tomographic representation of spin and quark states we present a short review of the general principles of constructing tomograms of quantum states we derive a general tomographic reconstruction formula for the quantum density operator of a system with a dynamical lie group in the reconstruction formula the multiplicity of irreducible representation in clebsch gordan decomposition is taken into account various approaches to spin tomography are discussed an integral representation for the tomographic probability is found and a contraction of the spin tomogram to the photon number tomography distribution is considered the case of su 3 tomography is discussed with the examples of quark states related to the simplest triplet representations and octet states

treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses finite element approximations of the stokes and navier stokes equations with in homogeneous essential boundary conditions are considered boundary conditions are enforced weakly by introducing lagrange multipliers optimal error estimates including some for the stress vector on the boundary are derived under minimal regularity assumptions on the data particular attention is paid to the analysis of a practical choice of finite element spaces for which the lagrange multiplier calculation uncouples from that for the velocity and pressure the results are also applicable to general second order elliptic systems

kernel of star product for spin tomograms the spin state tomogram is presented as the modulus squared of the matrix element of the su 2 group irreducible representation for the spin system we established explicitly a realization of the set of operators defining for spin tomograms the star product formalism in terms of irreducible tensors on the set of spin tomograms the delta function and standard and moyal like kernels of the tomogram star product are calculated explicitly in terms of clebsch gordan and racah coefficients and matrix elements of the su 2 irreducible representation in the limit of infinite spin the spin tomogram is shown to become the tomogram of the harmonic oscillator state

the scale representation the authors considers scale a physical attribute of a signal and develop its properties he presents an operator which represents scale and study its characteristics and representation this allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal he obtains explicit expressions for the mean scale scale bandwidth instantaneous scale and scale group delay furthermore he derives expressions for mean time mean frequency duration frequency bandwidth in terms of the scale variable the short time transform is defined and used to obtain the conditional value of scale for a given time he shows that as the windows narrows one obtains instantaneous scale convolution and correlation theorems for scale are derived a formulation is devised for studying linear scale invariant systems he derives joint representations of time scale and frequency scale general classes for each are presented using the same methodology as for the time frequency case as special cases the joint distributions of marinovich altes 1978 1986 and bertrand bertrand 1984 are recovered also joint representations of the three quantities time frequency scale are devised a general expression for the local scale autocorrelation function is given uncertainty principles for scale and time and scale and frequency are derived

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

fitting parameterized three dimensional models to images model based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3 d model to matching 2 d image features the author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation variable dimensions or surface deformations numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters the levenberg marquardt method is used to always ensure convergence of the solution these techniques allow model based vision to be used for a much wider class of problems than was possible with previous methods their application is demonstrated for tracking the motion of curved parameterized objects

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations this work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations the minimization of the tracking functional subject to implicit parabolic equations is examined existence of an optimal solution is proved and an optimality system of equations is derived semi discrete in space error estimates for the finite element approximations of the optimality system are presented these estimates are symmetric and applicable for higher order discretizations finally fully discrete error estimates of arbitrarily high order are presented based on a discontinuous galerkin in time and conforming in space scheme two examples related to the lagrangian moving mesh galerkin formulation for the convection diffusion equation are described

frame transforms star products and quantum mechanics on phase space using the notions of frame transform and of square integrable projective representation of a locally compact group g we introduce a class of isometries tight frame transforms from the space of hilbert schmidt operators in the carrier hilbert space of the representation into the space of square integrable functions on the direct product group g g these transforms have remarkable properties in particular their ranges are reproducing kernel hilbert spaces endowed with a suitable star product which mimics at the level of functions the original product of operators a phase space formulation of quantum mechanics relying on the frame transforms introduced in the present paper and the link of these maps with both the wigner transform and the wavelet transform are discussed

probabilistic motion estimation based on temporal coherence we develop a theory for the temporal integration of visual motion motivated by psychophysical experiments the theory proposes that input data are temporally grouped and used to predict and estimate the motion flows in the image sequence this temporal grouping can be considered a generalization of the data association techniques that engineers use to study motion sequences our temporal grouping theory is expressed in terms of the bayesian generalization of standard kalman filtering to implement the theory we derive a parallel network that shares some properties of cortical networks computer simulations of this network demonstrate that our theory qualitatively accounts for psychophysical experiments on motion occlusion and motion outliers in deriving our theory we assumed spatial factorizability of the probability distributions and made the approximation of updating the marginal distributions of velocity at each point this allowed us to perform local computations and simplified our implementation we argue that these approximations are suitable for the stimuli we are considering for which spatial coherence effects are negligible

on a special picture of dynamical evolution of nonlinear quantum systems in the phase space representation abstract a special picture of quantum evolution in the phase space representation is derived in this picture both the symbols of operators as well as the distribution density carry part of the time dependence the symbols of operators evolve classically whereas the distribution density carries the remaining time dependence which is needed to recover the full time dependence of quantum averages such representation is free of semiclassical expansions or a mixed classical quantum description the spin boson hamiltonian system is explicitly studied its phase space structure is established by obtaining analytical solutions for the three stable regions quantum averages are calculated

