Showing papers on "Piecewise published in 2015"

Distant Supervision for Relation Extraction via Piecewise Convolutional Neural Networks

Abstract: Two problems arise when using distant supervision for relation extraction. First, in this method, an already existing knowledge base is heuristically aligned to texts, and the alignment results are treated as labeled data. However, the heuristic alignment can fail, resulting in wrong label problem. In addition, in previous approaches, statistical models have typically been applied to ad hoc features. The noise that originates from the feature extraction process can cause poor performance. In this paper, we propose a novel model dubbed the Piecewise Convolutional Neural Networks (PCNNs) with multi-instance learning to address these two problems. To solve the first problem, distant supervised relation extraction is treated as a multi-instance problem in which the uncertainty of instance labels is taken into account. To address the latter problem, we avoid feature engineering and instead adopt convolutional architecture with piecewise max pooling to automatically learn relevant features. Experiments show that our method is effective and outperforms several competitive baseline methods.

Adaptive Control of Hydraulic Actuators With LuGre Model-Based Friction Compensation

Abstract: This paper concerns high-accuracy tracking control for hydraulic actuators with nonlinear friction compensation Typically, LuGre model-based friction compensation has been widely employed in sundry industrial servomechanisms However, due to the piecewise continuous property, it is difficult to be integrated with backstepping design, which needs the time derivation of the employed friction model Hence, nonlinear model-based hydraulic control rarely sets foot in friction compensation with nondifferentiable friction models, such as LuGre model, Stribeck effects, although they can give excellent friction description and prediction In this paper, a novel continuously differentiable nonlinear friction model is first derived by modifying the traditional piecewise continuous LuGre model, then an adaptive backstepping controller is proposed for precise tracking control of hydraulic systems to handle parametric uncertainties along with nonlinear friction compensation In the formulated nonlinear hydraulic system model, friction parameters, servovalve null shift, and orifice-type internal leakage are all uniformly considered in the proposed controller The controller theoretically guarantees asymptotic tracking performance in the presence of parametric uncertainties, and the robustness against unconsidered dynamics, as well as external disturbances, is also ensured via Lyapunov analysis The effectiveness of the proposed controller is demonstrated via comparative experimental results

3D Scene Flow Estimation with a Piecewise Rigid Scene Model

Abstract: 3D scene flow estimation aims to jointly recover dense geometry and 3D motion from stereoscopic image sequences, thus generalizes classical disparity and 2D optical flow estimation. To realize its conceptual benefits and overcome limitations of many existing methods, we propose to represent the dynamic scene as a collection of rigidly moving planes, into which the input images are segmented. Geometry and 3D motion are then jointly recovered alongside an over-segmentation of the scene. This piecewise rigid scene model is significantly more parsimonious than conventional pixel-based representations, yet retains the ability to represent real-world scenes with independent object motion. It, furthermore, enables us to define suitable scene priors, perform occlusion reasoning, and leverage discrete optimization schemes toward stable and accurate results. Assuming the rigid motion to persist approximately over time additionally enables us to incorporate multiple frames into the inference. To that end, each view holds its own representation, which is encouraged to be consistent across all other viewpoints and frames in a temporal window. We show that such a view-consistent multi-frame scheme significantly improves accuracy, especially in the presence of occlusions, and increases robustness against adverse imaging conditions. Our method currently achieves leading performance on the KITTI benchmark, for both flow and stereo.

Qualitative properties of certain piecewise deterministic Markov processes

Abstract: We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Working under the general assumption that the process stays in a compact set, we detail a possible construction of the process and characterize its support, in terms of the solutions set of a differential inclusion. We establish results on the long time behaviour of the process, in relation to a certain set of accessible points, which is shown to be strongly linked to the support of invariant measures. Under Hormander-type bracket conditions, we prove that there exists a unique invariant measure and that the processes converges to equilibrium in total variation. Finally we give examples where the bracket condition does not hold, and where there may be one or many invariant measures, depending on the jump rates between the flows.

