In this paper, we tackle the problem of video alignment, the process of matching the frames of a pair of videos containing similar actions. The main challenge in video alignment is that accurate correspondence should be established despite the differences in the execution processes and appearances between the two videos. We introduce an unsupervised method for alignment that uses global and local features of the frames. In particular, we introduce effective features for each video frame using three machine vision tools: person detection, pose estimation, and VGG network. Then, the features are processed and combined to construct a multidimensional time series that represents the video. The resulting time series are used to align videos of the same actions using a novel version of dynamic time warping named Diagonalized Dynamic Time Warping(DDTW). The main advantage of our approach is that no training is required, which makes it applicable for any new type of action without any need to collect training samples for it. For evaluation, we considered video synchronization and phase classification tasks on the Penn action dataset. Also, for an effective evaluation of the video synchronization task, we present a new metric called Enclosed Area Error(EAE). The results show that our method outperforms previous state-of-the-art methods, such as TCC, and other self-supervised and weakly supervised methods.
相關內容
Processing 是一門開源編程語言和與之配套的集成開發環境（IDE）的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎，并運用于大量的新媒體和互動藝術作品中。
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.
In this paper, we propose a computational interpretation of the generalized Kreisel-Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry-Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for the intuitionistic propositional logic. This will guide our process of formulating an appropriate program that would capture the corresponding computational content of the typed Split rule. In other words, we want to find an appropriate selector function for the Split rule by considering its typed variant. Our investigation can also be reframed as an effort to answer the following questions: is the Split rule constructively valid in the sense of BHK semantics? Our answer is positive for the Split rule as well as for its newly proposed generalized version called the S rule.
In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual Element Method (SH-VEM). In this method, the Hellinger$-$Reissner variational principle is adopted, wherein both the equilibrium equations and the strain-displacement relations are variationally enforced. We consider small-strain deformations of linear elastic solids in the compressible and near-incompressible regimes over quadrilateral (convex and nonconvex) meshes. Within an element, the displacement field is approximated as a linear combination of canonical shape functions that are $\textit{virtual}$. The stress field, similar to the stress-hybrid finite element method of Pian and Sumihara, is represented using a linear combination of symmetric tensor polynomials. A 5-parameter expansion of the stress field is used in each element, with stress transformation equations applied on distorted quadrilaterals. In the variational statement of the strain-displacement relations, the divergence theorem is invoked to express the stress coefficients in terms of the nodal displacements. This results in a formulation with solely the nodal displacements as unknowns. Numerical results are presented for several benchmark problems from linear elasticity. We show that SH-VEM is free of volumetric and shear locking, and it converges optimally in the $L^2$ norm and energy seminorm of the displacement field, and in the $L^2$ norm of the hydrostatic stress.
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach employs classical neural network architectures and supervised learning, but it is constructed in such a way that the resulting Reduced Order Model (ROM) is guaranteed to satisfy the linear constraints exactly. The procedure is based on a splitting of the PDE solution into a particular solution satisfying the constraint and a homogenous solution. The homogeneous solution is approximated by mapping a suitable potential function, generated by a neural network model, onto the kernel of the constraint operator; for the particular solution, instead, we propose an efficient spanning tree algorithm. Starting from this paradigm, we present three approaches that follow this methodology, obtained by exploring different choices of the potential spaces: from empirical ones, derived via Proper Orthogonal Decomposition (POD), to more abstract ones based on differential complexes. All proposed approaches combine computational efficiency with rigorous mathematical interpretation, thus guaranteeing the explainability of the model outputs. To demonstrate the efficacy of the proposed strategies and to emphasize their advantages over vanilla black-box approaches, we present a series of numerical experiments on fluid flows in porous media, ranging from mixed-dimensional problems to nonlinear systems. This research lays the foundation for further exploration and development in the realm of model order reduction, potentially unlocking new capabilities and solutions in computational geosciences and beyond.
