The Experts below are selected from a list of 189 Experts worldwide ranked by ideXlab platform
Weihua Deng - One of the best experts on this subject based on the ideXlab platform.
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Error Estimates for Backward Fractional Feynman–Kac Equation with Non-Smooth Initial Data
Journal of Scientific Computing, 2020Co-Authors: Jing Sun, Daxin Nie, Weihua DengAbstract:In this paper, we are concerned with the numerical solution for the backward fractional Feynman–Kac equation with non-smooth initial data. Here we first provide the regularity estimate of the solution. And then we use the backward Euler and second-order backward difference convolution quadratures to approximate the Riemann–Liouville fractional Substantial Derivative and get the first- and second-order convergence in time. The finite element method is used to discretize the Laplace operator with the optimal convergence rates. Compared with the previous works for the backward fractional Feynman–Kac equation, the main advantage of the current discretization is that we don’t need the assumption on the regularity of the solution in temporal and spatial directions. Moreover, the error estimates of the time semi-discrete schemes and the fully discrete schemes are also provided. Finally, we perform the numerical experiments to verify the effectiveness of the presented algorithms.
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Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes
Journal of Scientific Computing, 2019Co-Authors: Daxin Nie, Jing Sun, Weihua DengAbstract:This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both reaction and diffusion [Hou and Deng, J. Phys. A: Math. Theor., {\bf51}, 155001 (2018)]. Numerically solving the equation with the time tempered fractional Substantial Derivative and tempered fractional Laplacian consists in discretizing these two non-local operators. Here, using convolution quadrature, we provide a first-order and second-order schemes for discretizing the time tempered fractional Substantial Derivative, which doesn't require the assumption of the regularity of the solution in time; we use the finite difference method to approximate the two-dimensional tempered fractional Laplacian, and the accuracy of the scheme depends on the regularity of the solution on $\bar{\Omega}$ rather than the whole space. Lastly, we verify the predicted convergence orders and the effectiveness of the presented schemes by numerical examples.
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High Order Algorithm for the Time-Tempered Fractional Feynman–Kac Equation
Journal of Scientific Computing, 2018Co-Authors: Minghua Chen, Weihua DengAbstract:We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in Wu et al. (Phys Rev E 93:032151, 2016), being called the time-tempered fractional Feynman–Kac equation named after Richard Feynman and Mark Kac who first considered the model describing the functional distribution of normal motion. The key step of designing the algorithms is to discretize the time tempered fractional Substantial Derivative, being defined as $$\begin{aligned} {^S\!}D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t)\!=\!D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t)\!-\!\lambda ^\gamma G(x,p,t) \end{aligned}$$ with \(\widetilde{\lambda }=\lambda + pU(x),\, p=\rho +J\eta ,\, J=\sqrt{-1}\), where $$\begin{aligned} D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t) =\frac{1}{\varGamma (1-\gamma )} \left[ \frac{\partial }{\partial t}+\widetilde{\lambda } \right] \int _{0}^t{\left( t-z\right) ^{-\gamma }}e^{-\widetilde{\lambda }\cdot (t-z)}{G(x,p,z)}dz, \end{aligned}$$ and \(\lambda \ge 0\), \(0 0\), and \(\eta \) is a real number. The designed schemes are unconditionally stable and have the global truncation error \(\mathscr {O}(\tau ^2+h^2)\), being theoretically proved and numerically verified in complex space. Moreover, some simulations for the distributions of the first passage time are performed, and the second order convergence is also obtained for solving the ‘physical’ equation (without artificial source term).
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Numerical schemes of the time tempered fractional FeynmanKac equation
Computers & Mathematics with Applications, 2017Co-Authors: Weihua Deng, Z.j. ZhangAbstract:This paper focuses on providing the computation methods for the backward time tempered fractional FeynmanKac equation, being one of the models recently proposed in Wu etal. (2016). The discretization for the tempered fractional Substantial Derivative is derived, and the corresponding finite difference and finite element schemes are designed with well established stability and convergence. The performed numerical experiments show the effectiveness of the presented schemes.