Neural Network and Jacobian Method for Solving the Inverse Statics of a Cable-Driven Soft Arm With Nonconstant Curvature

Abstract: The solution of the inverse kinematics problem of soft manipulators is essential to generate paths in the task space. The inverse kinematics problem of constant curvature or piecewise constant curvature manipulators has already been solved by using different methods, which include closed-form analytical approaches and iterative methods based on the Jacobian method. On the other hand, the inverse kinematics problem of nonconstant curvature manipulators remains unsolved. This study represents one of the first attempts in this direction. It presents both a model-based method and a supervised learning method to solve the inverse statics of nonconstant curvature soft manipulators. In particular, a Jacobian-based method and a feedforward neural network are chosen and tested experimentally. A comparative analysis has been conducted in terms of accuracy and computational time.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

Abstract: This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element method and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of O ( τ + h r +1 )in the L 2 norm, where τ and h are the step sizes in time and space, respectively, and r is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are O ( τ 1 . 5 + h r +1 ). Furthermore, two improved algorithms are constructed, and they are also unconditionally stable and convergent of order O ( τ 2 + h r +1 ). Numerical examples are provided to verify the theoretical analysis. Comparisons between the present algorithms and the existing ones are included, showing that our numerical algorithms exhibit better performances than the known ones.

DPPTAM: Dense piecewise planar tracking and mapping from a monocular sequence

Abstract: This paper proposes a direct monocular SLAM algorithm that estimates a dense reconstruction of a scene in real-time on a CPU. Highly textured image areas are mapped using standard direct mapping techniques [1], that minimize the photometric error across different views. We make the assumption that homogeneous-color regions belong to approximately planar areas. Our contribution is a new algorithm for the estimation of such planar areas, based on the information of a superpixel segmentation and the semidense map from highly textured areas. We compare our approach against several alternatives using the public TUM dataset [2] and additional live experiments with a hand-held camera. We demonstrate that our proposal for piecewise planar monocular SLAM is faster, more accurate and more robust than the piecewise planar baseline [3]. In addition, our experimental results show how the depth regularization of monocular maps can damage its accuracy, being the piecewise planar assumption a reasonable option in indoor scenarios.

Exponential ergodicity for Markov processes with random switching

Abstract: We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second component is discrete and its jump rates may depend on the position of the whole process. Under regularity assumptions on the jump rates and Wasserstein contraction conditions for the underlying dynamics, we provide a concrete criterion for the convergence to equilibrium in terms of Wasserstein distance. The proof is based on a coupling argument and a weak form of the Harris theorem. In particular, we obtain exponential ergodicity in situations which do not verify any hypoellipticity assumption, but are not uniformly contracting either. We also obtain a bound in total variation distance under a suitable regularising assumption. Some examples are given to illustrate our result, including a class of piecewise deterministic Markov processes.

Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers

Abstract: A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Revisiting Lambert’s problem

Abstract: The orbital boundary value problem, also known as Lambert problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revolution case, in only two iterations. The resulting algorithm is compared, for single and multiple revolutions, to Gooding’s procedure revealing to be numerically as accurate, while having a significantly smaller computational complexity.

Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization

Abstract: In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions, respectively. We then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed-integer optimization. We demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems. We provide global lower bounds and show that our approach is (i) practically tractable and (ii) provides high quality solutions that outperform alternative methods.

Dense, accurate optical flow estimation with piecewise parametric model

Abstract: This paper proposes a simple method for estimating dense and accurate optical flow field. It revitalizes an early idea of piecewise parametric flow model. A key innovation is that, we fit a flow field piecewise to a variety of parametric models, where the domain of each piece (i.e., each piece's shape, position and size) is determined adaptively, while at the same time maintaining a global inter-piece flow continuity constraint. We achieve this by a multi-model fitting scheme via energy minimization. Our energy takes into account both the piecewise constant model assumption and the flow field continuity constraint, enabling the proposed method to effectively handle both homogeneous motions and complex motions. The experiments on three public optical flow benchmarks (KITTI, MPI Sintel, and Middlebury) show the superiority of our method compared with the state of the art: it achieves top-tier performances on all the three benchmarks.

