tree approximations to markov random fields methods for approximately computing the marginal probability mass functions and means of a markov random field mrf by approximating the lattice by a tree are described applied to the a posteriori mrf these methods solve bayesian spatial pattern classification and image restoration problems the methods are described several theoretical results concerning fixed point problems are proven and four numerical examples are presented including comparison with optimal estimators and the iterated conditional mode estimator and including two agricultural optical remote sensing problems

the monogenic signal this paper introduces a two dimensional 2 d generalization of the analytic signal this novel approach is based on the riesz transform which is used instead of the hilbert transform the combination of a 2 d signal with the riesz transformed one yields a sophisticated 2 d analytic signal the monogenic signal the approach is derived analytically from irrotational and solenoidal vector fields based on local amplitude and local phase an appropriate local signal representation that preserves the split of identity i e the invariance equivariance property of signal decomposition is presented this is one of the central properties of the one dimensional 1 d analytic signal that decomposes a signal into structural and energetic information we show that further properties of the analytic signal concerning symmetry energy allpass transfer function and orthogonality are also preserved and we compare this with the behavior of other approaches for a 2 d analytic signal as a central topic of this paper a geometric phase interpretation that is based on the relation between the 1 d analytic signal and the 2 d monogenic signal established by the radon 1986 transform is introduced possible applications of this relationship are sketched and references to other applications of the monogenic signal are given

image registration based on autocorrelation of local structure registration of images in the presence of intra image signal fluctuations is a challenging task the definition of an appropriate objective function measuring the similarity between the images is crucial for accurate registration this paper introduces an objective function that embeds local phase features derived from the monogenic signal in the modality independent neighborhood descriptor mind the image similarity relies on the autocorrelation of local structure alost which has two important properties 1 low sensitivity to space variant intensity distortions e g differences in contrast enhancement in mri 2 high distinctiveness for salient image features such as edges the alost method is quantitatively compared to the mind approach based on three different datasets thoracic ct images synthetic and real abdominal mr images the proposed method outperformed the nmi and mind similarity measures on these three datasets the registration of dynamic contrast enhanced and post contrast mr images of patients with crohn s disease led to relative contrast enhancement measures with the highest correlation rm r 0 56 to the crohn s disease endoscopic index of severity

a proximal projection bundle method for lagrangian relaxation including semidefinite programming we give a proximal bundle method for minimizing a convex function f over a convex set c it requires evaluating f and its subgradients with a fixed but possibly unknown accuracy epsilon 0 each iteration involves solving an unconstrained proximal subproblem and projecting a certain point onto c the method asymptotically finds points that are epsilon optimal in lagrangian relaxation of convex programs it allows for e accurate solutions of lagrangian subproblems and finds e optimal primal solutions for semidefinite programming problems it extends the highly successful spectral bundle method to the case of inexact eigenvalue computations

multiresolution moment filters theory and applications we introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales when the window function satisfies a two scale relation we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet like algorithm we show that b splines are well suited window functions because in addition to being refinable they are positive symmetric separable and very nearly isotropic gaussian shape we present three applications of these multiscale local moments the first is a feature extraction method for detecting and characterizing elongated structures in images the second is a noise reduction method which can be viewed as a multiscale extension of savitzky golay filtering the third is a multiscale optical flow algorithm that uses a local affine model for the motion field extending the lucas kanade optical flow method the results obtained in all cases are promising

identifying regional cardiac abnormalities from myocardial strains using nontracking based strain estimation and spatio temporal tensor analysis myocardial strain is a critical indicator of many cardiac diseases and dysfunctions the goal of this paper is to extract and use the myocardial strain pattern from tagged magnetic resonance imaging mri to identify and localize regional abnormal cardiac function in human subjects in order to extract the myocardial strains from the tagged images we developed a novel nontracking based strain estimation method for tagged mri this method is based on the direct extraction of tag deformation and therefore avoids some limitations of conventional displacement or tracking based strain estimators based on the extracted spatio temporal strain patterns we have also developed a novel tensor based classification framework that better conserves the spatio temporal structure of the myocardial strain pattern than conventional vector based classification algorithms in addition the tensor based projection function keeps more of the information of the original feature space so that abnormal tensors in the subspace can be back projected to reveal the regional cardiac abnormality in a more physically meaningful way we have tested our novel methods on 41 human image sequences and achieved a classification rate of 87 80 the regional abnormalities recovered from our algorithm agree well with the patient s pathology and clinical image interpretation and provide a promising avenue for regional cardiac function analysis

