Trajectory-based Methods Research Articles

Saliency-based foreground trajectory extraction using multiscale hybrid masks for action recognition

Action recognition in realistic scenes is a challenging task in the field of computer vision. Although trajectory-based methods have demonstrated promising performance, background trajectories cannot be filtered out effectively, which leads to a reduction in the ratio of valid trajectories. To address this issue, we propose a saliency-based sampling strategy named foreground trajectories on multiscale hybrid masks (HM-FTs). First, the motion boundary images of each frame are calculated to derive the initial masks. According to the characteristics of action videos, image priors and the synchronous updating mechanism based on cellular automata are exploited to generate an optimized weak saliency map, which will be integrated with a strong saliency map obtained via the multiple kernels boosting algorithm. Then, multiscale hybrid masks are achieved through the collaborative optimization strategy and masks intersection. The compensation schemes are designed to extract a set of foreground trajectories that are closely related to human actions. Finally, a hybrid fusion framework for combining trajectory features and pose features is constructed to enhance the recognition performance. The experimental results on two benchmark datasets demonstrate that the proposed method is effective and improves upon most of the state-of-the-art algorithms.

A novel trajectory planning-based adaptive control method for 3-D overhead cranes

ABSTRACT A three-dimensional (3-D) overhead crane is a complicated nonlinear underactuated mechanical system, for which high-speed positioning and anti-sway control are the kernel objective. Existing trajectory-based methods for 3-D overhead cranes focus on combining efficient and smooth trajectories with anti-sway tracking controllers without regard for payload motion; moreover, the exact value of plant parameters is required for accurate compensation during the control process. Motivated by these facts, we present a two-step design tracking strategy which consists of a trajectory planning stage and an adaptive tracking control design stage for 3-D overhead cranes. As shown by Lyapunov techniques and Barbalat's Lemma, the proposed controller guarantees asymptotic swing elimination and trolley positioning result in the presence of system uncertainties including unknown parameters and external disturbances. Simulation results also showed the applicability of the proposed method with good robustness against parameter uncertainties and external disturbances.

Disk-Based Indexing of Recent Trajectories

The plethora of location-aware devices has led to countless location-based services in which huge amounts of spatiotemporal data get created every day. Several applications require efficient processing of queries on the locations of moving objects over time, i.e., the moving object trajectories. This calls for efficient trajectory-based indexing methods that capture both the spatial and temporal dimensions of the data in a way that minimizes the number of disk I/Os required for both updating and querying. Most existing spatiotemporal index structures capture either the current locations of the moving objects or the entire history of the moving objects. Historical spatiotemporal indexing methods require multiple disk I/Os to process new updates and use a discrete trajectory representation that may result in incomplete query results. In this article, we introduce the trails-tree, a disk-based data structure for indexing recent trajectories. The trails-tree requires half the number of disk I/Os needed by other historical spatiotemporal indexing methods for the insertion and querying operations. We give a detailed description of the trails-tree, and we mathematically analyze its performance. Moreover, we present a novel query processing algorithm that ensures the completeness of the query result set. We experimentally verify the performance of the trails-tree using various real and synthetic datasets.

Computation of the S1 ← S0 Vibronic Absorption Spectrum of Formaldehyde by Variational Gaussian Wavepacket and Semiclassical IVR Methods.

The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S1(1 A2) ← S0(1 A1) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman ( J. Am. Chem. Soc. 2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman-Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼105 trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10-100 cm-1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.

Temporal segmentation and recognition of team activities in sports

A method for temporal segmentation and recognition of team activities in sports, based on a new activity feature extraction, is presented. Given the positions of team players from a plan view of the playground at any given time, we generate a smooth distribution on the whole playground, termed the position distribution of the team. Computing the position distribution for each frame provides a sequence of distributions, which we process to extract motion features for activity recognition. We can classify six different team activities in European handball and eight different team activities in field hockey datasets. The field hockey dataset is a new, large and challenging dataset that is presented for the first time for continuous segmentation of team activities. Our approach is different from other trajectory-based methods. These methods extract activity features using the explicitly defined trajectories, where the players have specific positions. In our work, given the specific positions of the team players at a frame, we construct a position distribution for the team on the whole playground and process the sequence of position distribution images to extract activity features. Extensive evaluation and results show that our approach is effective.

Importance sampling large deviations in nonequilibrium steady states. I.

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

Quasi-classical approaches to vibronic spectra revisited.

The framework to approach quasi-classical dynamics in the electronic ground state is well established and is based on the Kubo-transformed time correlation function (TCF), being the most classical-like quantum TCF. Here we discuss whether the choice of the Kubo-transformed TCF as a starting point for simulating vibronic spectra is as unambiguous as it is for vibrational ones. Employing imaginary-time path integral techniques in combination with the interaction representation allowed us to formulate a method for simulating vibronic spectra in the adiabatic regime that takes nuclear quantum effects and dynamics on multiple potential energy surfaces into account. Further, a generalized quantum TCF is proposed that contains many well-established TCFs, including the Kubo one, as particular cases. Importantly, it also provides a framework to construct new quantum TCFs. Applying the developed methodology to the generalized TCF leads to a plethora of simulation protocols, which are based on the well-known TCFs as well as on new ones. Their performance is investigated on 1D anharmonic model systems at finite temperatures. It is shown that the protocols based on the new TCFs may lead to superior results with respect to those based on the common ones. The strategies to find the optimal approach are discussed.

