multibody structure and motion segmentation by branch and bound model selection an efficient and robust framework is proposed for two view multiple structure and motion segmentation of unknown number of rigid objects the segmentation problem has three unknowns namely the object memberships the corresponding fundamental matrices and the number of objects to handle this otherwise recursive problem hypotheses for fundamental matrices are generated through local sampling once the hypotheses are available a combinatorial selection problem is formulated to optimize a model selection cost which takes into account the hypotheses likelihoods and the model complexity an explicit model for outliers is also added for robust segmentation the model selection cost is minimized through the branch and bound technique of combinatorial optimization the proposed branch and bound approach efficiently searches the solution space and guaranties optimality over the current set of hypotheses the efficiency and the guarantee of optimality of the method is due to its ability to reject solutions without explicitly evaluating them the proposed approach was validated with synthetic data and segmentation results are presented for real images

krylov subspace based model reduction for a class of bilinear descriptor systems we consider model order reduction for bilinear descriptor systems using an interpolatory projection framework such nonlinear descriptor systems can be represented by a series of generalized linear descriptor systems also called subsystems by utilizing the volterra wiener approach rugh 1981 standard projection techniques for bilinear systems utilize the generalized transfer functions of these subsystems to construct an interpolating approximation however the resulting reduced order system may not match the polynomial parts of the generalized transfer functions this may result in an unbounded error in terms of h 2 or h norms in this paper we derive an explicit expression for the polynomial part of each subsystem by assuming a special structure of the bilinear system which reduces to an index 1 linear descriptor system or differential algebraic equation dae if the bilinear terms are zero this allows us to propose an interpolatory technique for bilinear daes which not only achieves interpolation but also retains the polynomial parts of the bilinear systems the approach extends the interpolatory technique for index 1 linear daes beattie and gugercin 2009 to bilinear daes numerical examples are used to illustrate the theoretical results

a krylov stability corrected coordinate stretching method to simulate wave propagation in unbounded domains the krylov subspace projection approach is a well established tool for the reducedorder modeling of dynamical systems in the time domain in this paper we address the main issues obstructing the application of this powerful approach to the time domain solution of exterior wave problems we use frequency independent perfectly matched layers to simulate the extension to infinity pure imaginary stretching functions based on zolotarev s optimal rational approximation of the square root are implemented leading to perfectly matched layers with a controlled accuracy over a complete spectral interval of interest a new krylov based solution method via stabilitycorrected operator exponents is presented which allows us to construct reduced order models roms that respect the delicate spectral properties of the original scattering problem the roms are unconditionally stable and are based on a renormalized bi lanczos algorithm we give a theoretical foundation of our method and illustrate its performance through a number of numerical examples in which we simulate two dimensional electromagnetic wave propagation in unbounded domains including a photonic waveguide example the new algorithm outperforms the conventional finitedifference time domain method for problems on large time intervals

region oriented compression of color images using fuzzy inference and fast merging a new region based lossy compression scheme for color images is proposed the segmentation method belongs to the split and merge category splitting is carried out using the watershed transform in the merging stage a fuzzy color preserving rule based system and a novel one dimensional graph structure are introduced to provide accurate results with reduced computational complexity the compression part is based on the shape adaptive dct with dc correction method the quantization matrices used have been designed according to the properties of the employed transform promising perceptual results for the low bit rate range compared to previously reported compression methods have also been reported

multipoint interpolation of volterra series and h2 model reduction for a family of bilinear descriptor systems abstract in this paper we investigate interpolatory model order reduction for large scale bilinear descriptor systems recently it was shown in wyatt et al 2013 for linear descriptor systems that directly extending the standard rational interpolation conditions used in h 2 optimal model reduction to descriptor systems in general yields an unbounded error in the h 2 norm this is due to the possible mismatch of the polynomial part of the original and reduced order systems this conclusion holds for nonlinear systems as well in this paper we deal with bilinear descriptor systems and aim to pay attention to the polynomial part of the bilinear descriptor system along with interpolation to this end we have shown in goyal et al 2015 how to determine the polynomial part of each subsystem of the bilinear descriptor system explicitly by assuming special structures of the system matrices considering the same structured bilinear descriptor systems in this paper we first show how to achieve multipoint interpolation of the underlying volterra series of bilinear descriptor systems while retaining the polynomial part of each subsystem of the bilinear system then we extend the interpolation based first order necessary conditions for h 2 optimality to bilinear descriptor systems and propose an iterative scheme to obtain an h 2 optimal reduced order system by means of various numerical examples we demonstrate the efficiency of the proposed model order reduction technique and compare it with reduced bilinear systems obtained by using linear irka the loewner method for bilinear systems and pod based approximations