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

proximal level bundle methods for convex nondifferentiable optimization saddle point problems and variational inequalities we study proximal level methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates of the optimal value we show that they enjoy almost optimal efficiency estimates we give extensions for solving convex constrained problems convex concave saddle point problems and variational inequalities with monotone operators we present several variants establish their efficiency estimates and discuss possible implementations in particular our methods require bounded storage in contrast to the original level methods of lemarechal nemirovskii and nesterov

new variants of bundle methods in this paper we describe a number of new variants of bundle methods for nonsmooth unconstrained and constrained convex optimization convex concave games and variational inequalities we outline the ideas underlying these methods and present rate of convergence estimates

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

comparison of bundle and classical column generation when a column generation approach is applied to decomposable mixed integer programming problems it is standard to formulate and solve the master problem as a linear program seen in the dual space this results in the algorithm known in the nonlinear programming community as the cutting plane algorithm of kelley and cheney goldstein however more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard one of them is the bundle method our aim is to illustrate its differences with kelley s method in the process we review alternative stabilization techniques used in column generation comparing them from both primal and dual points of view numerical comparisons are presented for five applications cutting stock which includes bin packing vertex coloring capacitated vehicle routing multi item lot sizing and traveling salesman we also give a sketchy comparison with the volume algorithm

non euclidean restricted memory level method for large scale convex optimization we propose a new subgradient type method for minimizing extremely large scale nonsmooth convex functions over simple domains the characteristic features of the method are a the possibility to adjust the scheme to the geometry of the feasible set thus allowing to get nearly dimension independent and nearly optimal in the large scale case rate of convergence results for minimization of a convex lipschitz continuous function over a euclidean ball a standard simplex and a spectahedron the set of positive semidefinite symmetric matrices of given size with unit trace b flexible handling of accumulated information allowing for tradeoff between the level of utilizing this information and iteration s complexity we present extensions of the scheme for the cases of minimizing non lipschitzian convex objectives finding saddle points of convex concave functions and solving variational inequalities with monotone operators finally we report on encouraging numerical results of experiments with test problems of dimensions up to 66 000

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

multiscale recursive estimation data fusion and regularization we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and or noisy measurements which may also be at several scales in particular multiscale signal representations lead naturally to pyramidal or tree like data structures in which each level in the tree corresponds to a particular scale of representation a class of multiscale dynamic models evolving on dyadic trees is introduced the main focus of this paper is on the description analysis and application of an extremely efficient optimal estimation algorithm for this class of models this algorithm consists of a fine to coarse filtering sweep followed by a coarse to fine smoothing step corresponding to the dyadic tree generalization of kalman filtering and rauch tung striebel smoothing the kalman filtering sweep consists of the recursive application of three steps a measurement update step a fine to coarse prediction step and a fusion step we illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of fractal regularizations of ill posed signal and image processing problems encountered

classification of textures using gaussian markov random fields the problem of texture classification arises in several disciplines such as remote sensing computer vision and image analysis in this paper we present two feature extraction methods for the classification of textures using two dimensional 2 d markov random field mrf models it is assumed that the given m m texture is generated by a gaussian mrf model in the first method the least square ls estimates of model parameters are used as features in the second method using the notion of sufficient statistics it is shown that the sample correlations over a symmetric window including the origin are optimal features for classification simple minimum distance classifiers using these two feature sets yield good classification accuracies for a seven class problem