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High order algorithm for the time-tempered fractional Feynman-Kac equation
arXiv: Numerical Analysis, 2016Co-Authors: Minghua Chen, Weihua DengAbstract:We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu, Deng, and Barkai, Phys. Rev. E., 84 (2016), 032151], being called the time-tempered fractional Feynman-Kac equation. The key step of designing the algorithms is to discretize the time tempered fractional Substantial Derivative, being defined as $${^S\!}D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)\!=\!D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)\!-\!\lambda^\gamma G(x,p,t) ~{\rm with}~\widetilde{\lambda}=\lambda+ pU(x),\, p=\rho+J\eta,\, J=\sqrt{-1},$$ where $$D_t^{\gamma,\widetilde{\lambda}} G(x,p,t) =\frac{1}{\Gamma(1-\gamma)} \left[\frac{\partial}{\partial t}+\widetilde{\lambda} \right] \int_{0}^t{\left(t-z\right)^{-\gamma}}e^{-\widetilde{\lambda}\cdot(t-z)}{G(x,p,z)}dz,$$ and $\lambda \ge 0$, $0 0$, and $\eta$ is a real number. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being theoretically proved and numerically verified in {\em complex} space. Moreover, some simulations for the distributions of the first passage time are performed, and the second order convergence is also obtained for solving the `physical' equation (without artificial source term).
Yutaka Asako - One of the best experts on this subject based on the ideXlab platform.
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Numerical analysis of irreversible processes in a piston-cylinder system using LB1S turbulence model
International Journal of Heat and Mass Transfer, 2019Co-Authors: Siti Nurul Akmal Yusof, Yutaka Asako, Mohammad Faghri, Nor Azwadi Che Sidik, Wan Mohd Arif Aziz JaparAbstract:Abstract A numerical analysis for the irreversible processes in an adiabatic piston-cylinder system was conducted using the Lam & Bremhorst low Reynolds number turbulence model (LB1) modified for compressible flows by Sarkar and Balakrishnan (LB1S model). Two-dimensional compressible momentum equation and energy equation which includes the Substantial Derivative of pressure and the viscous dissipation terms were solved numerically to obtain the state quantities of the system. The computations were performed for a single compression process with constant piston velocity, u p = - 10 m/s and for cyclic compression and expansion processes with sinusoidal velocity variation. The selected rotation speed ranges from 1000 to 50,000 rpm. The computations were performed for 10 cycles. It was found that the sinusoidal piston velocities have effects on the state quantities of the piston-cylinder system and it experienced an irreversible process when the piston moved with a finite velocity. For the case of single compression process, the flow was laminar when the piston velocity was below 10 m/s. In the cyclic processes, the flow was turbulent when the rotation speed is in the range from 2000 to 50,000 rpm. However, for the case of 2000 rpm, the flow was laminar only at the first cycle. This is due to the turbulent viscosity that is lower than dynamic viscosity ( 1.862 × 10 - 5 Pa s). It was found increasing the rotation speed will increase the value of the turbulent viscosity. In the cyclic processes for the cases N = 1000, 10,000 and 50,000 rpm, the internal energy increased by 0.003%, 0.028% and 0.289% of the compression work in each cycle, respectively.
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on temperature jump condition for turbulent slip flow in a quasi fully developed region of micro channel with constant wall temperature
International Journal of Thermal Sciences, 2019Co-Authors: Yutaka Asako, Shye Yunn Heng, Chungpyo HongAbstract:Abstract Temperature variation of turbulent slip flows in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the Substantial Derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Karman. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a micro-tube with constant wall temperature when both viscous dissipation and Substantial Derivative of pressure terms are included in the energy equation. The total temperature in the quasi-fully developed region was lower than the wall temperature in the case of Kn ≥ 0.01.
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Energy equation of swirling flow in a cylindrical container
International Communications in Heat and Mass Transfer, 2019Co-Authors: Siti Nurul Akmal Yusof, Yutaka Asako, Mohammad Faghri, Nor Azwadi Che Sidik, Lit Ken Tan, Wan Mohd Arif Aziz JaparAbstract:Abstract The energy equation which includes the Substantial Derivative of pressure and the viscous dissipation terms was solved numerically to verify whether it can correctly calculate the energy conversion from kinetic to thermal energy in an irreversible process. The fluid temperature was obtained for a swirling flow in a cylindrical container with a constant initial angular velocity. The fluid in the container came to a halt after a short time because of the viscosity. The kinetic energy of the fluid was converted into thermal energy which resulted in an increase of the fluid temperature. The governing equations were discretized using the control volume based power-law scheme of Patankar and the discretized equations were solved by using a line-by-line method. The results showed that the kinetic energy at its initial state was converted into thermal energy with a conversion rate of 99.4%.
