Decomposition Of Motion Research Articles

Multi‐view registration based on weighted LRS matrix decomposition of motions

Recently, the low‐rank and sparse (LRS) matrix decomposition has been introduced as an effective mean to solve the multi‐view registration. It views each available relative motion as a block element to reconstruct one sparse matrix, which then is used to approximate the low‐rank matrix, where global motions can be recovered for multi‐view registration. However, this approach is sensitive to the sparsity of the reconstructed matrix and it treats all block elements equally in spite of their varied reliabilities. Therefore, this study proposes an effective approach for multi‐view registration by weighted LRS matrix decomposition. On the basis of the inverse symmetry property of relative motions, it first proposes a completion method to reduce the sparsity of the reconstructed matrix. The reduced sparsity of the reconstructed matrix can improve the robustness and efficiency of LRS matrix decomposition. Then, it proposes the weighted LRS matrix decomposition, where each block element is assigned with one estimated weight to denote its reliability. By introducing the weight, more accurate registration results can be efficiently recovered from the estimated low‐rank matrix. Experimental results tested on public datasets illustrate the superiority of the proposed approach over the state‐of‐the‐art approaches on robustness, accuracy and efficiency.

Bistatic ISAR Sparse Imaging Method for High-Speed Moving Target Based on Dechirping Processing

Bistatic inverse synthetic aperture radar (ISAR) can increase the probability of tracking the high-speed target and provide more angle information than monostatic ISAR. However, bistatic ISAR suffers from a serious defocusing problem, resulting from the high-speed motion. Furthermore, the inherent geometry distortion and calibration problems make bistatic ISAR (B-ISAR) imaging more complex. In response to these problems, we propose a bistatic ISAR imaging method for high-speed moving target with geometric distortion correction and calibration based on dechirping processing. At first, based on the motion decomposition idea, the B-ISAR echo model of the high-speed moving target is established. Then, by analyzing the imaging mechanism of the Range-Doppler algorithm (RDA), we eliminate the phase items influencing the imaging quality with speed compensation and Doppler compensation. After that, the analytic formula of the geometric distortion factor and calibration factor are deduced, which helps transform the geometric correction and calibration problem into a parameter estimation problem. Finally, with the sparsity of the scattering points, the required parameters are solved using the expectation maximization (EM) algorithm based on the maximum a posteriori probability criterion. With the estimated parameters, a clear B-ISAR image of a high-speed moving target with geometric correction and calibration is obtained. The simulations show that the proposed method has a better resolution and simultaneously attains geometric correction and calibration of the image.

Continuity in law of some additive functionals of bifractional Brownian motion

ABSTRACTLet be a bifractional Brownain motion with indices and . We prove the continuity in law, in some anisotropic Besov spaces, with respect to H and K. Our result generalizes those obtained by Jolis and Viles [Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion, J. Theor. Probab. 20(2) (2007), pp. 133–152] of the fractional Brownian motion local time and gives a new result for the generalized fractional derivatives with kernel depending on slowly varying function of the local time of . Notice that their result was generalized by Wu and Xiao [Continuity in the Hurst index of the local times of anisotropic gaussian random fields, Stoch. Proc. Their Appl. 119 (2009), pp. 1823–1844] for wide class of anisotropic gaussian random fields satisfying some condition (A) which is not satisfied by . To prove our result, we use the decomposition in law of given by Lei and Nualart [A decomposition of the bifractional Brownian motion and some applications, Statist. Probab. Lett. 79 (2009), pp. 619–624]. Our result is also new in the space of continuous functions.

Bistatic inverse synthetic aperture radar imaging method for the high-speed motion target

Bistatic inverse synthetic aperture radar (ISAR) can help image the high-speed target for its advantage in tracking and more observation angle to provide more information than monostatic ISAR. However, the complex image geometry makes it difficult to achieve a clear image of the target with geometry distortion correction and calibration. Furthermore, high-speed motion will make the image blurred or defocussed. To address these problems, a bistatic ISAR (B-ISAR) imaging method for high-speed motion target with geometric distortion correction and calibration is proposed. According to the motion decomposition idea, we established the B-ISAR echo model of the high-speed motion target. Then, based on the range Doppler algorithm, we deduce the analytic formula of the geometric distortion factor and calibration factor, and transform the imaging problem into a parameter estimation problem. With the sparsity of the scattering points, the required parameters are solved using the expectation maximization algorithm based on the maximum a posteriori probability criterion. With the estimated parameters, a clear B-ISAR image of a high-speed motion target with geometric correction and calibration is obtained. The simulations show that the proposed method has better resolution and simultaneously attains geometric distortion correction and calibration of the image.