mdl based segmentation and motion modeling in a long image sequence of scene with multiple independently moving objects this paper presents a method for spatiotemporal segmentation of long image sequences of scenes which include multiple independently moving objects based on the minimum description length mdl principle first a family of motion models is constructed each of which corresponds to a physically meaningful motion such as translation with constant velocity or a combination of translation and rotation then the motion description length is formulated when an object changes the type of the motion or a new part of an object appears the corresponding temporal or spatial segmentation is carried out ambiguous segmentation of two consecutive images can be resolved by minimizing the motion description length in a long sequence of images experiments on several real image sequences show the validity of our method

weyl ordered series form for the angle variable of the time dependent oscillator the definition of the phase variable for a classical time dependent oscillator as the natural variable canonically conjugated to the ermakov invariant is revised some implications of the result at the quantum level are discussed and an exact formal expression in terms of weyl ordered operators is given for the associated phase operator

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

spectral problems for the weyl ordered form of operators 1pnqn in this paper we consider quantization of powers of the ratio between the hamiltonian coordinates for position and momentum in one dimensional systems the domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self adjointness the spectral problems for the operators that result from using weyl ordering are discussed by introducing fredholm integral operator forms in position representation and the symmetry of the actions of the parity and time reversal operators on the kernels is discussed finally the general structures and properties of the eigenfunctions and eigenvalues are also derived and analyzed

a framework for the solution of the generalized realization problem in this paper we present a novel way of constructing generalized state space representations e a b c d of interpolants matching tangential interpolation data the loewner and shifted loewner matrices are the key tools in this approach

motion estimation with quadtree splines this paper presents a motion estimation algorithm based on a new multiresolution representation the quadtree spline this representation describes the motion field as a collection of smoothly connected patches of varying size where the patch size is automatically adapted to the complexity of the underlying motion the topology of the patches is determined by a quadtree data structure and both split and merge techniques are developed for estimating this spatial subdivision the quadtree spline is implemented using another novel representation the adaptive hierarchical basis spline and combines the advantages of adaptively sized correlation windows with the speedups obtained with hierarchical basis preconditioners results are presented on some standard motion sequences

pauli s theorem and quantum canonical pairs the consistency of a bounded self adjoint time operator canonically conjugate to a hamiltonian with non empty point spectrum in single hilbert space pauli s wellknown theorem implies that the existence of a selfadjoint time operator canonically conjugate to a given hamiltonian requires the hamiltonian to possess complet

motion based object segmentation and estimation using the mdl principle there are increasing demands for ultralow bit rate video image transmission we present a new formulation of moving object segmentation and motion estimation to quantify the potential gain in using object oriented motion compensation in image sequence coding motivated by real valued parameter estimation required in object oriented motion compensated video source coding a framework motivated by rissanen s 1983 minimum description length mdl principle is proposed to more tightly couple motion estimation and object segmentation algorithms to the overall objective of minimizing source bit rate a new objective function is constructed and a suboptimal procedure to segment and estimate moving objects in a scene is proposed each object is represented by chain coded block boundaries affine motion parameters and motion compensated prediction error a number of experimental comparisons between block and object oriented coding schemes suggests a significant potential coding gain using object oriented motion compensated coding

structure preserving tangential interpolation for model reduction of port hamiltonian systems port hamiltonian systems result from port based network modeling of physical systems and are an important example of passive state space systems in this paper we develop a framework for model reduction of large scale multi input multi output port hamiltonian systems via tangential rational interpolation the resulting reduced model is a rational tangential interpolant that retains the port hamiltonian structure hence it remains passive we introduce an h 2 inspired algorithm for effective choice of interpolation points and tangent directions and present several numerical examples illustrating its effectiveness

