diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

a multiphase dynamic labeling model for variational recognition driven image segmentation we propose a variational framework for the integration of multiple competing shape priors into level set based segmentation schemes by optimizing an appropriate cost functional with respect to both a level set function and a vector valued labeling function we jointly generate a segmentation by the level set function and a recognition driven partition of the image domain by the labeling function which indicates where to enforce certain shape priors our framework fundamentally extends previous work on shape priors in level set segmentation by directly addressing the central question of where to apply which prior it allows for the seamless integration of numerous shape priors such that while segmenting both multiple known and unknown objects the level set process may selectively use specific shape knowledge for simultaneously enhancing segmentation and recognizing shape

frequency weighted spl lscr sub spl infin norm and optimal hankel norm model reduction a new relative error model reduction method is proposed using frequency weighted balanced realization and explicit spl lscr sub spl infin norm error bounds are also derived for the relative error and multiplicative error the method only needs to solve two lyapunov equations it is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase this paper also gives a complete solution to the frequency weighted hankel norm approximation with antistable weighting these results are then applied to spl lscr sub spl infin norm model reduction and several numerically effective algorithms are proposed it is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

integration schemes for von mises plasticity models based on exponential maps numerical investigations and theoretical considerations summary we consider three different exponential map algorithms for associative von mises plasticity with linear isotropic and kinematic hardening the first scheme is based on a different formulation of the time continuous plasticity model which automatically grants the yield consistency of the method in the numerical solution the second one is the quadratically accurate but non yield consistent method already proposed in auricchio and beirao da veiga int j numer meth engng 2003 56 1375 1396 the third method is an improved version of the second one in which the yield consistency condition is enforced a posteriori we also compare the performance of the three methods with the classical radial return map algorithm we develop extensive numerical tests which clearly show the main advantages and disadvantages of the three methods copyright 2005 john wiley sons ltd

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

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

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

a semi analytical integration method for j2 flow theory of plasticity with linear isotropic hardening abstract in this paper an exact time integration scheme is presented for von mises elastoplasticity with linear isotropic hardening at small deformations the method is based on the constant strain rate assumption which is widely accepted in displacement based finite element applications the deviatoric form of the rate equation using the method proposed by krieg and krieg in r d krieg d b krieg accuracies of numerical solution methods for the elastic perfectly plastic model j press vess technol trans asme 99 1977 510 515 is rewritten to a system of nonlinear odes with two scalar functions the radius of the mises circle and an angle obtained by using the scalar product of the stress deviator and the strain rate the time integration of these functions gives an exact solution in implicit form using the incomplete beta function in addition by the exact linearization of this new semi analytical solution a stress updating algorithm and the consistent tangent operator are derived the numerical performance and accuracy of the proposed method are illustrated on numerical examples moreover a comparison of the proposed method with the well known radial return method is included

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

a novel optimal exponential based integration algorithm for von mises plasticity with linear hardening theoretical analysis on yield consistency accuracy convergence and numerical investigations summary in this communication we propose a new exponential based integration algorithm for associative von mises plasticity with linear isotropic and kinematic hardening which follows the ones presented by the authors in previous papers in the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential based schemes and in particular we address the yield consistency exactness under proportional loading accuracy and stability of the methods in the second part of the contribution we show a detailed numerical comparison between the new exponential based method and two classical radial return map methods based on backward euler and midpoint integration rules respectively the developed tests include pointwise stress strain loading histories iso error maps and global boundary value problems the theoretical and numerical results reveal the optimal properties of the proposed scheme copyright 2006 john wiley sons ltd

