tension in active shapes the concept of tension is introduced in the framework of active contours with prior shape information and it is used to improve image segmentation in particular two properties of this new quantity are shown 1 high values of the tension correspond to undesired equilibrium points of the cost function under minimization and 2 tension decreases if a curve is split into two or more parts based on these ideas a tree is generated whose nodes are different local minima of the cost function deeper nodes in the tree are expected to correspond to lower values of the cost function in this way the search for the global optimum is reduced to visiting and pruning a binary tree the proposed method has been applied to the problem of fish segmentation from low quality underwater images qualitative and quantitative comparison with existing algorithms based on the euler lagrange diffusion equations shows the superiority of the proposed approach in avoiding undesired local minima

classical to critical crossovers from field theory we extend our previous determinations of nonasymptotic critical behavior of phys rev b 32 7209 1985 and 35 3585 1987 to accurate expressions of the complete classical to critical crossover in three dimensional field theory in terms of the temperaturelike scaling field i e along the critical isochore for 1 the correlation length the susceptibility and the specific heat in the homogeneous phase for the n vector model n 1 to 3 and 2 the spontaneous magnetization coexistence curve the susceptibility and the specific heat in the inhomogeneous phase for the ising model n 1 the present calculations include the seventh loop order of murray and nickel and closely account for the up to date estimates of universal asymptotic critical quantities exponents and amplitude combinations provided by guida and zinn justin j phys a 31 8103 1998

eliminating leading corrections to scaling in the three dimensional o n symmetric φ 4 model n 3 and 4 we study corrections to scaling in the o 3 and o 4 symmetric 4 model on the three dimensional simple cubic lattice with nearest neighbour interactions for this purpose we use monte carlo simulations in connection with a finite size scaling method we find that a finite value of the coupling exists for both values of n where leading corrections to scaling vanish as a first application we compute the critical exponents 0 710 2 and 0 0380 10 for n 3 and 0 749 2 and 0 0365 10 for n 4

nonlinear aspects of the renormalization group flows of dyson s hierarchical model we review recent results concerning the renormalization group rg transformation of dyson s hierarchical model hm this model can be seen as an approximation of a scalar field theory on a lattice we introduce the hm and show that its large group of symmetry simplifies drastically the blockspinning procedure several equivalent forms of the recursion formula are presented with unified notations rigourous and numerical results concerning the recursion formula are summarized it is pointed out that the recursion formula of the hm is inequivalent to both wilson s approximate recursion formula and polchinski s equation in the local potential approximation despite the very small difference with the exponents of the latter we draw a comparison between the rg of the hm and functional rg equations in the local potential approximation the construction of the linear and nonlinear scaling variables is discussed in an operational way we describe the calculation of non universal critical amplitudes in terms of the scaling variables of two fixed points this question appears as a problem of interpolation between these fixed points universal amplitude ratios are calculated we discuss the large n limit and the complex singularities of the critical potential calculable in this limit the interpolation between the hm and more conventional lattice models is presented as a symmetry breaking problem we briefly introduce models with an approximate supersymmetry one important goal of this review is to present a configuration space counterpart suitable for lattice formulations of functional rg equations formulated in momentum space often called exact rg equations and abbreviated erge

master crossover functions for one component fluids by introducing three well defined dimensionless numbers we establish the link between the scale dilatation method able to estimate master i e unique singular behaviors of the one component fluid subclass and the universal crossover functions recently estimated garrabos and bervillier phys rev e 74 021113 2006 from the bounded results of the massive renormalization scheme applied to the ensuremath phi d 4 n model of scalar order parameter n 1 and three dimensions d 3 representative of the ising like universality class the master i e rescaled crossover functions are then able to fit the singular behaviors of any one component fluid without adjustable parameter using only one critical energy scale factor one critical length scale factor and two dimensionless asymptotic scale factors which characterize the fluid critical interaction cell at its liquid gas critical point an additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature the effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short range molecular interaction