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

linear signal synthesis using the radon wigner transform thresholding the radon wigner transform rwt followed by filtered backprojection to the time frequency plane reduces noise and cross term power for multicomponent linear fm signals although the rwt is bilinear it may be calculated as the magnitude squared of two linear functions in this paper we derive a linear synthesis algorithm from the rwt and demonstrate its efficacy

numerical identification of a robin coefficient in parabolic problems this paper studies a regularization approach for an inverse problem of estimating a spatially and temporally dependent robin coefficient arising in the analysis of convective heat transfer the parameter to state map is analyzed especially a differentiability result is established a regularization approach is proposed and the properties e g existence and optimality system of the functional are investigated a finite element method is adopted for discretizing the continuous optimization problem and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established numerical results by the conjugate gradient method for oneand two dimensional problems are presented

signals on graphs transforms and tomograms abstract development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks generalizations of the fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices by exploring mappings of the spectrum of these matrices we show how to construct more general transforms in particular wavelet like transforms on graphs for time series tomograms a generalization of the radon transforms to arbitrary pairs of non commuting operators are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise here the notion of tomogram is also extended to signals on arbitrary graphs

alternative commutation relations star products and tomography invertible maps from operators of quantum observables onto functions of c number arguments and their associative products are first assessed different types of maps such as the weyl wigner stratonovich map and s ordered quasi distribution are discussed the recently introduced symplectic tomography map of observables tomograms related to the heisenberg weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c number functions the star product for symbols of the quantum observable for each one of the maps including the tomographic map and explicit relations among different star products are obtained deformations of the moyal star product and alternative commutation relations are also considered

finite element approximation of parabolic time optimal control problems the numerical approximation of a parabolic time optimal control problem via piecewise linear splines is considered at each stage of the approximation a bang bang approximate control is selected by solving for its switching times as the solution of a constrained nonlinear least squares optimization problem the well posedness of the approximation scheme is shown and the rate of convergence to the exact solution investigated numerical results for some one and two dimensional parabolic control problems are given

probabilistic and sequential computation of optical flow using temporal coherence in the computation of dense optical flow fields spatial coherence constraints are commonly used to regularize otherwise ill posed problem formulations providing spatial integration of data we present a temporal multiframe extension of the dense optical flow estimation formulation proposed by horn and schunck 1981 in which we use a temporal coherence constraint to yield the optimal fusing of data from multiple frames of measurements conceptually standard kalman filtering algorithms are applicable to the resulting multiframe optical flow estimation problem providing a solution that is sequential and recursive in time experiments are presented to demonstrate that the resulting multiframe estimates are more robust to noise than those provided by the original single frame formulation in addition we demonstrate cases where the aperture problem of motion vision cannot be resolved satisfactorily without the temporal integration of data enabled by the proposed formulation practically the large matrix dimensions involved in the problem prohibit exact implementation of the optimal kalman filter to overcome this limitation we present a computationally efficient yet near optimal approximation of the exact filtering algorithm this approximation has a precise interpretation as the sequential estimation of a reduced order spatial model for the optical flow estimation error process at each time step and arises from an estimation theoretic treatment of the filtering problem experiments also demonstrate the efficacy of this near optimal filter

wigner distribution function for euclidean systems euclidean systems include poly and monochromatic wide angle optics acoustics and also infinite discrete data sets we use a recently defined wigner operator and quasiprobability distribution function to set up and study the phase space evolution of these models subject to differential and difference equations respectively infinite data sets and two dimensional monochromatic helmholtz fields are thus shown by their wigner function on a cylinder of direction and location the wigner function for polychromatic wavefields has c number coordinates of two dimensional wavenumber and position