Transporting random measures on the line and embedding excursions into Brownian motion

We consider two jointly stationary and ergodic random measures $\xi$ and $\eta$ on the real line $\mathbb{R}$ with equal intensities. An allocation is an equivariant random mapping from $\mathbb{R}$ to $\mathbb{R}$. We give sufficient and partially necessary conditions for the existence of allocations transporting $\xi$ to $\eta$. An important ingredient of our approach is to introduce a transport kernel balancing $\xi$ and $\eta$, provided these random measures are mutually singular. In the second part of the paper, we apply this result to the path decomposition of a two-sided Brownian motion into three independent pieces: a time reversed Brownian motion on $(-\infty,0]$, an excursion distributed according to a conditional It\^o's law and a Brownian motion starting after this excursion. An analogous result holds for Bismut's excursion law.

Experimental and Numerical Investigation of Optimized Blade Tip Shapes—Part II: Tip Flow Analysis and Loss Mechanisms

The leakage flows within the gap between the tips of unshrouded rotor blades and the stationary casing of high-speed turbines are the source of significant aerodynamic losses and thermal stresses. In the pursuit for higher component performance and reliability, shaping the tip geometry offers a considerable potential to modulate the rotor tip flows and to weaken the heat transfer onto the blade and casing. Nevertheless, a critical shortage of combined experimental and numerical studies addressing the flow and loss generation mechanisms of advanced tip profiles persists in the open literature. A comprehensive study is presented in this two-part paper that investigates the influence of blade tip geometry on the aerothermodynamics of a high-speed turbine. An experimental and numerical campaign has been performed on a high-pressure turbine stage adopting three different blade tip profiles. The aerothermal performance of two optimized tip geometries (one with a full three-dimensional contoured shape and the other featuring a multicavity squealer-like tip) is compared against that of a regular squealer geometry. In the second part of this paper, we report a detailed analysis on the aerodynamics of the turbine as a function of the blade tip geometry. Reynolds-averaged Navier-Stokes (RANS) simulations, adopting the Spalart–Allmaras turbulence model and experimental boundary conditions, were run on high-density unstructured meshes using the numecafine/open solver. The simulations were validated against time-averaged and time-resolved experimental data collected in an instrumented turbine stage specifically setup for the simultaneous testing of multiple blade tips at scaled engine-representative conditions. The tip flow physics is explored to explain variations in turbine performance as a function of the tip geometry. Denton's mixing loss model is applied to the predicted tip gap aerodynamic field to identify and quantify the loss reduction mechanisms of the alternative tip designs. An advanced method based on the local triple decomposition of relative motion is used to track the location, size and intensity of the vortical flow structures arising from the interaction between the tip leakage flow and the main gas path. Ultimately, the comparison between the unconventional tip profiles and the baseline squealer tip highlights distinct aerodynamic features in the associated gap flow field. The flow analysis provides guidelines for the designer to assess the impact of specific tip design strategies on the turbine aerodynamics and rotor heat transfer.

Inertial sensor aided multi-image nonuniform motion blur removal based on motion decomposition

Many factors lead to spatially varying blur kernels in a blurred image, such as camera shake, moving objects, and scene depth variation. The traditional camera shake removal methods either ignore the influence of varying depth values or object motion in dynamic scenes, while the methods not limited to removing camera shake always make simple assumptions about camera motion trajectory. We consider these factors in a unified framework, with the aid of an alternate-exposure capture strategy and simultaneously recorded inertial sensor readings. The inertial measurements relate the long-exposed blurred image to preceding and succeeding short-exposed noisy images. The special exposure arrangement effectively addresses the problem inherent in reconstructing camera motion from inertial measurements. In addition, the noisy image pair bracketing the blurred image is used for motion detection and initial depth map estimation, making the proposed method free of user interaction and additional expensive devices. Contrary to previous methods that individually parametrize the motion blur of the moving foreground layer and the static background layer, we exploit the fact that camera shake has a global influence to decompose the motion of the foreground layer such that a more tight constraint between the motion of layers is established. Given the motion and image data, we propose a single-energy model and minimize it using alternating optimization to estimate the spatially varying motion blur and the latent sharp image. Comparative experimental results demonstrate that our method outperforms conventional camera motion deblurring and object deblurring methods on both synthetic and real scenes.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition.