Hierarchical Decentralized Control of a 5-Link Biped Robot

Most of the biped robots are controlled using pre-computed trajectories methods or methods based on the multibody dynamics models. The pre-computed trajectory based methods are simple but the system gets highly vulnerable to the external disturbances. In contrast, the dynamically based methods make the system acts faster, but they need extensive knowledge about the kinematics and dynamics of the system. This fact gave rise to the main purpose of this study, i.e., developing a controller for a biped robot to take advantages of the simplicity and computational eciency of trajectory-based methods and the robustness of the dynamic-based approach. To do so, this paper presents a twolayer hierarchical control framework for an under-actuated, planar, 5-link biped robot model. The upper layer contains a centralized dynamic-based controller and uses all system sensory data to generate stable walking. The lower layer in this structure is a decentralized trajectory-based controller network which learns to control the system based on the upper layer controller output. Whenthe lower controller fails to control the system, upper layer controller takes action and makes the system stable. Then, when the lower layer controller gets ready, the control of the system will be handed to this layer.

Toward Abnormal Trajectory and Event Detection in Video Surveillance

In this paper, we present a unified approach for abnormal behavior detection and group behavior analysis in video scenes. Existing approaches for abnormal behavior detection do either use trajectory-based or pixel-based methods. Unlike these approaches, we propose an integrated pipeline that incorporates the output of object trajectory analysis and pixel-based analysis for abnormal behavior inference. This enables to detect abnormal behaviors related to speed and direction of object trajectories, as well as complex behaviors related to finer motion of each object. By applying our approach on three different data sets, we show that our approach is able to detect several types of abnormal group behaviors with less number of false alarms compared with existing approaches.

Quantum trajectory simulation for nonadiabatic molecular dynamics

The mixed quantum-classical (MQC) molecular dynamics (MD) approaches are extremely important in practice since, with the increase of atomic degrees of freedom, a full quantum mechanical evaluation for molecular dynamics would quickly become intractable. Moreover, in some cases, the nonadiabatic effects are of crucial importance in the proximity of conical intersection of potential energy surfaces (PESs), where the energy separation between different PESs becomes comparable to the nonadiabatic coupling. In the past decades, there has been great interest in developing and improving various nonadiabatic MQC-MD protocols. The widely known nonadiabatic MD proposals include the so-called Ehrenfest or time-dependent-Hartree mean-field approach, the trajectory surface-hopping method, and their mixed scheme. Among the trajectory-based surface hopping methods, the most popular one is Tully's fewest switches surface hopping approach. In this approach, the nonadiabatic dynamics is treated by allowing hops from one PES to another, with the hopping probability determined by a certain artificial hopping algorithm. In our present work, we extend the study of a recent work on the nonadiabatic MQC-MD scheme, which is based on a view that the nonadiabatic MQC-MD actually implies an effective quantum measurement on the electronic states by the classical motion of atoms. The new protocol, say, the quantum trajectory (QT) approach, provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also connects two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. In our present study, we implement further the QT approach to simulate several typical potential-surface models, i.e., including the single avoided crossing, dual avoided crossing, extended coupling, dumbbell and double arch potentials. In particular, we simulate and compare three decoherence rates, which are from different physical considerations, i.e., the frozen Gaussian approximation, energy discrimination and force discrimination. We also design simulation algorithms to properly account for the energy conservation and force direction change associated with the surface hopping. In most cases, we find that the QT results are in good agreement with those from the full quantum dynamics, which is insensitive to the specific form of the decoherence rate. But for the model involving strong quantum interference, like other nonadiabatic MQC-MD schemes, the QT approach cannot give desirable results. Developing better method should be useful for future investigations in this research area.

Reaction Coordinates and Mechanistic Hypothesis Tests.

Reaction coordinates are integral to several classic rate theories that can (a) predict kinetic trends across conditions and homologous reactions, (b) extract activation parameters with a clear physical interpretation from experimental rates, and (c) enable efficient calculations of free energy barriers and rates. New trajectory-based rare events methods can provide rates directly from dynamical trajectories without a reaction coordinate. Trajectory-based frameworks can also generate ideal (but abstract) reaction coordinates such as committors and eigenfunctions of the master equation. However, rates and mechanistic insights obtained from trajectory-based methods and abstract coordinates are not readily generalized across simulation conditions or reaction families. We discuss methods for identifying physically meaningful reaction coordinates, including committor analysis, variational transition state theory, Kramers-Langer-Berezhkovskii-Szabo theory, and statistical inference methods that can use path sampling data to screen, mix, and optimize thousands of trial coordinates. Special focus is given to likelihood maximization and inertial likelihood maximization approaches.

Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids.

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW(23.15) or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S(trip), is also studied. S(trip) is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (T(thr)). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.

Trajectory-based methods in clinical psychology: A person centred narrative approach

Abstract Life trajectories in clinical psychology research are often not treated as interactive trajectories but rather as static transversal variables. But developmental pathways are often cumulative and conditional and currently require sophisticated group-based modeling to tease out individual differences in trajectories. Clinical psychologists often require personal information on transitions and turning points in life which require eliciting information through qualitative life history approaches. A method is proposed for identifying life events within the person's narrative and describing trajectories as event spaces likely to reflect end-point psychopathology.

Newton Method and Trajectory-Based Method for Solving Power Flow Problems: Nonlinear Studies

This paper analyzes the convergence properties and convergence region of a class of trajectory-based power flow methods. The convergence region of the trajectory-based method is a connected set and possesses the near-by property. The convergence region of Newton method and trajectory-based method in solving power flow problems are numerically investigated. Since the convergence region of trajectory-based method corresponds to the stability region of the nonlinear dynamic system, the stability regions of two dynamic systems are computed. The numerical results indicate that the stability region of the dynamic system possesses better geometry features than the convergence region of Newton method. These properties make the trajectory-based power flow method robust, especially on heavy loading conditions.

Common features of extraordinary rate theories.

We examine the capabilities and foundations of three landmark rate theories: harmonic transition state theory, classical nucleation theory, and the Marcus theory of electron transfer. Each of the three classic rate theories is widely used to predict rates and trends. They are also used "in reverse" to interpret experimental data with no computation at all. Their common foundations include a quasi-equilibrium assumption and dimensionality reduction to a physically meaningful, one-dimensional, and broadly applicable reaction coordinate. Many applications lie beyond the scope of the classic theories, so rare events research has pursued trajectory-based methods that efficiently predict accurate rate constants even when the reaction coordinate and mechanistic details are unknown. Trajectory based rare events methods achieved these ambitious goals, but (by construction) they provide rates rather than mechanistic understanding. We briefly discuss recent efforts to identify reaction coordinates, including methods which provide abstract statistically defined coordinates and those which identify physical collective variables. Finally, we note some natural synergies between existing simulation methods which might help discover simple and powerful quasi-equilibrium theories for the many applications that fall beyond the scope of the classic rate theories.

Conditional Born-Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine.

We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born-Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically.

Parameter Identification of BLDC Motor Model Via Metaheuristic Optimization Techniques

The brushless dc (BLDC) motor has been increasingly used in industrial automation, automotive, aerospace, instrumentation and appliances. Analysis and design of the BLDC motor efficiently require its accurate model and parameters. In this paper, the parameter identification of the BLDC motor model via well-known metaheuristic optimization search techniques is proposed. Two trajectory-based methods, i.e. adaptive tabu search (ATS) and intensified current search (ICS) are employed to estimate the BLDC motor parameters. As simulation results of model identification and validation, both ATS and ICS can provide optimal BLDC model parameters. The BLDC models obtained show a very good agreement to actual system dynamics. However, the ICS can pro-vide optimal model parameters faster than the ATS.

Metaheuristic Algorithms Applied to Bioenergy Supply Chain Problems: Theory, Review, Challenges, and Future

Bioenergy is a new source of energy that accounts for a substantial portion of the renewable energy production in many countries. The production of bioenergy is expected to increase due to its unique advantages, such as no harmful emissions and abundance. Supply-related problems are the main obstacles precluding the increase of use of biomass (which is bulky and has low energy density) to produce bioenergy. To overcome this challenge, large-scale optimization models are needed to be solved to enable decision makers to plan, design, and manage bioenergy supply chains. Therefore, the use of effective optimization approaches is of great importance. The traditional mathematical methods (such as linear, integer, and mixed-integer programming) frequently fail to find optimal solutions for non-convex and/or large-scale models whereas metaheuristics are efficient approaches for finding near-optimal solutions that use less computational resources. This paper presents a comprehensive review by studying and analyzing the application of metaheuristics to solve bioenergy supply chain models as well as the exclusive challenges of the mathematical problems applied in the bioenergy supply chain field. The reviewed metaheuristics include: (1) population approaches, such as ant colony optimization (ACO), the genetic algorithm (GA), particle swarm optimization (PSO), and bee colony algorithm (BCA); and (2) trajectory approaches, such as the tabu search (TS) and simulated annealing (SA). Based on the outcomes of this literature review, the integrated design and planning of bioenergy supply chains problem has been solved primarily by implementing the GA. The production process optimization was addressed primarily by using both the GA and PSO. The supply chain network design problem was treated by utilizing the GA and ACO. The truck and task scheduling problem was solved using the SA and the TS, where the trajectory-based methods proved to outperform the population-based methods.

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory.

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.