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

ritz galerkin approximation of the time optimal boundary control problem for parabolic systems with dirichlet boundary conditions this paper deals with ritz galerkin approximations of the following two problems i boundary value problems with l 2 boundary data given in the form of dirichlet boundary conditions ii time optimal control problems for parabolic systems with control acting on the boundary in both cases optimal rates of convergence of approximation are obtained also the specialization is considered to approximating with nonconformal elements which are not required to satisfy boundary conditions corresponding rates of convergence are also proved

impsac synthesis of importance sampling and random sample consensus this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation either due to large rotation or wide baseline of the cameras the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation the method operates on a pyramid from coarse to fine resolution thus raising the problem of how to propagate information from one level to another in a statistically consistent way the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles at the coarsest level a random sample consensus monte carlo markov chain ransac mcmc estimator is used to initialize this set of particles the posterior can then be approximated as a mixture of gaussians fitted to these particles the distribution at a coarser level influences the distribution at a finer level using the technique of sampling importance resampling sir and mcmc which allows for asymptotically correct approximations of the posterior distribution the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles which can be further improved by mcmc it is shown that the method is superior to previous single resolution ransac style feature matchers

analysis and finite element approximation of optimal control problems for the stationary navier stokes equations with distributed and neumann controls we examine certain analytic and numerical aspects of optimal control problems for the stationary navier stokes equations the controls considered may be of either the distributed or neumann type the functionals minimized are either the viscous dissipation or the l4 distance of candidate flows to some desired flow we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider the approximation by finite element methods of solutions of the optimality system and derive optimal error estimates

a posteriori error estimates for optimal control problems governed by parabolic equations in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation we obtain a posteriori error estimates for both the state and the control approximation such estimates which are apparently not available in the literature are an important step towards developing reliable adaptive finite element approximation schemes for the control problem

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions semidiscrete finite element error estimates for linear parabolic equations are derived under minimal regularity with the help of l2 projectors then analogous minimal regularity semidiscrete error estimates for semilinear parabolic equations are derived

identical particle states in the probability representation of quantum mechanics we study the symmetry properties under permutation of tomograms describing the states of a system of identical particles in the probability representation starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution explicit calculations are performed for the two dimensional harmonic oscillator

tomograms and other transforms a unified view a general framework is presented which unifies the treatment of wavelet like quasidistribution and tomographic transforms explicit formulae relating the three types of transforms are obtained the case of transforms associated with the symplectic and affine groups is treated in some detail special emphasis is given to the properties of the scale time and scale frequency tomograms tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

conditional mean estimation via jump diffusion processes in multiple target tracking recognition a new algorithm is presented for generating the conditional mean estimates of functions of target positions orientations and type in recognition and tracking of an unknown number of targets and target types taking a bayesian approach a posterior measure is defined on the tracking target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model and a prior based on airplane dynamics the newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion the conditional mean estimates are generated using a random sampling algorithm based on jump diffusion processes for empirically generating mmse estimates of functions of these random target positions orientations and type under the posterior measure results are presented on target tracking and identification from an implementation of the algorithm on a networked silicon graphics workstation and decmpp maspar parallel machine

wigner distribution function for finite systems we construct a wigner distribution function for finite data sets it is based on a finite optical system a linear wave guide where the finite number of discrete sensors is equal to the number of modes which the guide can carry the dynamical group for this model is su 2 and the wave functions are sets of n 2l 1 data points the wigner distribution function assigns classical c numbers to the operators of position momentum and wave guide mode

bayesian neighborhood component analysis learning a distance metric in feature space potentially improves the performance of the k nearest neighbor classifier and is useful in many real world applications many metric learning ml algorithms are however based on the point estimation of a quadratic optimization problem which is time consuming susceptible to overfitting and lacks a natural mechanism to reason with parameter uncertainty a property useful especially when the training set is small and or noisy to deal with these issues we present a novel bayesian ml bml method called bayesian neighborhood component analysis nca based on the well known nca method in which the metric posterior is characterized by the local label consistency constraints of observations encoded with a similarity graph instead of independent pairwise constraints for efficient bayesian inference we explore the variational lower bound over the log likelihood of the original nca objective experiments on several publicly available data sets demonstrate that the proposed method is able to learn robust metric measures from small size data set and or from challenging training set with labels contaminated by errors the proposed method is also shown to outperform a previous pairwise constrained bml method

a mathematical analysis of the motion coherence theory in motion perception there are a number of important phenomena involving coherence examples include motion capture and motion cooperativity we propose a theoretical model called the motion coherence theory that gives a possible explanation for these effects 1 2 in this framework the aperture problem can also be thought of as a problem of coherence and given a similar explanation we propose the concept of a velocity field defined everywhere in the image even where there is no explicit motion information available theough a cost function the model imposes smoothness on the velocity field in a more general way than in previous theories in this paper we provide a detailed theoretical analysis of the motion coherence theory we discuss its relations with previous theories and show that some of them are approximations to it a second paper 3 provides extensions for temporal coherence and comparisons to psychophysical phenomena the theory applies to both short range and long range motion it places them in the same computational framework and provides a way to define interactions between the two processes