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

classification on the monogenic scale space application to target recognition in sar image this paper introduces a novel classification strategy based on the monogenic scale space for target recognition in synthetic aperture radar sar image the proposed method exploits monogenic signal theory a multidimensional generalization of the analytic signal to capture the characteristics of sar image e g broad spectral information and simultaneous spatial localization the components derived from the monogenic signal at different scales are then applied into a recently developed framework sparse representation based classification src moreover to deal with the data set whose target classes are not linearly separable the classification via kernel combination is proposed where the multiple components of the monogenic signal are jointly considered into a unifying framework for target recognition the novelty of this paper comes from 1 the development of monogenic feature via uniformly downsampling normalization and concatenation of the components at various scales 2 the development of score level fusion for srcs and 3 the development of composite kernel learning for classification in particular the comparative experimental studies under nonliteral operating conditions e g structural modifications random noise corruption and variations in depression angle are performed the comparative experimental studies of various algorithms including the linear support vector machine and the kernel version the src and the variants kernel src kernel linear representation and sparse representation of monogenic signal are performed too the feasibility of the proposed method has been successfully verified using moving and stationary target acquiration and recognition database the experimental results demonstrate that significant improvement for recognition accuracy can be achieved by the proposed method in comparison with the baseline algorithms

cutgen1 a problem generator for the standard one dimensional cutting stock problem in this paper a problem generator for the standard one dimensional cutting stock problem 1d csp is developed the problem is defined and its parameters are identified then it is shown what features have been included in the program in order to allow for the generation of easily reproducible random problem instances finally by applying the generator a set of benchmark problems is identified

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

a note on bounding a class of linear programming problems including cutting stock problems in lp problems with an extremely large number of possible structural variables solution to optimality is not always required a bound can be used to terminate such lps such a bound is presented for a class of problem that includes most cutting stock formulations

multiscale representations of markov random fields recently a framework for multiscale stochastic modeling was introduced based on coarse to fine scale recursive dynamics defined on trees this model class has some attractive characteristics which lead to extremely efficient statistically optimal signal and image processing algorithms the authors show that this model class is also quite rich in particular they describe how 1 d markov processes and 2 d markov random fields mrfs can be represented within this framework the recursive structure of 1 d markov processes makes them simple to analyze and generally leads to computationally efficient algorithms for statistical inference on the other hand 2 d mrfs are well known to be very difficult to analyze due to their noncausal structure and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification in contrast their multiscale representations are based on scale recursive models and thus lead naturally to scale recursive algorithms which can be substantially more efficient computationally than those associated with mrf models in 1 d the multiscale representation is a generalization of the midpoint deflection construction of brownian motion the representation of 2 d mrfs is based on a further generalization to a midline deflection construction the exact representations of 2 d mrfs are used to motivate a class of multiscale approximate mrf models based on one dimensional wavelet transforms they demonstrate the use of these latter models in the context of texture representation and in particular they show how they can be used as approximations for or alternatives to well known mrf texture models

classification via sparse representation of steerable wavelet frames on grassmann manifold application to target recognition in sar image automatic target recognition has been widely studied over the years yet it is still an open problem the main obstacle consists in extended operating conditions e g depression angle change configuration variation articulation and occlusion to deal with them this paper proposes a new classification strategy we develop a new representation model via the steerable wavelet frames the proposed representation model is entirely viewed as an element on grassmann manifolds to achieve target classification we embed grassmann manifolds into an implicit reproducing kernel hilbert space rkhs where the kernel sparse learning can be applied specifically the mappings of training sample in rkhs are concatenated to form an overcomplete dictionary it is then used to encode the counterpart of query as a linear combination of its atoms by designed grassmann kernel function it is capable to obtain the sparse representation from which the inference can be reached the novelty of this paper comes from 1 the development of representation model by the set of directional components of riesz transform 2 the quantitative measure of similarity for proposed representation model by grassmann metric and 3 the generation of global kernel function by grassmann kernel extensive comparative studies are performed to demonstrate the advantage of proposed strategy