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On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature
Journal of Heat Transfer, 2017Co-Authors: Yutaka Asako, Chungpyo HongAbstract:The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and Substantial Derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and Substantial Derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.
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turbulent temperature profile in the quasi fully developed region of a micro tube
Journal of Thermal Science and Technology, 2017Co-Authors: Yutaka Asako, Chungpyo HongAbstract:Turbulent temperature profiles in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the Substantial Derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Karman. The temperature profiles were compared with the laminar flow and previous numerical solutions. The total temperature was higher than the wall temperature depending on the Mach number. The static temperature in the quasi-fully developed region agrees well with the temperature results for an ideal gas flow obtained by solving the Navier-Stokes and energy equations.
Chungpyo Hong - One of the best experts on this subject based on the ideXlab platform.
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on temperature jump condition for turbulent slip flow in a quasi fully developed region of micro channel with constant wall temperature
International Journal of Thermal Sciences, 2019Co-Authors: Yutaka Asako, Shye Yunn Heng, Chungpyo HongAbstract:Abstract Temperature variation of turbulent slip flows in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the Substantial Derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Karman. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a micro-tube with constant wall temperature when both viscous dissipation and Substantial Derivative of pressure terms are included in the energy equation. The total temperature in the quasi-fully developed region was lower than the wall temperature in the case of Kn ≥ 0.01.
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On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature
Journal of Heat Transfer, 2017Co-Authors: Yutaka Asako, Chungpyo HongAbstract:The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and Substantial Derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and Substantial Derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.
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turbulent temperature profile in the quasi fully developed region of a micro tube
Journal of Thermal Science and Technology, 2017Co-Authors: Yutaka Asako, Chungpyo HongAbstract:Turbulent temperature profiles in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the Substantial Derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Karman. The temperature profiles were compared with the laminar flow and previous numerical solutions. The total temperature was higher than the wall temperature depending on the Mach number. The static temperature in the quasi-fully developed region agrees well with the temperature results for an ideal gas flow obtained by solving the Navier-Stokes and energy equations.
Minghua Chen - One of the best experts on this subject based on the ideXlab platform.
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High Order Algorithm for the Time-Tempered Fractional Feynman–Kac Equation
Journal of Scientific Computing, 2018Co-Authors: Minghua Chen, Weihua DengAbstract:We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in Wu et al. (Phys Rev E 93:032151, 2016), being called the time-tempered fractional Feynman–Kac equation named after Richard Feynman and Mark Kac who first considered the model describing the functional distribution of normal motion. The key step of designing the algorithms is to discretize the time tempered fractional Substantial Derivative, being defined as $$\begin{aligned} {^S\!}D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t)\!=\!D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t)\!-\!\lambda ^\gamma G(x,p,t) \end{aligned}$$ with \(\widetilde{\lambda }=\lambda + pU(x),\, p=\rho +J\eta ,\, J=\sqrt{-1}\), where $$\begin{aligned} D_t^{\gamma ,\widetilde{\lambda }} G(x,p,t) =\frac{1}{\varGamma (1-\gamma )} \left[ \frac{\partial }{\partial t}+\widetilde{\lambda } \right] \int _{0}^t{\left( t-z\right) ^{-\gamma }}e^{-\widetilde{\lambda }\cdot (t-z)}{G(x,p,z)}dz, \end{aligned}$$ and \(\lambda \ge 0\), \(0 0\), and \(\eta \) is a real number. The designed schemes are unconditionally stable and have the global truncation error \(\mathscr {O}(\tau ^2+h^2)\), being theoretically proved and numerically verified in complex space. Moreover, some simulations for the distributions of the first passage time are performed, and the second order convergence is also obtained for solving the ‘physical’ equation (without artificial source term).