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Seismic behavior of a low-rise horizontal cylindrical tank

Cylindrical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. The study herein presented deals with the dynamic analysis of a ground-based horizontal cylindrical tank containing butane and with its safety verification. The analyses are based on a detailed finite element (FE) model; a simplified one-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to sloshing and asynchronous seismic input effects. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an “impulsive-convective” decomposition of the container-fluid motion is adopted for the calculation of the seismic force. The effects of asynchronous ground motion are studied by suitable pseudo-static analyses. Comparison between seismic action effects, obtained with and without consideration of sloshing and asynchronous seismic input, shows a rather important influence of these conditions on the final results.

Correlation between Geometrically Nonlinear Elastoviscoplastic Constitutive Relations Formulated in Terms of the Actual and Unloaded Configurations for Crystallites

A correct description of severe plastic deformation requires the use of nonlinear kinematic and constitutive relations. The relations should meet certain criteria, such as the frame-independence, closed stress cycles and the absence of energy dissipation under elastic cyclic loading. A most complicated issue in formulating these relations is the decomposition of motion into quasi-rigid and strain-induced motions, which is an extremely difficult problem with no unambiguous solution. For the majority of structural metals and alloys, this decomposition can be done in a physically justified way on the level of crystallites. Earlier, using a multilevel approach we introduced a corotational coordinate system for crystallites responsible for quasi-rigid motion. This allowed us to formulate frame-independent mesoscopic constitutive relations in the actual configuration and to perform test calculations to show that the above criteria are satisfied with high accuracy. A new way of motion decomposition was proposed which is a multiplicative representation of the deformation gradient with an explicit extraction of the corotational frame motion. Elastoviscoplastic constitutive relations satisfying the above criteria were formulated in terms of an unloaded "lattice" configuration. However, it is more preferable to formulate nonlinear boundary value problems in terms of the actual configuration in rates. This paper is aimed to study correlation between the earlier derived constitutive relations formulated in terms of the actual configuration and in terms of the unloaded "lattice" configuration. Example problems are solved to demonstrate the closeness of results obtained with these constitutive relations.

Decomposition of leg movements during overground walking in individuals with traumatic brain injury

ABSTRACTObjective: Walking requires precise coordination of bilateral lower extremity motions at all joints. This ability can be affected by traumatic brain injury (TBI). The study investigated inter-joint coordination of lower extremities during overground walking after TBI.Methods: Ten individuals with post-injury ataxia, postural stability and gait abnormalities, as well as 10 sex- and age-matched control subjects were involved in the study. Participants walked at self-selected speed in three experimental conditions: normal walking without any additional task; walking with a narrow base of support, and walking while holding a cup full of water. Inter-joint coordination was analysed as the percentage of gait cycle during which the leg movement was decomposed with 0% indicating simultaneous motion of the two joints (i.e. hip-knee, knee-ankle, and hip-ankle) through the entire gait cycle or 100% indicating motion of only one joint. Decomposition was calculated for each pair of joints and for the left and right leg separately.Results: Participants with TBI showed greater decomposition indices and poorer inter-joint coordination respectively than control individuals for all joint pairs (p < 0.01). Walking with the narrower base of support or with a cup, increased movement decomposition in the TBI group, but not in the control group.Conclusion: The results revealed post-injury gait impairment that manifests as decomposition of multi-joint motions of the lower extremities during overground walking.

Seismic performance of spherical liquid storage tanks: a case study

Spherical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. On this topic, a significant case study is described in this paper, dealing with the dynamic analysis of a spherical storage tank containing butane. The analyses are based on a detailed finite element (FE) model; moreover, a simplified single-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to the influence of sloshing effects and of the soil–structure interaction for which no special provisions are contained in technical codes for this reference case. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an “impulsive–convective” decomposition of the container-fluid motion is adopted for the calculation of the seismic force. With regard to the second point, considering that the tank is founded on piles, soil–structure interaction is taken into account by computing the dynamic impedances. Comparison between seismic action effects, obtained with and without consideration of sloshing and soil–structure interaction, shows a rather important influence of these parameters on the final results. Sloshing effects and soil–structure interaction can produce, for the case at hand, beneficial effects. For soil–structure interaction, this depends on the increase of the fundamental period and of the effective damping of the overall system, which leads to reduced design spectral values.

Motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Widespread approaches to generalizing geometrically linear constitutive relations to the case of large displacement gradients have been considered. These approaches are based on the replacement of the material derivatives of stress and strain tensors by frame-indifferent corotational or convective derivatives. The correctness of choosing the indifferent derivatives is analyzed from a more general viewpoint of motion decomposition into rigid and strain-induced motion. It is shown that the use of the Zaremba-Jaumann derivative in constitutive relations corresponds to motion decomposition by the Cauchy-Helmholtz theorem according to which instantaneous rigid rotation of a material particle with small neighborhood is described by the vorticity tensor. The relations derived with the use of the so-called "logarithmic spin" are analyzed. It is noted that the spin tensors entering into these relations are not associated with the material fibers (in particular with the symmetry axes of anisotropic materials) during the entire studied process of deformation. Hence these spins do not describe the rotation of the reference frame (crystallographic one for metals) in which the material property tensor is defined. A new method of motion decomposition is proposed on the basis of a two-level (macro and meso) approach for single and polycrystalline metals. The mesoscopic spin is determined by the rotation rate of the corotational coordinate system associated with the crystallographic direction and crystallographic plane. Mesoscopic constitutive relations are formulated using the proposed spin. The spin of a representative macrovolume is determined by averaging the spins of the crystallites contained in this volume. This spin is used to formulate rate-type elastic constitutive equations. Examples are given to illustrate the stress state determination for loading along closed strain paths and two-segment paths for isotropic and anisotropic (with cubic symmetry, hcp) elastic materials, and an elastoviscoplastic fcc crystallite. The determination is carried out by using the corotational derivatives in the constitutive relations which are obtained by different motion decomposition methods.

On motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites

The formulation of geometrically nonlinear boundary value problems is a necessary component in modeling real technological processes of thermomechanical material processing, wherein the main issues are the description of nonlinear kinematics and the formulation of constitutive relations. Most of the existing works do not explicitly consider the used method of motion decomposition that implies the extraction of the part responsible for quasi-rigid motion from the motion of a deformed solid. On our opinion, when choosing a method of motion decomposition and the corresponding corotational frame, the latter must be associated with the material to correctly describe the loading history and symmetry properties of the modeled body. Note that crystalline materials (including metals and alloys) at different scale levels are always anisotropic to a certain extent, and their properties can differ significantly in different directions. Even initially isotropic (at the level of the representative macrovolume) polycrystalline materials also become anisotropic under severe plastic deformation due to texturing. A multilevel approach allows the determination of symmetry elements (planes and axes of symmetry) at the crystallite level in metals, and we propose to relate these elements to the axes of the corotational frame that defines quasi-rigid motion. A new way of motion decomposition is proposed, namely, a multiplicative representation of the deformation gradient with an explicit extraction of the corotational frame motion. Elastoviscoplastic constitutive relations are formulated in terms of a stress free configuration. As the used stresses and strains are energetically conjugate, the requirements of no stress hysteresis and no energy dissipation in arbitrary closed elastic strain cycles are automatically satisfied, which is exemplified for anisotropic crystals. ©hus, an approach is proposed for the construction of geometrically nonlinear kinematic and constitutive relations for metal crystallites using a physically justified method of motion decomposition, with taking into account the symmetry properties of materials.

Renewal structure of the Brownian taut string

In a recent paper Lifshits and Setterqvist (2015), M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion w, defined as the function of minimal quadratic energy on [0,T] staying in a tube of fixed width h>0 around w. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time T.In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in terms of its h-extrema (as first introduced by Neveu and Pitman (1989)). Using this renewal structure, we derive an expression for the constant in the L.L.N. given in Lifshits and Setterqvist (2015) . In addition, we provide an invariance principle for the (renormalized) energy spent by the Brownian taut string.

Flow characterization of high-pressure dense-phase pneumatic conveying of coal powder using multi-scale signal analysis

Flow characterization of high-pressure dense-phase pneumatic conveying of coal powder is not fully understood. To further reveal the dynamic behavior of coal particles in dense-phase pneumatic conveying pipelines, a method for the scale decomposition of particle motion based on empirical mode decomposition and Hurst analysis of experimental electrostatic signals is reported. This allows the multi-scale motion characteristics of single coal particles and particle clusters to be determined. Micro-, meso-, and macro-scale subsets were reconstructed, which reflected the different behaviors of the coal particles: specifically, dynamic features of the micro-scale subset represented features of single particle collisions and frictional interactions; dual fractal characteristics of the meso-scale subset described the motion of coal particle clusters; and features of the macro-scale subset reflected persistent dynamic behavior of the entire pneumatic conveying system. Motion behavior of single particles and particle clusters could be respectively investigated by considering the relative energies of the micro- and meso-scale contributions to the electrostatic signal. This was verified both by theoretical analysis and experiment.