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

geometrically non linear and elastoplastic three dimensional shear flexible beam element of von mises type hardening material a three dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures the continuum type equations of plastic model of j2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses an effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so called multistep method which is a method of successive control of residuals on yield surfaces it avoids severe divergence when the displacement increments become large which is usual for the continuation methods material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix different from other elements the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion a great number of numerical examples are analysed and compared with the literature the proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre buckling and large deflection collapse of spatial framed structures

controller reduction for linear parameter varying systems with a priori bounds in this paper we develop a controller reduction procedure for linear parameter varying lpv systems the method uses synthesis riccati inequalities for the normalized robust stabilization problem as a basis for the approximation the technique provides a priori error bounds which are used to obtain closed loop stability conditions and performance degradation level we also generalize the relative model reduction method to lpv systems and give an energy interpretation to the controller reduction procedure to illustrate the method a reduced order controller is synthesized and tested on a nonlinear missile model

using prior shapes in geometric active contours in a variational framework in this paper we report an active contour algorithm that is capable of using prior shapes the energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape the model provides the segmentation and the transformation that maps the segmented contour to the prior shape the active contour is able to find boundaries that are similar in shape to the prior even when the entire boundary is not visible in the image i e when the boundary has gaps a level set formulation of the active contour is presented the existence of the solution to the energy minimization is also established we also report experimental results of the use of this contour on 2d synthetic images ultrasound images and fmri images classical active contours cannot be used in many of these images

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

a c2 continuous approximation to the mohr coulomb yield surface abstract in spite of the development of more sophisticated constitutive models for soil the mohr coulomb yield criterion remains a popular choice for geotechnical analysis due to its simplicity and ease of use by practising engineers the implementation of the criterion in finite element programs however presents some numerical difficulties due to the gradient discontinuities which occur at both the edges and the tip of the hexagonal yield surface pyramid furthermore some implicit techniques utilising consistent tangent stiffness formulations are unable to achieve full quadratic convergence as the yield criteria is not c2 continuous this paper extends the previous work of abbo and sloan 1995 through the introduction of c2 continuous rounding of the mohr coulomb yield surface in the octahedral plane this approximation when combined with the hyperbolic approximation in the meridional plane abbo and sloan 1995 describes a yield surface that is c2 continuous at all stress states the new smooth yield surface can be made to approximate the mohr coulomb yield function as closely as required by adjusting only two parameters and is suitable for consistent tangent stiffness formulations

performance bounds for coprime factor controller reductions this paper investigates the performance of coprime factor based controller reduction methods we show that under some mild conditions closed loop performance bounds can be derived for observer based controllers the results in this paper lay a mathematical foundation for using coprime factor controller reduction methods in certain classes of controller reduction problems

controller reduction by h sub infinity balanced truncation h sub infinity balanced truncation may be used to obtain reduced order plants or controllers the plant possibly unstable is compensated using a particular robustly stabilizing controller the two riccati equations involved are then used to define a set of closed loop input output invariants called the h sub infinity characteristic values that part of the plant or controller corresponding to small h sub infinity characteristic values is discarded to give a reduced order plant or controller by exploiting an intimate connection with coprime factorization a simple a priori test is derived for the ability of such a reduced order controller to stabilize the full order plant the performance of the resulting closed loop may also be bounded a priori i e in terms of the prespecified level of robustness and the discarded h sub infinity characteristic values

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

normalized h sub spl infin controller reduction with a priori error bounds this paper describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized h sub spl infin problem it is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented when the approximation is performed on the controller generator guaranteed a priori stability and performance bounds are obtained in terms of the synthesis riccati equation solutions of the normalized h sub spl infin control problems

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

linearization and return mapping algorithms for elastoplasticity models the return mapping algorithm is one of the most efficient procedures to solve elasto plastic problems however a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non radial much research has been done to handle this matrix in this paper a unified approach is presented in such a way that a simple closed form expression gives the consistent tangent matrix for the classical constitutive relations von mises tresca mohr coulomb drucker prager the basic ideas are in the properties of eikonal equations appearing in several fields as image treatment short time computation in elastic waves and others the same kinds of ideas can be extended to non classical models copyright 2003 john wiley sons ltd