Residual a posteriori error estimation for the Virtual Element Method for elliptic problems

Abstract: A posteriori error estimation and adaptivity are very useful in the context of the virtual element and mimetic discretization methods due to the flexibility of the meshes to which these numerical schemes can be applied. Nevertheless, developing error estimators for virtual and mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. In the new virtual element setting, we develop a residual based a posteriori error estimator for the Poisson problem with (piecewise) constant coefficients, that is proven to be reliable and efficient. We moreover show the numerical performance of the proposed estimator when it is combined with an adaptive strategy for the mesh refinement.

Synchronization of Chaotic Lur’e Systems With Time Delays Using Sampled-Data Control

Abstract: The asymptotical synchronization problem is investigated for two identical chaotic Lur’e systems with time delays. The sampled-data control method is employed for the system design. A new synchronization condition is proposed in the form of linear matrix inequalities. The error system is shown to be asymptotically stable with the constructed new piecewise differentiable Lyapunov–Krasovskii functional (LKF). Different from the existing work, the new LKF makes full use of the information in the nonlinear part of the system. The obtained stability condition is less conservative than some of the existing ones. A longer sampling period is achieved with the new method. The numerical examples are given and the simulations are performed on Chua’s circuit. The results show the superiorities and effectiveness of the proposed control method.

A Variational Approach to Simultaneous Image Segmentation and Bias Correction

Abstract: This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

An improved Maxwell creep model for rock based on variable-order fractional derivatives

Abstract: For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed. The order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. Through the segmentation treatment, according to different creep stages of the experimental results, it is found that the improved creep model based on variable-order fractional derivatives agrees well with the experimental data. In addition, the fact is verified that variable order of fractional derivatives can be regarded as a step function, which is reasonable and reliable. In addition, through further piecewise fitting, the parameters in the model are determined on the basis of existing experimental results. All estimated results show that the theoretical model proposed in the paper properly depicts the creep properties, providing an excellent agreement with the experimental data.

Variational Mesh Denoising Using Total Variation and Piecewise Constant Function Space

Abstract: Mesh surface denoising is a fundamental problem in geometry processing The main challenge is to remove noise while preserving sharp features (such as edges and corners) and preventing generating false edges We propose in this paper to combine total variation (TV) and piecewise constant function space for variational mesh denoising We first give definitions of piecewise constant function spaces and associated operators A variational mesh denoising method will then be presented by combining TV and piecewise constant function space It is proved that, the solution of the variational problem (the key part of the method) is in some sense continuously dependent on its parameter, indicating that the solution is robust to small perturbations of this parameter To solve the variational problem, we propose an efficient iterative algorithm (with an additional algorithmic parameter) based on variable splitting and augmented Lagrangian method, each step of which has closed form solution Our denoising method is discussed and compared to several typical existing methods in various aspects Experimental results show that our method outperforms all the compared methods for both CAD and non-CAD meshes at reasonable costs It can preserve different levels of features well, and prevent generating false edges in most cases, even with the parameters evaluated by our estimation formulae

Bi-Normal Filtering for Mesh Denoising

Abstract: Most mesh denoising techniques utilize only either the facet normal field or the vertex normal field of a mesh surface. The two normal fields, though contain some redundant geometry information of the same model, can provide additional information that the other field lacks. Thus, considering only one normal field is likely to overlook some geometric features. In this paper, we take advantage of the piecewise consistent property of the two normal fields and propose an effective framework in which they are filtered and integrated using a novel method to guide the denoising process. Our key observation is that, decomposing the inconsistent field at challenging regions into multiple piecewise consistent fields makes the two fields complementary to each other and produces better results. Our approach consists of three steps: vertex classification , bi-normal filtering , and vertex position update . The classification step allows us to filter the two fields on a piecewise smooth surface rather than a surface that is smooth everywhere. Based on the piecewise consistence of the two normal fields, we filtered them using a piecewise smooth region clustering strategy. To benefit from the bi-normal filtering, we design a quadratic optimization algorithm for vertex position update. Experimental results on synthetic and real data show that our algorithm achieves higher quality results than current approaches on surfaces with multifarious geometric features and irregular surface sampling.