In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs), including additive, diagonal and scalar noise types. The central idea is to view the splitting method as a replacement of the driving signal of an SDE, namely Brownian motion and time, with a piecewise linear path that yields a sequence of ODEs $-$ which can be discretised to produce a numerical scheme. This new way of understanding splitting methods is inspired by, but does not use, rough path theory. We show that when the driving piecewise linear path matches certain iterated stochastic integrals of Brownian motion, then a high order splitting method can be obtained. We propose a general proof methodology for establishing the strong convergence of these approximations that is akin to the general framework of Milstein and Tretyakov. That is, once local error estimates are obtained for the splitting method, then a global rate of convergence follows. This approach can then be readily applied in future research on SDE splitting methods. By incorporating recently developed approximations for iterated integrals of Brownian motion into these piecewise linear paths, we propose several high order splitting methods for SDEs satisfying a certain commutativity condition. In our experiments, which include the Cox-Ingersoll-Ross model and additive noise SDEs (noisy anharmonic oscillator, stochastic FitzHugh-Nagumo model, underdamped Langevin dynamics), the new splitting methods exhibit convergence rates of $O(h^{3/2})$ and outperform schemes previously proposed in the literature.
In this paper, a machine learning-based decentralized time division multiple access (TDMA) algorithm for visible light communication (VLC) Internet of Things (IoT) networks is proposed. The proposed algorithm is based on Q-learning, a reinforcement learning algorithm. This paper considers a decentralized condition in which there is no coordinator node for sending synchronization frames and assigning transmission time slots to other nodes. The proposed algorithm uses a decentralized manner for synchronization, and each node uses the Q-learning algorithm to find the optimal transmission time slot for sending data without collisions. The proposed algorithm is implemented on a VLC hardware system, which had been designed and implemented in our laboratory. Average reward, convergence time, goodput, average delay, and data packet size are evaluated parameters. The results show that the proposed algorithm converges quickly and provides collision-free decentralized TDMA for the network. The proposed algorithm is compared with carrier-sense multiple access with collision avoidance (CSMA/CA) algorithm as a potential selection for decentralized VLC IoT networks. The results show that the proposed algorithm provides up to 61% more goodput and up to 49% less average delay than CSMA/CA.
Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).
We propose and compare methods for the analysis of extreme events in complex systems governed by PDEs that involve random parameters, in situations where we are interested in quantifying the probability that a scalar function of the system's solution is above a threshold. If the threshold is large, this probability is small and its accurate estimation is challenging. To tackle this difficulty, we blend theoretical results from large deviation theory (LDT) with numerical tools from PDE-constrained optimization. Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events, using adjoint methods to compute the gradient of this rate function. The minimizers give information about the mechanism of the extreme events as well as estimates of their probability. We then propose a series of methods to refine these estimates, either via importance sampling or geometric approximation of the extreme event sets. Results are formulated for general parameter distributions and detailed expressions are provided when Gaussian distributions. We give theoretical and numerical arguments showing that the performance of our methods is insensitive to the extremeness of the events we are interested in. We illustrate the application of our approach to quantify the probability of extreme tsunami events on shore. Tsunamis are typically caused by a sudden, unpredictable change of the ocean floor elevation during an earthquake. We model this change as a random process, which takes into account the underlying physics. We use the one-dimensional shallow water equation to model tsunamis numerically. In the context of this example, we present a comparison of our methods for extreme event probability estimation, and find which type of ocean floor elevation change leads to the largest tsunamis on shore.
In this paper, we introduce an Abaqus UMAT subroutine for a family of constitutive models for the viscoelastic response of isotropic elastomers of any compressibility -- including fully incompressible elastomers -- undergoing finite deformations. The models can be chosen to account for a wide range of non-Gaussian elasticities, as well as for a wide range of nonlinear viscosities. From a mathematical point of view, the structure of the models is such that the viscous dissipation is characterized by an internal variable $\textbf{C}^v$, subject to the physically-based constraint $\det\textbf{C}^v=1$, that is solution of a nonlinear first-order ODE in time. This ODE is solved by means of an explicit Runge-Kutta scheme of high order capable of preserving the constraint $\det\textbf{C}^v=1$ identically. The accuracy and convergence of the code is demonstrated numerically by comparison with an exact solution for several of the Abaqus built-in hybrid finite elements, including the simplicial elements C3D4H and C3D10H and the hexahedral elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing the capabilities of the code by deploying it to compute the homogenized response of a bicontinuous rubber blend.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191