semidiscrete approximations of optimal robin boundary control problems constrained by semilinear parabolic pde an optimal robin boundary control problem associated with semilinear parabolic partial differential equations is considered existence of an optimal solution is proved and an optimality system of equations is derived semidiscrete finite element approximations of the optimality system are defined and error estimates are obtained

optimal nonlinear filtering of quantum state the aim of this paper is to give an interpretation of the linear or nonlinear filtration problem as a quantization problem based on this we extend the optimal filtering equation known from the stratonovich filtering theory on the quantum process case in contrast to the kalman filter often used in such problems the stratonovich equation provides the optimal solution for nonlinear observation models the observation model is based on an indirect measurement method where the measurement is performed on an ancilla system that is interacted with an unknown one the latter model is interpreted in case of a single qudit system since the measured random variables and experiment are fundamentally different from each other the obtained single qudit observation model has a substantially different physical nature from the two qubit one however in both problems the stratonovich optimal filter equation is equally applicable

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

motion based prediction is sufficient to solve the aperture problem in low level sensory systems it is still unclear how the noisy information collected locally by neurons may give rise to a coherent global percept this is well demonstrated for the detection of motion in the aperture problem as luminance of an elongated line is symmetrical along its axis tangential velocity is ambiguous when measured locally here we develop the hypothesis that motion based predictive coding is sufficient to infer global motion our implementation is based on a context dependent diffusion of a probabilistic representation of motion we observe in simulations a progressive solution to the aperture problem similar to physio logy and behavior we demonstrate that this solution is the result of two underlying mechanisms first we demonstrate the formation of a tracking behavior favoring temporally coherent features independent of their texture second we observe that incoherent features are explained away while coherent information diffuses progressively to the global scale most previous models included ad hoc mechanisms such as end stopped cells or a selection layer to track specific luminance based features as necessary conditions to solve the aperture problem here we have proved that motion based predictive coding as it is implemented in this functional model is sufficient to solve the aperture problem this solution may give insights into the role of prediction underlying a large class of sensory computations

the contracting curve density algorithm fitting parametric curve models to images using local self adapting separation criteria the task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications such as image segmentation pose estimation object tracking and 3 d reconstruction in this article we propose the contracting curve density ccd algorithm as a solution to the curve fitting problem the ccd algorithm extends the state of the art in two important ways first it applies a novel likelihood function for the assessment of a fit between the curve model and the image data this likelihood function can cope with highly inhomogeneous image regions because it is formulated in terms of local image statistics the local image statistics are learned on the fly from the vicinity of the expected curve they provide therefore locally adapted criteria for separating the adjacent image regions these local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties the second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters these blurred curve models enable the algorithm to trade off two conflicting objectives namely heaving a large area of convergence and achieving high accuracy we apply the ccd algorithm to several challenging image segmentation and 3 d pose estimation problems our experiments with rgb images show that the ccd algorithm achieves a high level of robustness and sub pixel accuracy even in the presence of severe texture shading clutter partial occlusion and strong changes of illumination

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

a class of affine wigner functions with extended covariance properties affine wigner functions are phase space representations based on the affine group in place of the usual weyl heisenberg group of quantum mechanics such representations are relevant to the time frequency analysis of real signals an interesting family is singled out by the requirement of covariance with respect to each solvable three parameter group containing the affine group explicit forms are given in each case and properties such as unitarity and localization are discussed some particular distributions are recovered

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

particle filter with a mode tracker for visual tracking across illumination changes in this correspondence our goal is to develop a visual tracking algorithm that is able to track moving objects in the presence of illumination variations in the scene and that is robust to occlusions we treat the illumination and motion x y translation and scale parameters as the unknown state sequence the observation is the entire image and the observation model allows for occasional occlusions modeled as outliers the nonlinearity and multimodality of the observation model necessitate the use of a particle filter pf due to the inclusion of illumination parameters the state dimension increases thus making regular pfs impractically expensive we show that the recently proposed approach using a pf with a mode tracker can be used here since even in most occlusion cases the posterior of illumination conditioned on motion and the previous state is unimodal and quite narrow the key idea is to importance sample on the motion states while approximating importance sampling by posterior mode tracking for estimating illumination experiments demonstrate the advantage of the proposed algorithm over existing pf based approaches for various face and vehicle tracking we are also able to detect illumination model changes e g those due to transition from shadow to sunlight or vice versa by using the generalized expected log likelihood statistics and successfully compensate for it without ever loosing track