linear system approximation via covariance equivalent realizations abstract a truncation technique for model reduction to simultaneously match a specified number of output covariance derivatives is described these covariance equivalent realizations which match q 1 covariance derivatives are called q covers in general q covers are not unique the additional freedom is used herein so that the q cover obtained also matches q markov parameters the truncation technique uses a form of the observability matrices of the full order system to determine a priori the order required of the reduced order model to match a specified number of output covariance derivatives and markov parameters the resulting realization is shown to be independent of the basis of the complete model to within a unitary transformation stability conditions for the reduced order model are also described and the relationships are established between stochastically equivalent realizations and the q covers

a structured quasi arnoldi procedure for model order reduction of second order systems abstract existing krylov subspace based structure preserving model order reduction methods for the second order systems proceed in two stages the first stage is to generate a basis matrix of the underlying krylov subspace the second stage is to employ an explicit subspace projection to obtain a reduced order model with a moment matching property an open problem is how to avoid explicit projection so that it will be efficient for truly large scale systems in addition it is also desired that a structure preserving reduced system of order n matches maximum 2 n moments in this paper we propose a new procedure to compute a so called structured quasi arnoldi sqa decomposition once the sqa decomposition is computed a structure preserving reduced order model can be defined immediately from the decomposition without the explicit subspace projection furthermore the reduced model of order n matches maximum 2 n moments numerical examples demonstrate that the transpose free sqa based reduced model is compatible with the two sided structure preserving explicit projection methods and is more accurate than the one sided structure preserving explicit projection methods due to the higher number of matched moments

an adaptive strategy for the bivariate solution of finite element problems using multivariate nested pade approximants most engineering applications involving solutions by numerical methods are dependent on several parameters whose impact on the solution may significantly vary from one to the other at times an ev

pade approximants and the modal connection towards increased robustness for fast parametric sweeps summary in order to increase the robustness of a pade based approximation of parametric solutions to finite element problems an a priori estimate of the poles is proposed the resulting original approach is shown to allow for a straightforward efficient subsequent pade based expansion of the solution vector components overcoming some of the current convergence and robustness limitations in particular this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of pade approximants the choice of these approximants as shown in the present work is theoretically supported by the montessus de ballore theorem concerning the convergence of a series of approximants with fixed denominator degrees key features and originality of the proposed approach are i a component wise expansion which allows to specifically target subsets of the solution field and ii the a priori simultaneous choice of the pade approximants and their associated interval of convergence for an effective and more robust approximation an academic acoustic case study a structural acoustic application and a larger acoustic problem are presented in order to demonstrate the potential of the approach proposed this article is protected by copyright all rights reserved

fast frequency sweeps with many forcing vectors through adaptive interpolatory model order reduction summary the goal of this work is to examine the efficacy of interpolatory model order reduction on frequency sweep problems with many forcing vectors the adaptive method proposed relies on the implicit interpolatory properties of subspace projection with basis vectors spanning the forced response of the system and its derivatives the algorithm is similar to a recently proposed adaptive scheme in that it determines both interpolation location and order within the frequency domain of interest the bounds of efficiency of the approach as the number of forcing vectors grows are explored through the use of rough floating operation counts this in turn guides choices made in the adaptive algorithm including a new technique that prevents excessive subspace growth by capitalizing on subspace direction coupling in order to demonstrate the algorithm s utility a series of frequency sweep problems drawn from the field of structural acoustics is analyzed it is demonstrated that increased order of interpolation can actually degrade the efficiency of the algorithm as the number of forcing vectors grows but that this can be limited by the subspace size throttling procedure developed here copyright 2014 john wiley sons ltd

a generalized weyl relation approach to the time operator and its connection to the survival probability the time operator an operator which satisfies the canonical commutation relation with the hamiltonian is investigated on the basis of a certain algebraic relation for a pair of operators t and h where t is symmetric and h self adjoint this relation is equivalent to the weyl relation in the case of self adjoint t and is satisfied by the aharonov bohm time operator t0 and the free hamiltonian h0 for the one dimensional free particle system in order to see the qualitative properties of t0 the operators t and h satisfying this algebraic relation are examined in particular it is shown that the standard deviation of t is directly connected to the survival probability and h is absolutely continuous hence it is concluded that the existence of the operator t implies the existence of scattering states it is also shown that the minimum uncertainty states do not exist other examples of these operators t and h than the one dimensional free particle system are demonstrated

interpolatory projection methods for structure preserving model reduction abstract we present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization c s s 1 b s d this includes rational krylov based interpolation methods as a special case the broader framework allows retention of special structure in reduced models such as symmetry second and higher order structure state constraints internal delays and infinite dimensional subsystems two numerical examples are provided for systems associated with viscoelastic dynamics and with an internal state delay that demonstrate the effectiveness and flexibility of the approach

