identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

a local algorithm for the computation of image velocity via constructive interference of global fourier components a novel fourier based technique for local motion detection from image sequences is proposed in this method the instantaneous velocities of local image points are inferred directly from the global 3d fourier components of the image sequence this is done by selecting those velocities for which the superposition of the corresponding fourier gratings leads to constructive interference at the image point hence image velocities can be assigned locally even though position is computed from the phases and amplitudes of global fourier components spanning the whole image sequence that have been filtered based on the motion constraint equation reducing certain aperture effects typically arising from windowing in other methods regularization is introduced for sequences having smooth flow fields aperture effects and their effect on optic flow regularization are investigated in this context the algorithm is tested on both synthetic and real image sequences and the results are compared to those of other local methods finally we show that other motion features i e motion direction can be computed using the same algorithmic framework without requiring an intermediate representation of local velocity which is an important characteristic of the proposed method

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

adaptive grid refinement procedures for efficient optical flow computation two approaches are described that improve the efficiency of optical flow computation without incurring loss of accuracy the first approach segments images into regions of moving objects the method is based on a previously defined galerkin finite element method on a triangular mesh combined with a multiresolution segmentation approach for object flow computation images are automatically segmented into subdomains of moving objects by an algorithm that employs a hierarchy of mesh coarseness for the flow computation and these subdomains are reconstructed over a finer mesh on which to recompute flow more accurately the second approach uses an adaptive mesh in which the resolution increases where motion is found to occur optical flow is computed over a reasonably coarse mesh and this is used to construct an optimal adaptive mesh in a way that is different from the gradient methods reported in the literature the finite element mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene i e those areas where motion is detected the proposed methods were tested on real and synthetic image sequences and promising results are reported

motion competition a variational approach to piecewise parametric motion segmentation we present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence our model is based on a conditional probability for the spatio temporal image gradient given a particular velocity model and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length exploiting the bayesian framework we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions the resulting functional can be interpreted as an extension of the mumford shah functional from intensity segmentation to motion segmentation in contrast to most alternative approaches the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set we propose two different representations of this motion boundary an explicit spline based implementation which can be applied to the motion based tracking of a single moving object and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects numerical results both for simulated ground truth experiments and for real world sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

a convex optimization approach for depth estimation under illumination variation illumination changes cause serious problems in many computer vision applications we present a new method for addressing robust depth estimation from a stereo pair under varying illumination conditions first a spatially varying multiplicative model is developed to account for brightness changes induced between left and right views the depth estimation problem based on this model is then formulated as a constrained optimization problem in which an appropriate convex objective function is minimized under various convex constraints modelling prior knowledge and observed information the resulting multiconstrained optimization problem is finally solved via a parallel block iterative algorithm which offers great flexibility in the incorporation of several constraints experimental results on both synthetic and real stereo pairs demonstrate the good performance of our method to efficiently recover depth and illumination variation fields simultaneously

generalised nonlocal image smoothing we propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches one of such dissimilarity measures is the weighted l 2 distance between patches in such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain it can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels but also the similarity of their corresponding neighbours this leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure by slightly modifying the way the similarities are computed we obtain two related filters the nl means filter of buades et al siam multiscale model simul 4 2 490 530 2005b and the nds filter of mrazek et al geometric properties for incomplete data computational imaging and vision vol 31 pp 335 352 springer dordrecht 2006 in fact the proposed approach can be considered as a generalisation of the latter filter to the space of patches we also provide novel insights into relations of the nds filter with diffusion regularisation methods as well as with some recently proposed graph regularisation techniques we evaluate our method for the task of denoising greyscale and colour images degraded with gaussian and salt and pepper noise demonstrating that it compares very well to other more sophisticated approaches

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

drift estimation in sparse sequential dynamic imaging with application to nanoscale fluorescence microscopy summary a major challenge in many modern superresolution fluorescence microscopy techniques at the nanoscale lies in the correct alignment of long sequences of sparse but spatially and temporally highly resolved images this is caused by the temporal drift of the protein structure e g due to temporal thermal inhomogeneity of the object of interest or its supporting area during the observation process we develop a simple semiparametric model for drift correction in single marker switching microscopy then we propose an m estimator for the drift and show its asymptotic normality this is used to correct the final image and it is shown that this purely statistical method is competitive with state of the art calibration techniques which require the incorporation of fiducial markers in the specimen moreover a simple bootstrap algorithm allows us to quantify the precision of the drift estimate and its effect on the final image estimation we argue that purely statistical drift correction is even more robust than fiducial tracking rendering the latter superfluous in many applications the practicability of our method is demonstrated by a simulation study and by a single marker switching application this serves as a prototype for many other typical imaging techniques where sparse observations with high temporal resolution are blurred by motion of the object to be reconstructed