myocardial motion estimation from medical images using the monogenic signal we present a method for the analysis of heart motion from medical images the algorithm exploits monogenic signal theory recently introduced as an n dimensional generalization of the analytic signal the displacement is computed locally by assuming the conservation of the monogenic phase over time a local affine displacement model is considered to account for typical heart motions as contraction expansion and shear a coarse to fine b spline scheme allows a robust and effective computation of the model s parameters and a pyramidal refinement scheme helps to handle large motions robustness against noise is increased by replacing the standard point wise computation of the monogenic orientation with a robust least squares orientation estimate given its general formulation the algorithm is well suited for images from different modalities in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption this paper evaluates the method s feasibility on two emblematic cases cardiac tagged magnetic resonance and cardiac ultrasound in order to quantify the performance of the proposed method we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known a comparison is presented with state of the art methods for cardiac motion analysis on the data considered these conventional approaches are outperformed by the proposed algorithm a recent global optical flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison with respect to the latter the proposed framework provides along with higher accuracy superior robustness to noise and a considerably shorter computation time

an inexact bundle variant suited to column generation we give a bundle method for constrained convex optimization instead of using penalty functions it shifts iterates towards feasibility by way of a slater point assumed to be known besides the method accepts an oracle delivering function and subgradient values with unknown accuracy our approach is motivated by a number of applications in column generation in which constraints are positively homogeneous so that zero is a natural slater point and an exact oracle may be time consuming finally our convergence analysis employs arguments which have been little used so far in the bundle community the method is illustrated on a number of cutting stock problems

estimation of myocardial strain and contraction phase from cine mri using variational data assimilation this paper presents a new method to estimate left ventricle deformations using variational data assimilation that combines image observations from cine mri and a dynamic evolution model of the heart the main contribution of the model is that it embeds parameters modeling the contraction relaxation process it estimates myocardial motion and contraction parameters simultaneously providing accurate complementary information for diagnosis the method was applied to synthetic datasets with known ground truth motion and to 47 patients mri datasets acquired at three slice locations base mid ventricle and apex radial and circumferential strain components were compared to those obtained with a reference tag tracking software exhibiting good agreement with intraclass correlation coefficients icc above 0 8 results were also evaluated against wall motion score indices used to assess cardiac kinetics in clinical practice the assimilation process overcame issues caused by temporal artifacts as a result of the dynamic model compared to using the observation term alone moreover we found that the new dynamic model consisting of a piecewise transport model acting independently on systole and diastole performed better than the standard continuous transport model which oversmooths temporal variations estimated strain and contraction parameters significantly correlated to clinical scores making them promising features for diagnosing not only hypokinesia but also dyskinesia

new fast smoothers for multiscale systems we consider the smoothing problem for multiscale stochastic systems based on the wavelet transform these models involve processes indexed by the nodes of a dyadic tree each level of the dyadic tree represents one scale or resolution of the process therefore moving upward on the tree divides the resolution by 2 whereas moving downward multiplies it by 2 the processes are built according to a recursion in scale from coarse to fine to which random details are added to operate the change in scale one must perform an interpolation this is achieved using the qmf pair of operators attached to a wavelet transform these models have proved to be of great value to capture textures or fractal like processes as well as to perform multiresolution sensor fusion an example of which is given here up to now however only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms those relying on haar s wavelet and those involving only one of the two wavelet interpolators we provide here a unifying framework that handles any system based on orthogonal wavelets a smoothing theory is presented to define the field of fast algorithms for markov random fields and give intuition on how to design them this theory reveals the difficulties arising with general multiscale systems we then prove that orthogonality properties of wavelets are the gate to fastness

efficient multiscale regularization with applications to the computation of optical flow a new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence the solution of the new problem formulation is computed with an efficient multiscale algorithm experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size the new approach also has a number of other important advantages specifically multiresolution flow field estimates are available allowing great flexibility in dealing with the tradeoff between resolution and accuracy multiscale error covariance information is also available which is of considerable use in assessing the accuracy of the estimates in particular these error statistics can be used as the basis for a rational procedure for determining the spatially varying optimal reconstruction resolution furthermore if there are compelling reasons to insist upon a standard smoothness constraint the new algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation finally the usefulness of the approach should extend to a wide variety of ill posed inverse problems in which variational techniques seeking a smooth solution are generally used

an algorithm for nonsmooth convex minimization with errors a readily implementable algorithm is given for minimizing any convex not necessarily differentiable function f of several variables at each iteration the method requires only one approximate evaluation of f and its e subgradient and finds a search direction by solving a small quadratic programming problem the algorithm generates a minimizing sequence of points which converges to a solution wheneverf has any minimizers