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

self adjoint time operator is the rule for discrete semi bounded hamiltonians we prove explicitly that to every discrete semibounded hamiltonian with constant degeneracy and with a finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span th

on certain canonoid transformations and invariants for the parametric oscillator in classical mechanics a transformation in phase space is said to be canonoid if it maps only some hamiltonian systems into hamiltonian systems once canonoid transformations are considered these systems can be classically described by means of lagrangians or hamiltonians other than the conventional ones in this context a basic role is played by the dynamical invariants generated through the poisson brackets of the new independent variables in phase space here we obtain the explicit form of special canonoid transformations of the polynomial type for systems which can be classically described by an equation of the parametric oscillator type and discuss some algebraic properties shown by the associated dynamical invariants

hamiltonian dynamics on the symplectic extended phase space for autonomous and non autonomous systems we will present a consistent description of hamiltonian dynamics on the symplectic extended phase space that is analogous to that of a time independent hamiltonian system on the conventional symplectic phase space the extended hamiltonian h1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional hamiltonian h will be derived from a generalized formulation of hamilton s variational principle the extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system while preserving the extended hamiltonian h1 and hence the form of the canonical equations derived from h1 the lorentz transformation as well as time scaling transformations in celestial mechanics will be shown to represent particular canonical transformations in the symplectic extended phase space furthermore the generalized canonical transformation approach allows us to directly map explicitly time dependent hamiltonians into time independent ones an extended generating function that defines transformations of this kind will be presented for the time dependent damped harmonic oscillator and for a general class of explicitly time dependent potentials in the appendix we will re establish the proper form of the extended hamiltonian h1 by means of a legendre transformation of the extended lagrangian l1

solution of 3d time domain electromagnetic problems using optimal subspace projection abstracttime domain problems for controlled source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales therefore forward simulation using conventional computational methods becomes computationally expensive even without accounting for induced polarization ip effects these effects create another complication caused by the presence of a convolution integral in the time domain maxwell system we suggested a novel fast and robust algorithm to solve the 3d time domain electromagnetic em problems that can be considered as a generalization of the spectral lanczos decomposition method the new method also allowed us to incorporate the ip effects without significant cost increase the discretized large scale maxwell system was projected onto a small subspace consisting of the laplace domain solutions the so called parameter dependent krylov subspace for an optimally chosen set of laplace parameters the projected system preserved stabilit

spatio temporal segmentation based on region merging this paper proposes a technique for spatio temporal segmentation to identify the objects present in the scene represented in a video sequence this technique processes two consecutive frames at a time a region merging approach is used to identify the objects in the scene starting from an oversegmentation of the current frame the objects are formed by iteratively merging regions together regions are merged based on their mutual spatio temporal similarity we propose a modified kolmogorov smirnov test for estimating the temporal similarity the region merging process is based on a weighted directed graph two complementary graph based clustering rules are proposed namely the strong rule and the weak rule these rules take advantage of the natural structures present in the graph experimental results on different types of scenes demonstrate the ability of the proposed technique to automatically partition the scene into its constituent objects

an a contrario decision framework for region based motion detection the aim of motion detection is to decide whether a given part of an image belongs to a moving object or to the static background this paper proposes an automatic decision rule for the detection of moving regions the proposed framework is derived from a perceptual grouping principle namely the helmholtz principle this principle basically states that perceptually relevant events are perceived because they deviate from a model of complete randomness detections are then said to be performed a contrario moving regions appear as low probability events in a model corresponding to the absence of moving objects in the scene a careful design of the events considered under the hypothesis of absence of moving objects results in a general and robust motion detection algorithm no posterior parameter tuning is necessary furthermore a confidence level is attached to each detected region

the shifted proper orthogonal decomposition a mode decomposition for multiple transport phenomena transport dominated phenomena provide a challenge for common mode based model reduction approaches we present a model reduction method which is suited for these kinds of systems it extends the proper orthogonal decomposition pod by introducing time dependent shifts of the snapshot matrix the approach called shifted proper orthogonal decomposition spod features a determination of the multiple transport velocities and a separation of these one and two dimensional test examples reveal the good performance of the spod for transport dominated phenomena and its superiority in comparison to the pod