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

global inverse optimal control with guaranteed convergence rates of input affine nonlinear systems in earlier works global inverse optimal controllers were proposed for input affine nonlinear systems with given control lyapunov functions however these controllers do not provide information about the convergence rates if the systems have local homogeneous approximations we can employ homogeneous controllers which locally asymptotically stabilize the origin and specify the convergence rates however homogeneous controllers generally do not attain global stability for nonhomogeneous systems in this paper we design global inverse optimal controllers with guaranteed local convergence rates by utilizing local homogeneity of input affine nonlinear systems if we do not consider inverse optimality we can liberally adjust the sector margins we also clarify that local convergence rates and sector margins are invariant under coordinate transformations

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

gaussian process morphable models models of shape variations have become a central component for the automated analysis of images an important class of shape models are point distribution models pdms these models represent a class of shapes as a normal distribution of point variations whose parameters are estimated from example shapes principal component analysis pca is applied to obtain a low dimensional representation of the shape variation in terms of the leading principal components in this paper we propose a generalization of pdms which we refer to as gaussian process morphable models gpmms we model the shape variations with a gaussian process which we represent using the leading components of its karhunen loeve expansion to compute the expansion we make use of an approximation scheme based on the nystrom method the resulting model can be seen as a continuous analog of a standard pdm however while for pdms the shape variation is restricted to the linear span of the example data with gpmms we can define the shape variation using any gaussian process for example we can build shape models that correspond to classical spline models and thus do not require any example data furthermore gaussian processes make it possible to combine different models for example a pdm can be extended with a spline model to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the pdm we introduce a simple algorithm for fitting a gpmm to a surface or image this results in a non rigid registration approach whose regularization properties are defined by a gpmm we show how we can obtain different registration schemes including methods for multi scale or hybrid registration by constructing an appropriate gpmm as our approach strictly separates modeling from the fitting process this is all achieved without changes to the fitting algorithm to demonstrate the applicability and versatility of gpmms we perform a set of experiments in typical usage scenarios in medical image analysis and computer vision the model based segmentation of 3d forearm images and the building of a statistical model of the face to complement the paper we have made all our methods available as open source

field theoretic and monte carlo analysis of the domb joyce model we present a field theoretic analysis of high precision monte carlo data for the domb joyce model on the sc lattice we vary the repulsion between two segments at the same point from zero random walk to infinity self avoiding walk eventually we even include a repulsion between segments at neighbour points to increase the excluded volume beyond that of self avoiding walks the data for the end to end distance the radius of gyration and the partition function clearly show the existence of two branches of universal behaviour these two branches can be identified with the weak and strong coupling branch of the renormalization group respectively a quantitative analysis shows the ability of the standard field theoretic approach to describe the data including the data for strong coupling i e renormalized coupling u greater than its fixed point value we conclude in contrast with some claims in the literature that the standard formalism of the renormalized field theory can be used even for strong coupling branch in addition exploiting the fast approach to asymptotic behaviour at the transition between weak and strong coupling we obtain very precise estimates for the critical exponents of self avoiding walks

a game theoretic framework for landmark based image segmentation a novel game theoretic framework for landmark based image segmentation is presented landmark detection is formulated as a game in which landmarks are players landmark candidate points are strategies and likelihoods that candidate points represent landmarks are payoffs determined according to the similarity of image intensities and spatial relationships between the candidate points in the target image and their corresponding landmarks in images from the training set the solution of the formulated game theoretic problem is the equilibrium of candidate points that represent landmarks in the target image and is obtained by a novel iterative scheme that solves the segmentation problem in polynomial time the object boundaries are finally extracted by applying dynamic programming to the optimal path searching problem between the obtained adjacent landmarks the performance of the proposed framework was evaluated for segmentation of lung fields from chest radiographs and heart ventricles from cardiac magnetic resonance cross sections the comparison to other landmark based segmentation techniques shows that the results obtained by the proposed game theoretic framework are highly accurate and precise in terms of mean boundary distance and area overlap moreover the framework overcomes several shortcomings of the existing techniques such as sensitivity to initialization and convergence to local optima