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

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

optical flow a curve evolution approach a novel approach for the computation of optical flow based on an l sup 1 type minimization is presented it is shown that the approach has inherent advantages since it does not smooth the flow velocity across the edges and hence preserves edge information a numerical approach based on computation of evolving curves is proposed for computing the optical flow field computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach

an analysis of physics based optical flow a variational solution of the physics based optical flow equation is studied for extraction of high resolution velocity fields from flow visualization images the solution to preserve discontinuities in a fluid velocity field is mathematically justified the uniqueness of the solution and the convergence of a successive approximation sequence are proven a numerical algorithm is developed and examined through numerical experiments

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

symmetrical dense optical flow estimation with occlusions detection traditional techniques of dense optical flow estimation do not generally yield symmetrical solutions the results will differ if they are applied between images i 1 and i 2 or between images i 2 and i 1 in this work we present a method to recover a dense optical flow field map from two images while explicitely taking into account the symmetry across the images as well as possible occlusions in the flow field the idea is to consider both displacements vectors from i 1 to i 2 and i 2 to i 1 and to minimise an energy functional that explicitely encodes all those properties this variational problem is then solved using the gradient flow defined by the euler lagrange equations associated to the energy to prove the importance of the concepts of symmetry and occlusions for optical flow computation we have extended a classical approach to handle those experiments clearly show the added value of these properties to improve the accuracy of the computed flows figures appear in color in the online version of this paper

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

complex valued b spline neural networks for modeling and inverting hammerstein systems many communication signal processing applications involve modeling and inverting complex valued cv hammerstein systems we develop a new cv b spline neural network approach for efficient identification of the cv hammerstein system and effective inversion of the estimated cv hammerstein model in particular the cv nonlinear static function in the hammerstein system is represented using the tensor product from two univariate b spline neural networks an efficient alternating least squares estimation method is adopted for identifying the cv linear dynamic model s coefficients and the cv b spline neural network s weights which yields the closed form solutions for both the linear dynamic model s coefficients and the b spline neural network s weights and this estimation process is guaranteed to converge very fast to a unique minimum solution furthermore an accurate inversion of the cv hammerstein system can readily be obtained using the estimated model in particular the inversion of the cv nonlinear static function in the hammerstein system can be calculated effectively using a gaussian newton algorithm which naturally incorporates the efficient de boor algorithm with both the b spline curve and first order derivative recursions the effectiveness of our approach is demonstrated using the application to equalization of hammerstein channels

combining total variation regularization with window based time delay estimation in ultrasound elastography a major challenge of free hand palpation ultrasound elastography use is estimating the displacement of rf samples between pre and post compressed rf data the problem of displacement estimation is ill posed since the displacement of one sample by itself cannot be uniquely calculated to resolve this problem two categories of methods have emerged the first category assumes that the displacement of samples within a small window surrounding the reference sample is constant the second class imposes smoothness regularization and optimizes an energy function herein we propose a novel method that combines both approaches and as such is more robust to noise the second contribution of this work is the introduction of the l1 norm as the regularization term in our cost function which is often referred to as the total variation tv regularization compared to previous work that used the l2 norm regularization optimization of the new cost function is more challenging however the advantages of using the l1 norm are twofold first it leads to substantial improvement in the sharpness of displacement estimates second to optimize the cost function with the l1 norm regularization we use an iterative method that further increases the robustness we name our proposed method total variation regularization and window based time delay estimation overwind and show that it is robust to signal decorrelation and generates sharp displacement and strain maps for simulated experimental phantom and in vivo data in particular overwind improves strain contrast to noise ratio cnr by 27 26 144 05 and 49 90 on average in simulation phantom and in vivo data respectively compared to our recent global ultrasound elastography glue method

series expansion approach to the analysis and identification of discrete hammerstein systems in this paper a finite series expansion method is presented for the analysis and parameter identification of a discrete non linear system that is described by a hammerstein model consisting of a memoryless gain of polynomial form followed by a linear discrete system by expanding the system variables in discrete legendre orthogonal polynomials dlops and using the shift and product operational properties of dlops the hammerstein model is converted into a set of linear equations in the dlop coefficients of unknown output variables and in the system parameters this converted set of linear algebraic equations is convenient for finding the dlop coefficients of unknown variables also it allows one to determine the unknown system parameters using the least squares method when the system input and output data are available

dense estimation and object based segmentation of the optical flow with robust techniques we address the issue of recovering and segmenting the apparent velocity field in sequences of images as for motion estimation we minimize an objective function involving two robust terms the first one cautiously captures the optical flow constraint while the second a priori term incorporates a discontinuity preserving smoothness constraint to cope with the nonconvex minimization problem thus defined we design an efficient deterministic multigrid procedure it converges fast toward estimates of good quality while revealing the large discontinuity structures of flow fields we then propose an extension of the model by attaching to it a flexible object based segmentation device based on deformable closed curves different families of curve equipped with different kinds of prior can be easily supported experimental results on synthetic and natural sequences are presented including an analysis of sensitivity to parameter tuning

on the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction gradient based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field the author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey level image intensity function based on three simple assumptions about the smoothness constraint 1 it must be expressed in a form that is independent of the choice of cartesian coordinate system in the image 2 it must be positive definite and 3 it must not couple different component of the optical flow it is shown that there are essentially only four such constraints any smoothness constraint satisfying 1 2 or 3 must be a linear combination of these four possibly multiplied by certain quantities invariant under a change in the cartesian coordinate system beginning with the three assumptions mentioned above the author mathematically demonstrates that all best known smoothness constraints appearing in the literature are special cases of this general form and in particular that the weight matrix introduced by h h nagel is essentially modulo invariant quantities the only physically plausible such constraint

dense estimation of fluid flows in this paper we address the problem of estimating and analyzing the motion of fluids in image sequences due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids the standard techniques from computer vision originally designed for quasi rigid motions with stable salient features are not well adapted in this context we thus investigate a dedicated minimization based motion estimator the cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics which is compatible with large displacements this term is associated with an original second order div curl regularization which prevents the washing out of the salient vorticity and divergence structures the performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images in addition we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence

highly accurate optic flow computation with theoretically justified warping in this paper we suggest a variational model for optic flow computation based on non linearised and higher order constancy assumptions besides the common grey value constancy assumption also gradient constancy as well as the constancy of the hessian and the laplacian are proposed since the model strictly refrains from a linearisation of these assumptions it is also capable to deal with large displacements for the minimisation of the rather complex energy functional we present an efficient numerical scheme employing two nested fixed point iterations following a coarse to fine strategy it turns out that there is a theoretical foundation of so called warping techniques hitherto justified only on an experimental basis since our algorithm consists of the integration of various concepts ranging from different constancy assumptions to numerical implementation issues a detailed account of the effect of each of these concepts is included in the experimental section the superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

on functionals with greyvalue controlled smoothness terms for determining optical flow the modification by h h nagel 1987 of the approach developed by b k p horn and b g schunck 1981 for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation applying this scheme to three constraint equations reported in the literature as a special case a generalization of nagel s approach is obtained an existence and uniqueness result of solutions under very general conditions that in turn ensures the applicability of standard techniques to compute an approximate solution is presented

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

output error convergence of adaptive filters with compensation for output nonlinearities output error convergence of a wiener model based nonlinear stochastic gradient algorithm is analyzed the normalized scheme estimates the parameters of a linear finite impulse response model in cascade with a known output nonlinearity the algorithm can be interpreted as a normalized least mean square algorithm with compensation for an output nonlinearity linearizing inversion of the nonlinearity is not utilized global output error convergence is then proved provided that the nonlinearity is monotone not strictly monotone and provided that a previously observed mechanism resulting in deadlock does not occur the algorithm and the analysis include important practical cases like sensor saturation and dead zones that must be excluded when global parametric convergence is studied

weighted curvature preserving pde image filtering method the tensor driven curvature preserving partial differential equation is an outstanding anisotropic diffusion filtering model to effectively preserve image edge well a weighted curvature preserving pde based filtering method is proposed which employ local image directional information to design weight coefficient for different vector fields experimental results indicate that new approach shows superior performance on preserving image edge and curvature geometric structure

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

a hyperelastic regularization energy for image registration image registration is one of the most challenging problems in image processing where ill posedness arises due to noisy data as well as nonuniqueness and hence the choice of regularization is crucial this paper presents hyperelasticity as a regularizer and introduces a new and stable numerical implementation on one hand hyperelastic registration is an appropriate model for large and highly nonlinear deformations for which a linear elastic model needs to fail on the other hand the hyperelastic regularizer yields very regular and diffeomorphic transformations while hyperelasticity might be considered as just an additional outstanding regularization option for some applications it becomes inevitable for applications involving higher order distance measures like mass preserving registration the paper gives a short introduction to image registration and hyperelasticity the hyperelastic image registration problem is phrased in a variational setting and an existence proof is provided the focus of th

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

variational optical flow estimation based on stick tensor voting variational optical flow techniques allow the estimation of flow fields from spatio temporal derivatives they are based on minimizing a functional that contains a data term and a regularization term recently numerous approaches have been presented for improving the accuracy of the estimated flow fields among them tensor voting has been shown to be particularly effective in the preservation of flow discontinuities this paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than full tensor voting in addition an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields finally a weighted non local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field the proposed approach yields state of the art results on the middlebury benchmark

estimation of optical flow based on higher order spatiotemporal derivatives in interlaced and non interlaced image sequences abstract this contribution 1 investigates local differential techniques for estimating optical flow and its derivatives based on the brightness change constraint by using the tensor calculus representation we build the taylor expansion of the gray value derivatives as well as of the optical flow in a spatiotemporal neighborhood such a formulation provides a unifying framework for all existing local differential approaches and allows to derive new systems of equations for the estimation of the optical flow and of its derivatives we also tested various optical flow estimation approaches on real image sequences recorded by a calibrated camera which was fixed on the arm of a robot by moving the arm of the robot along a precisely defined trajectory we can determine the true displacement rate of scene surface elements projected into the image plane and compare it quantitatively with the results of different optical flow estimators since the optical flow estimators are based on gray value derivatives of up to fourth order we were forced to develop modified gaussian derivative filters to obtain acceptable estimates for the derivatives further we show quantitatively that these filters contribute to a much more robust optical flow estimation in addition successive lines of tv cameras have an offset in time due to the interlace technique we demonstrate the adaptation of filter kernels for estimating higher order spatiotemporal derivatives in interlaced image sequences

brief paper computational complexity analysis of set membership identification of hammerstein and wiener systems this paper analyzes the computational complexity of set membership identification of hammerstein and wiener systems its main results show that even in cases where a portion of the plant is known the problems are generically np hard both in the number of experimental data points and in the number of inputs wiener or outputs hammerstein of the nonlinearity these results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point out the need for developing computationally tractable relaxations

an analytic geometry approach to wiener system frequency identification this paper addresses the problem of wiener system identification the underlying linear subsystem is stable but not necessarily parametric the nonlinear element in turn is allowed to be nonparametric noninvertible and nonsmooth as wiener models are uniquely defined up to an uncertain multiplicative factor it makes sense to start the frequency identification process estimating the system phase which is common to all models to this end a consistent estimator is designed using analytic geometry tools accordingly the system frequency behavior is characterized by a family of lissajous curves interestingly all these curves are candidates to modelling the system nonlinearity but the most convenient one is the less spread of them finally the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates

identification of wiener systems with clipped observations in this paper we consider the parametric version of wiener systems where both the linear and nonlinear parts are identified with clipped observations in the presence of internal and external noises also the static functions are allowed noninvertible we propose a classification based support vector machine svm and formulate the identification problem as a convex optimization the solution to the optimization problem converges to the true parameters of the linear system if it is an finite impulse response fir system even though clipping reduces a great deal of information about the system characteristics in identifying a wiener system with a stable infinite impulse response iir system an fir system is used to approximate it and the problem is converted to identifying the fir system together with solving a set of nonlinear equations this leads to biased estimates of parameters in the iir system while the bias can be controlled by choosing the order of the approximated fir system

towards identification of wiener systems with the least amount of a priori information on the nonlinearity in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the fir linear part is identifiable in the non gaussian input case three types of a priori information are considered including quadrant information point information and locally monotonous information in all three cases identifiability has been established and corresponding identification algorithms are developed with their convergence proofs

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

towards identification of wiener systems with the least amount of a priori information iir cases in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non gaussian input case under the white noise input three types of a priori information are considered quadrant information point information and monotonic information in all three cases identifiability has been established and the corresponding nonparametric identification algorithms are developed along with their convergence proofs

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

optical flow estimation for a periodic image sequence we propose a temporal modeling approach for determining image motion from a sequence of images wherein the inherent motion is periodic over time to exploit the periodic nature of the motion we use a fourier harmonic representation to model the temporal evolution of the motion field for the entire sequence we then determine the motion field simultaneously for the different image frames by estimating the parameters of this representation model where the model order in the fourier representation serves as a regularization parameter on the temporal coherence of the motion field this approach can take advantage of the statistics of all the available data in the image sequence in our experiments we tested the proposed approach on several motion types at different noise levels including translational motion convergent divergent motion and cardiac motion our results demonstrate that this approach could lead to more robust estimation of the motion field in the presence of strong imaging noise compared to a frame by frame estimation approach