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High order algorithm for the time-tempered fractional Feynman-Kac equation
arXiv: Numerical Analysis, 2016Co-Authors: Minghua Chen, Weihua DengAbstract:We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu, Deng, and Barkai, Phys. Rev. E., 84 (2016), 032151], being called the time-tempered fractional Feynman-Kac equation. The key step of designing the algorithms is to discretize the time tempered fractional Substantial Derivative, being defined as $${^S\!}D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)\!=\!D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)\!-\!\lambda^\gamma G(x,p,t) ~{\rm with}~\widetilde{\lambda}=\lambda+ pU(x),\, p=\rho+J\eta,\, J=\sqrt{-1},$$ where $$D_t^{\gamma,\widetilde{\lambda}} G(x,p,t) =\frac{1}{\Gamma(1-\gamma)} \left[\frac{\partial}{\partial t}+\widetilde{\lambda} \right] \int_{0}^t{\left(t-z\right)^{-\gamma}}e^{-\widetilde{\lambda}\cdot(t-z)}{G(x,p,z)}dz,$$ and $\lambda \ge 0$, $0 0$, and $\eta$ is a real number. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being theoretically proved and numerically verified in {\em complex} space. Moreover, some simulations for the distributions of the first passage time are performed, and the second order convergence is also obtained for solving the `physical' equation (without artificial source term).
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High order algorithms for the fractional Substantial diffusion equation with truncated L\'evy flights
SIAM Journal on Scientific Computing, 2015Co-Authors: Minghua Chen, Weihua DengAbstract:The equation with the time fractional Substantial Derivative and space fractional Derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time random walk in unbounded domain and the L\'evy flights have divergent second order moments. However, in more practical problems, the physical domain is bounded and the involved observables have finite moments. Then the modified equation can be derived by tempering the probability of large jump length of the L\'evy flights and the corresponding tempered space fractional Derivative is introduced. This paper focuses on providing the high order algorithms for the modified equation, i.e., the equation with the time fractional Substantial Derivative and space tempered fractional Derivative. More concretely, the contributions of this paper are as follows: 1. the detailed numerical stability analysis and error estimates of the schemes with first order accuracy in time and second order in space are given in {\textsl{complex}} space, which is necessary since the inverse Fourier transform needs to be made for getting the distribution of the functionals after solving the equation; 2. we further propose the schemes with high order accuracy in both time and space, and the techniques of treating the issue of keeping the high order accuracy of the schemes for {\textsl{nonhomogeneous}} boundary/initial conditions are introduced; 3. the multigrid methods are effectively used to solve the obtained algebraic equations which still have the Toeplitz structure; 4. we perform extensive numerical experiments, including verifying the high convergence orders, simulating the physical system which needs to numerically make the inverse Fourier transform to the numerical solutions of the equation.
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discretized fractional Substantial calculus
Mathematical Modelling and Numerical Analysis, 2014Co-Authors: Minghua Chen, Weihua DengAbstract:This paper discusses the properties and the numerical discretizations of the fractional Substantial integral I-s(v) f(x) = 1/Gamma(v) integral(x)(a) (x-tau)(v-1)e(-sigma(x-tau)) f(tau)d tau, v>0, and the fractional Substantial Derivative D-s(mu) f(x) = D-s(m) [I-s(v) f(x)], v = m - mu, where D-s = partial Derivative/partial Derivative x + sigma, sigma can be a constant or a function not related to x, say sigma(y); and m is the smallest integer that exceeds mu. The Fourier transform method and fractional linear multistep method are used to analyze the properties or derive the discretized schemes. And the convergences of the presented discretized schemes with the global truncation error O(h(p)) (p = 1, 2, 3, 4, 5) are theoretically proved and numerically verified.
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Numerical algorithms for the forward and backward fractional Feynman-Kac equations
Journal of Scientific Computing, 2014Co-Authors: Weihua Deng, Minghua Chen, Eli BarkaiAbstract:The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schr\"{o}dinger equation in imaginary time. The functionals of no-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac equation [J. Stat. Phys. 141, 1071-1092, 2010], where the fractional Substantial Derivative is involved. Based on recently developed discretized schemes for fractional Substantial Derivatives [arXiv:1310.3086], this paper focuses on providing algorithms for numerically solving the forward and backward fractional Feynman-Kac equations; since the fractional Substantial Derivative is non-local time-space coupled operator, new challenges are introduced comparing with the general fractional Derivative. Two ways (finite difference and finite element) of discretizing the space Derivative are considered. For the backward fractional Feynman-Kac equation, the numerical stability and convergence of the algorithms with first order accuracy are theoretically discussed; and the optimal estimates are obtained. For all the provided schemes, including the first order and high order ones, of both forward and backward Feynman-Kac equations, extensive numerical experiments are performed to show their effectiveness.
Vittorio Murino - One of the best experts on this subject based on the ideXlab platform.