controller approximation approaches for preserving h sub spl infin performance investigates the design of reduced order controllers using an h sub spl infin framework given a stabilizing controller which satisfies a prespecified level of closed loop h sub spl infin performance sufficient conditions are derived for another controller to be stabilizing and satisfy the same level of h sub spl infin performance such controllers are said to be p spl gamma admissible where p is the model of the plant under consideration and spl gamma is the required level of prespecified h sub spl infin performance the conditions are expressed as norm bounds on particular frequency weighted errors where the weights are selected to make a specific transfer function a contraction the design of reduced order p spl gamma admissible controllers is then formulated as a frequency weighted model reduction problem it is advantageous for the required weights to be large in some sense solutions which minimize either the trace or the determinant of the inverse weights are characterized we show that the procedure for minimizing the determinant of the inverse weights always gives a direction where the weights are the best possible to conclude we demonstrate by way of a numerical example that when used in conjunction with a combined model reduction convex optimization scheme the proposed design procedures are effective in substantially reducing controller complexity

shape statistics in kernel space for variational image segmentation we present a variational integration of nonlinear shape statistics into a mumford shah based segmentation process the nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel pca to a probabilistic framework we assume that the training data forms a gaussian distribution after a nonlinear mapping to a higher dimensional feature space due to the strong nonlinearity the corresponding density estimate in the original space is highly non gaussian applications of the nonlinear shape statistics in segmentation and tracking of 2d and 3d objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real world shapes it makes the segmentation process robust against misleading information due to noise clutter and occlusion 2003 pattern recognition society published by elsevier science ltd all rights reserved

model reduction with relative multiplicative error bounds and relations to controller reduction balanced model reduction with a priori relative multiplicative error bounds in l sub spl infin norm is studied inverse weighted balanced truncation iwbt is proposed that is a variant of the enns algorithm it is shown that iwbt is equivalent to the balanced stochastic truncation bst this equivalence leads to the extension of an improved relative multiplicative error bound for bst obtained by wang and safonov to general nonsquare transfer matrices natural relations between iwbt and observer based controller reduction are investigated which motivate the simultaneous reduction of the plant and controller robust stability conditions for simultaneous reduction of the plant and the controller are established for the closed loop system consisting of full order plant and reduced order controller as a by product robust stability and stabilization problems are solved for general coprime factor plant descriptions with relative multiplicative h sub spl infin norm bounded uncertainties similar results are obtained for general coprime factors of the feedback controller involving relative multiplicative h sub spl infin norm bounded uncertainties

accurate stress updating algorithm based on constant strain rate assumption abstract the calculation of the stresses for path dependent materials possesses a delicate problem here the constitutive equations are reformulated using the assumption of constant strain rate within an increment this assumption allows the constitutive laws to be rewritten as ordinary differential equations and thus a large set of tools is available to solve the constitutive equations within this concept the possibility to form an algorithmic stiffness tensor is investigated and it turns out that the true tensor is expensive to calculate but it is of interest that an inexpensive well behaving approximative algorithmic stiffness tensor can be formulated to investigate the properties of the solution method both with respect to stress calculation and convergence properties in a newton raphson method an elasto plastic damage model based on von mises plasticity is considered an interesting observation is that for the usual closest point projection method the damage evolution is very sensitive to the size of load step

a new set of invariants for linear systems application to reduced order compensator design a new set of invariants for linear systems weighting the contribution of each state component to the inherent closed loop lqg behavior of the system is presented together with applications to model order reduction and reduced order compensator design

hidden markov measure field models for image segmentation parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region a new bayesian formulation for the solution of this problem is presented based on the key idea of using a doubly stochastic prior model for the label field which allows one to find exact optimal estimators for both this field and the model parameters by the minimization of a differentiable function an efficient minimization algorithm and comparisons with existing methods on synthetic images are presented as well as examples of realistic applications to the segmentation of magnetic resonance volumes and to motion segmentation

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

assessments of methods for locating the point of initial yield numerical methods for locating the intersection point of the loading path with the temperature sensitive yield surface are discussed the newton method is found to be suitable for this purpose it is concluded that the iterates should begin at the plastic state rather than at the stress point estimated by a linear interpolation the influence of temperature changes on the iterative process is analyzed

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes