A Local Reference Frame Construction Method Based on the Signed Surface Variation

A fast local reference frame(LRF)construction method based on the signed surface variation is proposed,which can adapt to the real-time applications such as self-driving,face recognition,object detection.The z-axis of the LRF is generated based on the concavity of the local surface of keypoint.The x-axis is constructed by the weighted vector sum of a set of projection vectors of the local neighborhoods around keypoint.The performance of the proposed LRF is evaluated on six standard datasets and compared with six state-of-the-art LRF construction methods(e.g.,BOARD,FLARE,SHOT,RoPS and TOLDI).Experimental results validate the high repeatability,robustness,universality and time efficiency of our method.

Novel 3D local feature descriptor of point clouds based on spatial voxel homogenization for feature matching

Obtaining a 3D feature description with high descriptiveness and robustness under complicated nuisances is a significant and challenging task in 3D feature matching.This paper proposes a novel feature description consisting of a stable local reference frame(LRF)and a feature descriptor based on local spatial voxels.First,an improved LRF was designed by incorporating distance weights into Z-and X-axis calculations.Subsequently,based on the LRF and voxel segmentation,a feature descriptor based on voxel homogenization was proposed.Moreover,uniform segmentation of cube voxels was performed,considering the eigenvalues of each voxel and its neighboring voxels,thereby enhancing the stability of the description.The performance of the descriptor was strictly tested and evaluated on three public datasets,which exhibited high descriptiveness,robustness,and superior performance compared with other current methods.Furthermore,the descriptor was applied to a 3D registration trial,and the results demonstrated the reliability of our approach.

2-D distributed pose estimation of multi-agent systems using bearing measurements

This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.

A Conceptual Deficiency for the Use of Christoffel Connection in Gravity Theories

Christoffel connection (or Levi-Civita affine connection) did not enter gravity as an axiom of minimal length for the free fall of particles (where anyway length action is not defined for massless particles), nor out of economy, but from the weak equivalence principle (gravitational force is equivalent to acceleration according to Einstein) together with the identification of the local inertial frame with the local Lorentz one. This identification implies that the orbits of all particles are given by the geodesics of the Christoffel connection. Here, we show that in the presence of only massless particles (absence of massive particles), the above identification is inconsistent and does not lead to any connection. The proof is based on the existence of projectively equivalent connections and the absence of proper time for null particles. If a connection derived by some kinematical principles for the particles is to be applied in the world, it is better for these principles to be valid in all relevant spacetime rather than different principles to give different connections in different spacetime regions. Therefore, our result stated above may imply a conceptual insufficiency of the use of the Christoffel connection in the early universe where only massless particles are expected to be present (whenever at least some notions, like orbits, are meaningful), and thus of the total use of this connection. If in the early universe, the notion of a massive particle, which appears latter in time, cannot be used, in an analogous way in a causally disconnected high-energy region (maybe deep interior of astrophysical objects or black holes), the same conclusions could be extracted if only massless particles are present.

Digital ridgelet reconstruction based on local dual frame

A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.

Leader-Following Entrapping Control of AUVs Using Bearing Measurements in Local Coordinate Frames

In this paper,the entrapping control problem of discrete-time AUVs with local coordinate frames is studied.To achieve entrapment in arbitrarily shaped orbits and formations,we design a bearingbased leader-following framework fully in the discrete-time domain with four parts:the orientation estimation unit,estimator unit,controller unit and parameters tuning unit.With bearing measurements and communication information,the orientation estimation unit can estimate orientations of local coordinate frames infinite time,and the estimator unit can achieve local localization.Based on estimation,the controller unit can drive each AUV to track the desired orbit or formation with an arbitrary shape.We present su±cient conditions under which stability of the overall system is proved using the theorem offinite-time stability and LaSalle's theorem for the discrete-time system.Moreover,the parameters tuning unit can calculate optimal parameters to improve overall performance.Additionally,we extend our schemes to nonholonomic AUVs with unicycle models.Finally,simulation results demonstrate the effectiveness of the proposed scheme.

Weak type heterodimensional cycle bifurcation with orbit-flip

In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for the persistent heterodimensional cycle and multiple periodic orbits due to the weak type of the transversal heteroclinic orbit. Moreover, an analytical example is presented for this subcase.

Nongeneric Bifurcations Near a Nontransversal Heterodimensional Cycle

In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields,where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs.By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles,the authors construct a Poincar′e return map under the nongeneric conditions and further obtain the bifurcation equations.By means of the bifurcation equations,the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles.Moreover,an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system.

Base pair distance analysis in single DNA molecule by direct stochastic optical reconstruction microscopy

Precise fluorescence imaging of single l-DNA molecules for base pair distance analysis requires a superresolution technique, as these distances are on the order of diffraction limit. Individual l-DNA molecules intercalated with the fluorescent dye YOYO-1 were investigated at subdiffraction spatial resolution by direct stochastic optical reconstruction microscopy（d STORM）. Various dye-to-DNA base pair ratios were imaged by photoswitching YOYO-1 between the fluorescent state and the dark state using two laser sources. The acquired images were reconstructed into a super-resolution image by applying Gaussian fitting to the centroid of the point spread function. By measuring the distances between localized fluorophores, the base pair distances in single DNA molecules for dye-to-DNA base pair ratios of 1：50,1：100, and 1：500 were calculated to be 17.1 0.8 nm, 34.3 2.2 nm, and 170.3 8.1 nm[17_TD$IF], respectively,which were in agreement with theoretical values. These results demonstrate that intercalating dye in a single DNA molecule can be photoswitched without the use of an activator fluorophore, and that super-localization precision at a spatial resolution of 17 nm was experimentally achieved.