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Group and Crowd Behavior for Computer Vision - Physics-Inspired Models for Detecting Abnormal Behaviors in Crowded Scenes
Group and Crowd Behavior for Computer Vision, 2017Co-Authors: Sadegh Mohammadi, Alessandro Perina, Hamed Kiani Galoogahi, Vittorio MurinoAbstract:Crowd scene analysis has recently attracted intense attention from the vision community due to its crucial role for a wide range of surveillance applications such as crowd flow segmentation, detecting and tracking people in crowds, and analyzing their behaviors. Recently, there has been significant research effort dedicated to the development of automated computer vision techniques, intended to enhance safety of our societies by monitoring human behaviors and their actions in crowd situations. Among the several proposed methods, physics-based approaches have shown very promising performance. The most notable example in this regard is the Social Force Model which was initially deployed in computer vision to detect abnormal behaviors in crowd videos. Particularly, the SFM approach and its variation exploited physical concepts such as motion equations, repulsive and attractive forces to describe pedestrian interactions and their motion patterns in crowd situations. Inspired by the success of the SFM, several physics-based models have been proposed to describe motions within a scene by the means of physics equations. These descriptors along with machine learning techniques have been widely applied to analyze crowd behaviors for detecting abnormal behaviors, or in some cases recognizing different types of crowd anomalies such as riot, violence, or panic. The main goal of this chapter is to give an overall review of current physics-based models in the vision literature designed to analyze crowd behaviors. Moreover, we will inspect the application of Substantial Derivative, borrowed from fluid mechanics, to detect violent actions in crowd scenarios. Unlike previous physics-based approaches that are only based on motion over the temporal domain, Substantial Derivative is able to capture motion information both in spatial and temporal domains simultaneously. More specifically, this new framework captures motion patterns at the spatial and temporal domains which we refer as convective and local accelerations, respectively. After estimating the convective and local fields from optical flow, following the previous standard frameworks, this method employs the standard Bag-of-Words (BoW) technique to separately encode the motion information of each field in the histogram form. We extended the experiments in the original paper with additional evaluations comparing with the prior physics-based techniques on several challenging datasets, showing the superiority of this method compared to the state-of-the-art methods.
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Violence detection in crowded scenes using Substantial Derivative
2015 12th IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), 2015Co-Authors: Sadegh Mohammadi, Hamed Kiani, Alessandro Perina, Vittorio MurinoAbstract:This paper presents a novel video descriptor based on Substantial Derivative, an important concept in fluid mechanics, that captures the rate of change of a fluid property as it travels through a velocity field. Unlike standard approaches that only use temporal motion information, our descriptor exploits the spatio-temporal characteristic of Substantial Derivative. In particular, the spatial and temporal motion patterns are captured by respectively the convective and local accelerations. After estimating the convective and local field from the optic flow, we followed the standard bag-of-word procedure for each motion pattern separately, and we concatenated the two resulting histograms to form the final descriptor. We extensively evaluated the effectiveness of the proposed method on five benchmarks, including three standard datasets (Violence in Movies, Violence In Crowd, and BEHAVE), and two new video-survelliance sequences downloaded from Youtube. Our experiments show how the proposed approach sets the new state-of-the-art on all benchmarks and how the structural information captured by convective acceleration is essential to detect violent episodes in crowded scenarios.
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AVSS - Violence detection in crowded scenes using Substantial Derivative
2015 12th IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), 2015Co-Authors: Sadegh Mohammadi, Hamed Kiani, Alessandro Perina, Vittorio MurinoAbstract:This paper presents a novel video descriptor based on Substantial Derivative, an important concept in fluid mechanics, that captures the rate of change of a fluid property as it travels through a velocity field. Unlike standard approaches that only use temporal motion information, our descriptor exploits the spatio-temporal characteristic of Substantial Derivative. In particular, the spatial and temporal motion patterns are captured by respectively the convective and local accelerations. After estimating the convective and local field from the optic flow, we followed the standard bag-of-word procedure for each motion pattern separately, and we concatenated the two resulting histograms to form the final descriptor. We extensively evaluated the effectiveness of the proposed method on five benchmarks, including three standard datasets (Violence in Movies, Violence In Crowd, and BEHAVE), and two new video-survelliance sequences downloaded from Youtube. Our experiments show how the proposed approach sets the new state-of-the-art on all benchmarks and how the structural information captured by convective acceleration is essential to detect violent episodes in crowded scenarios.