Cascade Synthesis of Electromechanical Tracking Systems with Respect to Restrictions on State Variables

The paper deals with electromechanical systems under uncertainties and incomplete measurements. A tracking problem for the given trajectories of generalized coordinates with the given accuracy is studied. For the solution of the problem two procedures of cascade synthesis with different local feedbacks and corrective actions of observers are developed: procedure 1 with standard linear feedbacks with high gains and procedure 2 with non-linear, S-shaped sigmoidal feedbacks. Linear controls are simple to implement, but it leads to a peak effect in the beginning of a transient response and at the sudden change of external disturbances. In the second procedure restrictions on the state variables are met. It is shown that properties, which are similar to the properties of systems with discontinuous controls operating in the sliding mode, are provided in the control and observation loops via smooth and bounded signals. The decomposition of the total motion on multi-rate components and invariance with respect to disturbances with the given accuracy are provided. For these procedures the simulation results are presented.

Motion sketch based crowd video retrieval

Crowd video retrieval with desired motion flow segmentation is an important problem in surveillance video management, e.g., video indexing and browsing, especially in the age of big data. In this paper, we address this issue from the motion-level perspective by using hand-drawn sketches as queries. Motion sketch based crowd video retrieval naturally suffers from challenges in crowd motion representation and similarity measurement. To tackle them, we propose to (1) leverage the motion structure coding algorithm for motion-level video indexing and hand-drawn sketch representation and (2) exploit distance metric fusion strategy incorporated with Ranking SVM for measuring the relevant degree between a sketch query and crowd videos. Specifically, for video indexing, motion decomposition is utilized to separate sub-motion vector fields with typical patterns from a set of optical flows. Then, the motion-level descriptors of the vector fields are computed and stored in an index database. To represent motion sketches, we propose a mechanism by vectorizing the sketches followed by motion structure coding. In the retrieval stage, we first compute the pairwise distance with different metrics between a new sketch query and crowd videos, and then stack them into a feature vector as the input of the Ranking SVM algorithm. Finally, we use the learned retrieval model to predict the ranking score of each crowd video in the database. Experimental results on the publicly available crowd datasets show the robustness and effectiveness of the proposed sketch based crowd video retrieval system.

Crowd Behavior Analysis via Curl and Divergence of Motion Trajectories

In the field of crowd behavior analysis, existing methods mainly focus on using local representations inspired by models found in other disciplines (e.g., fluid dynamics and social dynamics) to describe motion patterns. However, less attention is paid to exploiting motion structures (e.g., visual information contained in trajectories) for behavior analysis. In this paper, we consider both local characteristics and global structures of a motion vector field, and propose the Curl and Divergence of motion Trajectories (CDT) descriptors to describe collective motion patterns. To this end, a trajectory-based motion coding algorithm is designed to extract the CDT descriptors. For each motion vector field we construct its conjugate field, in which each vector is perpendicular to the counterpart in the original vector field. The trajectories in the motion and corresponding conjugate fields indicate the tangential and radial motion structures, respectively. By integrating curl (and divergence, respectively) along the tangential paths (and the radial paths, respectively), the CDT descriptors are extracted. We show that the proposed motion descriptors are scale- and rotation-invariant for effective crowd behavior analysis. For concreteness, we apply the CDT descriptors to identify five typical crowd behaviors (lane, clockwise arch, counterclockwise arch, bottleneck and fountainhead) with a pipeline including motion decomposition. Extensive experimental results on two benchmark datasets demonstrate the effectiveness of the CDT descriptors for describing and classifying crowd behaviors.

МНОГОУРОВНЕВЫЕ МОДЕЛИ ПОЛИКРИСТАЛЛИЧЕСКИХ МЕТАЛЛОВ: СОПОСТАВЛЕНИЕ ОПРЕДЕЛЯЮЩИХ СООТНОШЕНИЙ ДЛЯ КРИСТАЛЛИТОВ

Different formulations of geometrically nonlinear elasticviscoplastic constitutive relations for the mesolevel (the level of an individual crystallite), which are a key element of multilevel models of polycrystalline met als and alloys, are given and compared; various elastic relationships are used to determine the stresses. The most popular relations in finite form in the unloaded configuration, the relations in finite form using the motion decomposition with an explicit separation of the moving coordinate system motion, equivalent to the last constitutive relations in the rate form, as well as their linear approximation, and the relations in the rate form in the current configuration are considered. The estimations are given showing the equivalence or proximity of the stresses determined in the considered formulations with the same kinematic impacts. The results of numerical calculations carried out for randomly chosen kinematic impacts confirm the above conclusions about the similarity of mesolevel model formulations. It is noted that the formulation using the motion decomposition with an explicit separation of the moving coordinate system motion allows theoretically justified to go to the close formulation in the rate form in the current configuration, which is preferable for the numerical solution of boundary value problems with varying contact conditions (necessary for modeling of thermomechanical processing technological processes). Keywords: multilevel models of polycrystals, large deformations, constitutive relations, internal variables, elastoviscoplasticity.