error estimates for discontinuous galerkin time stepping schemes for robin boundary control problems constrained to parabolic pdes we consider fully discrete finite element approximations of a robin optimal boundary control problem constrained by linear parabolic pdes with rough initial data conforming finite element methods for spatial discretization combined with discontinuous time stepping galerkin schemes are being used for the space time discretization error estimates are proved under weak regularity hypotheses for the state adjoint and control variables computational examples validating our expected rates of convergence are also provided

finite dimensional approximation of a class of constrained nonlinear optimal control problems an abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed nonlinearities occur in both the objective functional and the constraints the framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces an approximate problem posed on finite dimensional spaces together with a number of hypotheses concerning the two problems the framework is used to show that optimal solutions exist to show that lagrange multipliers may be used to enforce the constraints to derive an optimality system from which optimal states and controls may be deduced and to derive existence results and error estimates for solutions of the approximate problem the abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods the first involves the von k arm an plate equations of nonlinear elasticity the second the ginzburg landau equations of superconductivity and the third the navier stokes equations for incompressible viscous flows

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

differential earth mover s distance with its applications to visual tracking the earth mover s distance emd is a similarity measure that captures perceptual difference between two distributions its computational complexity however prevents a direct use in many applications this paper proposes a novel differential emd demd algorithm based on the sensitivity analysis of the simplex method and offers a speedup at orders of magnitude compared with its brute force counterparts the demd algorithm is discussed and empirically verified in the visual tracking context the deformations of the distributions for objects at different time instances are accommodated well by the emd and the differential algorithm makes the use of emd in real time tracking possible to further reduce the computation signatures i e variable size descriptions of distributions are employed as an object representation the new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard mean shift tracker is demonstrated

shape tracking with occlusions via coarse to fine region based sobolev descent we present a method to track the shape of an object from video the method uses a joint shape and appearance model of the object which is propagated to match shape and radiance in subsequent frames determining object shape self occlusions and dis occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking they are unable to adapt to new shape and appearance information leading to inaccurate shape detection in this work we model self occlusions and dis occlusions in a joint shape and appearance tracking framework self occlusions and the warp to propagate the model are coupled thus we formulate a joint optimization problem we derive a coarse to fine optimization method advantageous in tracking that initially perturbs the model by coarse perturbations before transitioning to finer scale perturbations seamlessly this coarse to fine behavior is automatically induced by gradient descent on a novel infinite dimensional riemannian manifold that we introduce the manifold consists of planar parameterized regions and the metric that we introduce is a novel sobolev metric experiments on video exhibiting occlusions dis occlusions complex radiance and background show that occlusion dis occlusion modeling leads to superior shape accuracy

mesh independence of the gradient projection method for optimal control problems the gradient projection method and its application to optimal control have been analyzed with regard to the rate of convergence quite extensively here another aspect of this method is considered in finite dimension the set of active indices is identified after finitely many iterations under mild nondegeneracy assumptions however it is clear that this property is restricted to the finite dimensional case in this paper for example a sequence of discretized optimal control problems is considered and it is observed that the number of steps to identify all active indices increases with the refinement of the discretization a result analogous to the finite dimensional result is valid in this situation if identification of active indices is understood in the correct light this paper shows that if a different termination criterion is imposed then the number of necessary steps for termination is indeed mesh independent numerical observations illustrating this result are reported for various examples fr

asymptotic stabilization of vibrating composite plates this paper presents a solution to the boundary stabilization problem of free vibration of composite plates it is assumed that an object such as a flange which has mass and mass moment of inertia can be attached to the free portion of the boundary of the plate both cases of with and without boundary object have been analyzed for other types of plates by many researches in the presence of boundary mass and mass moment of inertia two ordinary differential equations govern their motion for both cases the plate dynamics is presented by a linear fourth order partial differential equation pde linear boundary control laws are constructed to stabilize the composite plates asymptotically the control forces and moments consist of feedbacks of the velocity and normal derivative of the velocity at the boundaries of the plate asymptotic stabilization of free vibration of composite plates in both cases i e with and without boundary object is achieved via boundary actions finally it is shown that exponentially stability of the hybrid system cannot be fulfilled in the other words the asymptotical stability is the best our main tools in this article are semigroup techniques spectral theory of the linear operators and lyapunov stability method