Results 1  10
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90
A general framework for motion segmentation: Independent, articulated, rigid, nonrigid, degenerate and nondegenerate
 In ECCV
, 2006
"... Abstract. We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constra ..."
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Cited by 133 (0 self)
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Abstract. We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constraint states that the trajectories of the same motion lie in a low dimensional linear manifold and different motions result in different linear manifolds; locality, by which we mean in a transformed space a data and its neighbors tend to lie in the same linear manifold, provides a cue for efficient estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown beforehand, and segment the trajectories accordingly. It first transforms and normalizes the trajectories; secondly, for each trajectory it estimates a local linear manifold through local sampling; then it derives the affinity matrix based on principal subspace angles between these estimated linear manifolds; at last, spectral clustering is applied to the matrix and gives the segmentation result. Our algorithm is general without restriction on the number of linear manifolds and without prior knowledge of the dimensions of the linear manifolds. We demonstrate in our experiments that it can segment a wide range of motions including independent, articulated, rigid, nonrigid, degenerate, nondegenerate or any combination of them. In some highly challenging cases where other stateoftheart motion segmentation algorithms may fail, our algorithm gives expected results. 2 1
An Algebraic Geometric Approach to the Identification of a Class of Linear Hybrid Systems
 In Proc. of IEEE Conference on Decision and Control
, 2003
"... We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the ..."
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Cited by 55 (14 self)
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We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the switches to be separated by a minimum dwell time. The decoupling is obtained from the socalled hybrid decoupling constraint, which establishes a connection between linear hybrid system identification, polynomial factorization and hyperplane clustering. In essence, we represent the number of discrete states n as the degree of a homogeneous polynomial p and the model parameters as factors of p. We then show that one can estimate n from a rank constraint on the data, the coe#cients of p from a linear system, and the model parameters from the derivatives of p. The solution is closed form if and only if n 4. Once the model parameters have been identified, the estimation of the hybrid state becomes a simpler problem. Although our algorithm is designed for noiseless data, we also present simulation results with noisy data. 1
Identification of piecewise affine systems via mixedinteger programming
 AUTOMATICA
, 2004
"... This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming ..."
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Cited by 45 (5 self)
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This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where switches occur only seldom in the estimation data, we also suggest a way of trading off between optimality and complexity by using a change detection approach.
A boundederror approach to piecewise affine system identification
 IEEE Transactions on Automatic Control
, 2005
"... Abstract — This paper proposes a threestage procedure for ..."
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Cited by 44 (1 self)
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Abstract — This paper proposes a threestage procedure for
From experiment design to closedloop control
, 2005
"... The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any m ..."
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Cited by 41 (1 self)
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The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a fullorder model always is necessary as well designed experiments allow for restricted complexity models to be nearoptimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.
Heemels: A Bayesian Approach to Identification of Hybrid Systems
 IEEE Trans. on Automatic Control
, 2005
"... Abstract—In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a blackbox method. We treat the unkno ..."
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Cited by 38 (3 self)
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Abstract—In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a blackbox method. We treat the unknown parameters as random variables, described by their probability density functions. The identification problem is posed as the problem of computing the a posteriori probability density function of the model parameters, and subsequently relaxed until a practically implementable method is obtained. A particle filtering method is used for a numerical implementation of the proposed procedure. A modified version of the multicategory robust linear programming classification procedure, which uses the information derived in the previous steps of the identification algorithm, is used for estimating the partition of the piecewise ARX map. The proposed procedure is applied for the identification of a component placement process in pickandplace machines. Index Terms—Hybrid systems, identification. I.
Hybrid modeling and simulation of genetic regulatory networks: a qualitative approach
 ERCIM News
, 2003
"... The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, socalled genetic regulatory networks. The concerted efforts of genetics, molecular biology, biochemistry, and physiology have led to the accum ..."
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Cited by 35 (1 self)
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The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, socalled genetic regulatory networks. The concerted efforts of genetics, molecular biology, biochemistry, and physiology have led to the accumulation of enormous amounts of data on the molecular components of genetic regulatory networks and their interactions. Notwithstanding the advances in the mapping of the network structure, surprisingly little is understood about how the dynamic behavior of the system emerges from the interactions between the network components. This has incited an increasingly large group of researchers to turn from the structure to the behavior of genetic regulatory networks, against the background of a broader movement nowadays often referred to as systems biology
A.: Reconstruction of switching thresholds in piecewiseaffine models of genetic regulatory networks
, 2005
"... Abstract. Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWiseAffine (PWA) models of genetic regulatory networks from exp ..."
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Cited by 34 (10 self)
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Abstract. Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWiseAffine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli. 1
Identification of hybrid systems: a tutorial
"... This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing ..."
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Cited by 29 (3 self)
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This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clusteringbased procedure, and a boundederror procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested.
A sparsification approach to set membership identification of a class of affine hybrid systems
 In Proc. IEEE Conf. Dec. Contr
, 2008
"... Abstract—This paper addresses the problem of robust identification of a class of discretetime affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and some minimal a priori information about the set of admissible plants, ..."
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Cited by 26 (11 self)
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Abstract—This paper addresses the problem of robust identification of a class of discretetime affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and some minimal a priori information about the set of admissible plants, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information, while minimizing either the number of switches or subsystems. For the case where it is desired to minimize the number of switches, the key idea of the paper is to reduce this problem to a sparsification form, where the goal is to maximize sparsity of a suitably constructed vector sequence. Our main result shows that in the case of bounded noise, this sparsification problem can be exactly solved via convex optimization. In the general case where the noise is only known to belong to a convex set, the problem is generically NPhard. However, as we show in the paper, efficient convex relaxations can be obtained by exploiting recent results on sparse signal recovery. Similarly, we present both a sparsification formulation and a convex relaxation for the (known to be NP hard) case where it is desired to minimize the number of subsystems. These results are illustrated using two nontrivial problems arising in computer vision applications: videoshot and dynamic texture segmentation. Index Terms—Hybrid systems, piecewise affine systems, set membership identification, sparse signal recovery. I.