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

multiply rooted multiscale models for large scale estimation divide and conquer or multiscale techniques have become popular for solving large statistical estimation problems the methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems each more straightforward than the original however this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound leading to problems of computational complexity and numerical stability in this paper we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided and the problem is instead addressed piece by piece the approach possesses promising attributes it is not a local method the estimate at every point is based on all measurements it is numerically stable for problems of arbitrary size and the approach retains the benefits of the multiscale framework on which it is based a broad class of statistical models a stochastic realization theory an algorithm to calculate statistical likelihoods and the ability to fuse local and nonlocal measurements

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

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

a canonical correlations approach to multiscale stochastic realization we develop a realization theory for a class of multiscale stochastic processes having white noise driven scale recursive dynamics that are indexed by the nodes of a tree given the correlation structure of a 1 d or 2 d random process our methods provide a systematic way to realize the given correlation as the finest scale of a multiscale process motivated by akaike s use of canonical correlation analysis to develop both exact and reduced order models for time series we too harness this tool to develop multiscale models we apply our realization scheme to build reduced order multiscale models for two applications namely linear least squares estimation and generation of random field sample paths for the numerical examples considered least squares estimates are obtained having nearly optimal mean square errors even with multiscale models of low order although both field estimates and field sample paths exhibit a visually distracting blockiness this blockiness is not an important issue in many applications for such applications our approach to multiscale stochastic realization holds promise as a valuable general tool

an overlapping tree approach to multiscale stochastic modeling and estimation recently a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale recursive dynamic trees a major advantage of this framework is that it leads to an extremely efficient statistically optimal algorithm for least squares estimation in certain applications however estimates based on the types of multiscale models previously proposed may not be adequate as they have tended to exhibit a visually distracting blockiness we eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain instead we allow a correspondence to overlapping portions of the image domain we use these so called overlapping tree models for both modeling and estimation in particular we develop an efficient multiscale algorithm for generating sample paths of a random field whose second order statistics match a prespecified covariance structure to any desired degree of fidelity furthermore we demonstrate that under easily satisfied conditions we can lift a random field estimation problem to one defined on an overlapped tree resulting in an estimation algorithm that is computationally efficient directly produces estimation error covariances and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine scale detail

spatio temporal nonrigid registration for ultrasound cardiac motion estimation we propose a new spatio temporal elastic registration algorithm for motion reconstruction from a series of images the specific application is to estimate displacement fields from two dimensional ultrasound sequences of the heart the basic idea is to find a spatio temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame the key feature of our method is the use of a semi local spatio temporal parametric model for the deformation using splines and the reformulation of the registration task as a global optimization problem the scale of the spline model controls the smoothness of the displacement field our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness we evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package together with a realistic cardiac motion model we compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency finally we applied the algorithm to the regional analysis of the left ventricle displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments thereby illustrating the clinical applicability of our method

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

myocardial motion analysis from b mode echocardiograms the quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction we present a new optical flow based method for estimating heart motion from two dimensional echocardiographic sequences to account for typical heart motions such as contraction expansion and shear we analyze the images locally by using a local affine model for the velocity in space and a linear model in time the regional motion parameters are estimated in the least squares sense inside a sliding spatiotemporal b spline window robustness and spatial adaptability is achieved by estimating the model parameters at multiple scales within a coarse to fine multiresolution framework we use a wavelet like algorithm for computing b spline weighted inner products and moments at dyadic scales to increase computational efficiency in order to characterize myocardial contractility and to simplify the detection of myocardial dysfunction the radial component of the velocity with respect to a reference point is color coded and visualized inside a time varying region of interest the algorithm was first validated on synthetic data sets that simulate a beating heart with a speckle like appearance of echocardiograms the ability to estimate motion from real ultrasound sequences was demonstrated by a rotating phantom experiment the method was also applied to a set of in vivo echocardiograms from an animal study motion estimation results were in good agreement with the expert echocardiographic reading

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow