and work with multidimensional datasets, which are needed to utilize big data and machine learning. However, our intuition from 3D space can fall down when dealing with higher dimensions and a lack of intuition can lead to mistakes in analysis. In this talk I will discuss how to think about the best dimensional space to use to describe chemical problems, how multi-dimensional space is different, techniques for using it and analysing the outputs of machine learning.

The 3d spin-3 gravity theory is holographically dual to a 2d W3-extended CFT. In a large-c limit the symmetry algebra of the CFT reduces to SU(1,2)×SU(1,2). On ground of symmetry the dual bulk space–time will be given by an 8d group manifold SU(1,2). Hence we need to introduce five extra coordinates in addition to three ordinary ones. The 3d space–time is a 3d hyper-surface Σ embedded at constant values of the extra variables. Operators in the CFT at the boundary of Σ are expressed in terms of W descendants of the operators at the boundary of Σ0, where the extra variables vanish. In this paper it is shown that AdS/CFT correspondence for a scalar field coupled to 3d spin-3 gravity is realized in this auxiliary 8d space. A bulk-to-boundary propagator of a scalar field is found and a generating functional of boundary two-point functions of scalar W-descendant operators is obtained by using the classical action for the scalar field. Classically, the scalar field must satisfy both Klein–Gordon equation and a third-order differential equation, which are related to the quadratic and cubic Casimir operators of su(1,2). It is found that the coefficient function of the derivatives of the scalar field in the latter equation is the spin-3 gauge field, when restricted to the hypersurface. An action integral in the 8d auxiliary space for the 3d spin-3 gravity coupled to a scalar field is presented. In general, this 8d auxiliary space is a deformation of the manifold SU(1,2). An 8d local frame is introduced and the equations of motion for the 8d connections Aμ, A‾μ are solved. By restricting those solutions onto Σ, flat connections in 3d SL(3,R)×SL(3,R) Chern–Simons theory are obtained and new 3d black hole solutions with and without spin-3 charge are found by this method.

Dynamic scene novel view synthesis via deferred spatio-temporal consistency

In type-II superconductors, the dynamics of magnetic flux vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter field. Earlier, in Phillips et al. [Phys. Rev. E 91, 023311 (2015)], we introduced a method for extracting vortices from the discretized complex order parameter field generated by a large-scale simulation of vortex matter. With this method, at a fixed time step, each vortex [simplistically, a one-dimensional (1D) curve in 3D space] can be represented as a connected graph extracted from the discretized field. Here we extend this method as a function of time as well. A vortex now corresponds to a 2D space-time sheet embedded in 4D space time that can be represented as a connected graph extracted from the discretized field over both space and time. Vortices that interact by merging or splitting correspond to disappearance and appearance of holes in the connected graph in the time direction. This method of tracking vortices, which makes no assumptions about the scale or behavior of the vortices, can track the vortices with a resolution as good as the discretization of the temporally evolving complex scalar field. Additionally, even details of the trajectory between time steps can be reconstructed from the connected graph. With this form of vortex tracking, the details of vortex dynamics in a model of a superconducting materials can be understood in greater detail than previously possible.