Detection of Multiple Structural Breaks in Multivariate Time Series

Abstract: We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of m...

A vector forward mode of automatic differentiation for generalized derivative evaluation

Abstract: Numerical methods for non-smooth equation-solving and optimization often require generalized derivative information in the form of elements of the Clarke Jacobian or the B-subdifferential. It is shown here that piecewise differentiable functions are lexicographically smooth in the sense of Nesterov, and that lexicographic derivatives of these functions comprise a particular subset of both the B-subdifferential and the Clarke Jacobian. Several recently developed methods for generalized derivative evaluation of composite piecewise differentiable functions are shown to produce identical results, which are also lexicographic derivatives. A vector forward mode of automatic differentiation AD is presented for evaluation of these derivatives, generalizing established methods and combining their computational benefits. This forward AD mode may be applied to any finite composition of known smooth functions, piecewise differentiable functions such as the absolute value function, , and , and certain non-smooth functions which are not piecewise differentiable, such as the Euclidean norm. This forward AD mode may be implemented using operator overloading, does not require storage of a computational graph, and is computationally tractable relative to the cost of a function evaluation. An implementation in C is discussed.

Event-triggered consensus control for second-order multi-agent systems

Abstract: In this study, an event-triggered control strategy is proposed to achieve consensus in a multi-agent system under a directed topology. The proposed control strategy utilises a piecewise continuous control law and an event-triggering function for each agent. The control law only updates at discrete event instants computed using an event-triggering function, which depends on the states of the agents at the current and outdated event instant. This control approach is first applied to a first-order system and is further extended to a second-order system. Simulation examples are presented to illustrate the efficiency of the proposed control strategy.

Off-the-Grid Recovery of Piecewise Constant Images from Few Fourier Samples

Abstract: We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric polynomial, we show the Fourier coefficients of the partial derivatives of the image satisfy a linear annihilation relation. We present necessary and sufficient conditions for unique recovery of the image from finite low-pass Fourier samples using the annihilation relation. We also propose a practical two-stage recovery algorithm which is robust to model-mismatch and noise. In the first stage we estimate a continuous domain representation of the edge set of the image. In the second stage we perform an extrapolation in Fourier domain by a least squares two-dimensional linear prediction, which recovers the exact Fourier coefficients of the underlying image. We demonstrate our algorithm on the super-resolution recovery of MRI phantoms and real MRI data from low-pass Fourier samples, which shows benefits over standard approaches for single-image super-resolution MRI.

Event-triggered average consensus for multi-agent systems with nonlinear dynamics and switching topology

Abstract: The average consensus problem for a multi-agent system with nonlinear dynamics is studied in this paper by employing a distributed event-triggered control strategy. The strategy uses a piecewise continuous control law and an event-triggering function to control the system. The piecewise continuous control law only updates at infrequent instants and keeps steady at the previous value in the period between two instants. The event-triggering function determines these instants based on the state information of the agents at current and previous instants. This control approach is first applied to a first-order system under a connected topology in a centralized pattern. Then the switching topology case is considered. At last, both the first-order and the second-order system are considered under distributed event-triggered strategy. The distributed event-triggering function, which only employs the information of the corresponding agent and the states of its neighbors, is designed for each agent in the system. By utilizing Lyapunov method and graph theory, it is proven that the systems can reach consensus by using the event-triggered control strategy. Numerical examples are provided to show the efficacy of the proposed control strategy.