an adaptive scheme for a class of interpolatory model reduction methods for frequency response problems frequency sweep problems arise in many structural dynamic acoustic and structural acoustic applications in each case they incur the evaluation of a frequency response function for a typically large number of frequencies because each function evaluation requires the solution of an often large scale system of equations frequency sweep problems are computationally intensive interpolatory model order reduction is a powerful tool for reducing their cost however the performance of this tool depends on the location and number of the interpolation frequency points it also depends on the number of consecutive frequency derivatives of the response function that are matched at each frequency point so far these two choices have been made in the literature in a heuristic manner in contrast this paper proposes an automatic adaptive strategy based on monitoring the euclidean norm of the relative residual associated with the function to be evaluated over the frequency band of interest more specifically the number of interpolation points and the number of matched frequency derivatives are adaptively increased until the global euclidean norm of the relative residual is reduced below a user specified tolerance the robustness accuracy and computational efficiency of this adaptive strategy are highlighted with the solution of several frequency sweep problems associated with large scale structural dynamic acoustic and structural acoustic finite element models copyright 2012 john wiley sons ltd

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

time dependent diffeomorphisms as quantum canonical transformations and the time dependent harmonic oscillator quantum canonical transformations corresponding to time dependent diffeomorphisms of the configuration space are studied a special class of these transformations which correspond to time dependent dilatations is used to identify a previously unknown class of exactly solvable time dependent harmonic oscillators the caldirola kanai oscillator belongs to this class for a general time dependent harmonic oscillator it is shown that choosing the dilatation parameter to satisfy the classical equation of motion one obtains the solution of the schrodinger equation a simple generalization of this result leads to the reduction of the schrodinger equation to a second order ordinary differential equation whose special case is the auxiliary equation of the lewis riesenfeld invariant theory the time evolution operator is expressed in terms of a positive real solution of this equation in a closed form and the time dependent position and momentum operators are calculated

a survey of projection based model reduction methods for parametric dynamical systems numerical simulation of large scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena however the inherent large scale nature of the models often leads to unmanageable demands on computational resources model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate yet accurately represent the original large scale system behavior model reduction of linear nonparametric dynamical systems has reached a considerable level of maturity as reflected by several survey papers and books however parametric model reduction has emerged only more recently as an important and vibrant research area with several recent advances making a survey paper timely thus this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods parametric model reduction targets the broad class of problems for wh

optimal image and video closure by superpixel grouping detecting independent objects in images and videos is an important perceptual grouping problem one common perceptual grouping cue that can facilitate this objective is the cue of contour closure reflecting the spatial coherence of objects in the world and their projections as closed boundaries separating figure from background detecting contour closure in images consists of finding a cycle of disconnected contour fragments that separates an object from its background searching the entire space of possible groupings is intractable and previous approaches have adopted powerful perceptual grouping heuristics such as proximity and co curvilinearity to constrain the search we introduce a new formulation of the problem by transforming the problem of finding cycles of contour fragments to finding subsets of superpixels whose collective boundary has strong edge support few gaps in the image our cost function a ratio of a boundary gap measure to area promotes spatially coherent sets of superpixels moreover its properties support a global optimization procedure based on parametric maxflow extending closure detection to videos we introduce the concept of spatiotemporal closure analogous to image closure we formulate our spatiotemporal closure cost over a graph of spatiotemporal superpixels our cost function is a ratio of motion and appearance discontinuity measures on the boundary of the selection to an internal homogeneity measure of the selected spatiotemporal volume the resulting approach automatically recovers coherent components in images and videos corresponding to objects object parts and objects with surrounding context providing a good set of multiscale hypotheses for high level scene analysis we evaluate both our image and video closure frameworks by comparing them to other closure detection approaches and find that they yield improved performance

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

dimension reduction of large scale second order dynamical systems via a second order arnoldi method a structure preserving dimension reduction algorithm for large scale second order dynamical systems is presented it is a projection method based on a second order krylov subspace a second order arnoldi soar method is used to generate an orthonormal basis of the projection subspace the reduced system not only preserves the second order structure but also has the same order of approximation as the standard arnoldi based krylov subspace method via linearization the superior numerical properties of the soar based method are demonstrated by examples from structural dynamics and microelectromechanical systems