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

domain decomposition for variational optical flow computation we present an approach to parallel variational optical flow computation by using an arbitrary partition of the image plane and iteratively solving related local variational problems associated with each subdomain the approach is particularly suited for implementations on pc clusters because interprocess communication is minimized by restricting the exchange of data to a lower dimensional interface our mathematical formulation supports various generalizations to linear nonlinear convex variational approaches three dimensional image sequences spatiotemporal regularization and unstructured geometries and triangulations results concerning the effects of interface preconditioning as well as runtime and communication volume measurements on a pc cluster are presented our approach provides a major step toward real time two dimensional image processing using off the shelf pc hardware and facilitates the efficient application of variational approaches to large scale image processing problems

dense versus sparse approaches for estimating the fundamental matrix there are two main strategies for solving correspondence problems in computer vision sparse local feature based approaches and dense global energy based methods while sparse feature based methods are often used for estimating the fundamental matrix by matching a small set of sophistically optimised interest points dense energy based methods mark the state of the art in optical flow computation the goal of our paper is to show that this separation into different application domains is unnecessary and can be bridged in a natural way as a first contribution we present a new application of dense optical flow for estimating the fundamental matrix comparing our results with those obtained by feature based techniques we identify cases in which dense methods have advantages over sparse approaches motivated by these promising results we propose as a second contribution a new variational model that recovers the fundamental matrix and the optical flow simultaneously as the minimisers of a single energy functional in experiments we show that our coupled approach is able to further improve the estimates of both the fundamental matrix and the optical flow our results prove that dense variational methods can be a serious alternative even in classical application domains of sparse feature based approaches

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

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

coping with model error in variational data assimilation using optimal mass transport classical variational data assimilation methods address the problem of optimally combining model predictions with observations in the presence of zero mean gaussian random errors however in many natural systems uncertainty in model structure and or model parameters often results in systematic errors or biases prior knowledge about such systematic model error for parametric removal is not always feasible in practice limiting the efficient use of observations for improved prediction the main contribution of this work is to advocate the relevance of transportation metrics for quantifying nonrandom model error in variational data assimilation for nonnegative natural states and fluxes transportation metrics also known as wasserstein metrics originate in the theory of optimal mass transport omt and provide a nonparametric way to compare distributions which is natural in the sense that it penalizes mismatch in the values and relative position of masses in the two distributions we demonstrate the promise of the proposed methodology using 1 d and 2 d advection diffusion dynamics with systematic error in the velocity and diffusivity parameters moreover we combine this methodology with additional regularization functionals such as the l1 norm of the state in a properly chosen domain to incorporate both model error and potential prior information in the presence of sparsity or sharp fronts in the underlying state of interest

bayesian inference of models and hyperparameters for robust optical flow estimation selecting optimal models and hyperparameters is crucial for accurate optical flow estimation this paper provides a solution to the problem in a generic bayesian framework the method is based on a conditional model linking the image intensity function the unknown velocity field hyperparameters and the prior and likelihood motion models inference is performed on each of the three levels of this so defined hierarchical model by maximization of marginalized a posteriori probability distribution functions in particular the first level is used to achieve motion estimation in a classical a posteriori scheme by marginalizing out the motion variable the second level enables to infer regularization coefficients and hyperparameters of non gaussian m estimators commonly used in robust statistics the last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data the method is evaluated on image sequences of fluid flows and from the middlebury database experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state of the art methods

a multigrid platform for real time motion computation with discontinuity preserving variational methods variational methods are among the most accurate techniques for estimating the optic flow they yield dense flow fields and can be designed such that they preserve discontinuities estimate large displacements correctly and perform well under noise and varying illumination however such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution consequently variational methods are considered to be too slow for real time performance in our paper we address this problem in two ways i we present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions thereby our work focuses particularly on regularisation strategies that preserve discontinuities ii we show by the examples of five classical and two recent variational techniques that real time performance is possible in all cases even for very complex optic flow models that offer high accuracy experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 120 can be achieved on a standard pc compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

optical flow and advection on 2 riemannian manifolds a common framework dynamic pattern analysis and motion extraction can be efficiently addressed using optical flow techniques this paper presents a generalization of these questions to nonflat surfaces where optical flow is tackled through the problem of evolution processes on non euclidean domains the classical equations of optical flow in the euclidean case are transposed to the theoretical framework of differential geometry we adopt this formulation for the regularized optical flow problem prove its mathematical well posedness and combine it with the advection equation the optical flow and advection problems are dual a motion field may be retrieved from some scalar evolution using optical flow conversely a scalar field may be deduced from a velocity field using advection these principles are illustrated with qualitative and quantitative evaluations from numerical simulations bridging both approaches the proof of concept is further demonstrated with preliminary results from time resolved functional brain imaging data where organized propagations of cortical activation patterns are evidenced using our approach

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data