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

critical exponents hyperscaling and universal amplitude ratios for two and three dimensional self avoiding walks we make a high precision monte carlo study of two and three dimensional self avoiding walks saws of length up to 80 000 steps using the pivot algorithm and the karp luby algorithm we study the critical exponents v and 2 triangle sub 4 gamma as well as several universal amplitude ratios in particular we make an extremely sensitive test of the hyperscaling relation dv 2 triangle sub 4 gamma in two dimensions we confirm the predicted exponent v 3 4 and the hyperscaling relation we estimate the universal ratios 0 14026 0 00007 0 43961 0 00034 and psi 0 66296 0 00043 68 confidence limits in three dimensions we estimate v 0 5877 0 0006 with a correction to scaling exponent triangle sub 1 0 56 0 03 subjective 68 confidence limits this value for v agrees excellently with the field theoretic renormalization group prediction but there is some discrepancy for triangle 1 earlier monte carlo estimates of v which were approximately 0 592 are now seen to be biased by corrections to scaling we estimate the universal ratios 0 1599 0 0002 and psi 0 2471 0 0003 since psi 0 hyperscaling holds the approach to psi is from above contrary to the prediction of the two parameter renormalization group theory we critically reexamine this theory and explain where the error lies in an appendix we prove rigorously modulo some standard scalingmore assumptions the hyperscaling relation dv 2 triangle sub 4 gamma for two dimensional saws less

discriminative wavelet shape descriptors for recognition of 2 d patterns in this paper we present a set of wavelet moment invariants together with a discriminative feature selection method for the classification of seemingly similar objects with subtle di erences these invariant features are selected automatically based on the discrimination measures defined for the invariant features using a minimum distance classifier our wavelet moment invariants achieved the highest classification rate for all four di erent sets tested compared with zernike s moment invariants and li s moment invariants for a test set consisting of 26 upper cased english letters wavelet moment invariants could obtain 100 classification rate when applied to 26 30 randomly generated noisy and scaled letters whereas zernike s moment invariants and li s moment invariants obtained only 98 7 and 75 3 respectively the theoretical and experimental analyses in this paper prove that the proposed method has the ability to classify many types of image objects and is particularly suitable for classifying seemingly similar objects with subtle di erences 1999 pattern recognition society published by elsevier science ltd all rights reserved

critical crossover functions for simple fluids non analytical scaling determination of the ising like crossover parameter a non analytical scaling determination of the ising like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature the mean crossover functions estimated from the bounded results of the massive renormalization scheme in field theory applied to the left phi 2 right d 2 left n right model in three dimensions d 3 and scalar order parameter n 1 are used to formulate the corresponding scaling equations valid in two well defined temperature ranges from the critical temperature the validity range and the ising like nature of the corresponding crossover description are discussed in terms of a single ising like scale factor characterizing the critical isochore the asymptotic value of this scale factor can be predicted within the ising like preasymptotic domain unfortunately the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible a contrario from our scaling equations and the use of precise measurements performed at finite distance from the critical point its local value can be estimated beyond the ising like preasymptotic domain this non analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids this latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor liquid critical point of each fluid are known xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the ising like crossover parameter with the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain and the vapor liquid coexisting densities in the non homogeneous domain our scaling equations provide the local estimate of this crossover parameter as a function of the temperature distance from the critical temperature our results compare favorably with the single asymptotic value calculated only using four critical coordinates of xenon

outlier detection and handling for robust 3 d active shape models search this paper presents a new outlier handling method for volumetric segmentation with three dimensional 3 d active shape models the method is based on a shape metric that is invariant to scaling rotation and translation by using the ratio of interlandmark distances as a local shape dissimilarity measure tolerance intervals for the descriptors are calculated from the training samples and used as a statistical tolerance model to infer the validity of the feature points a replacement point is then suggested for each outlier based on the tolerance model and the position of the valid points a geometrically weighted fitness measure is introduced for feature point detection which limits the presence of outliers and improves the convergence of the proposed segmentation framework the algorithm is immune to the extremity of the outliers and can handle a highly significant presence of erroneous feature points the practical value of the technique is validated with 3 d magnetic resonance mr segmentation tasks of the carotid artery and myocardial borders of the left ventricle

a monte carlo study of leading order scaling corrections of phi 4 theory on a three dimensional lattice we present a monte carlo study of the one component 4 model on a cubic lattice in three dimensions leading order scaling corrections are studied using the finite size scaling method we compute the corrections to scaling exponent with high precision we determine the value of the coupling at which leading order corrections to scaling vanish using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods

monte carlo investigations of phase transitions status and perspectives abstract using the concept of finite size scaling monte carlo calculations of various models have become a very useful tool for the study of critical phenomena with the system linear dimension as a variable as an example several recent studies of ising models are discussed as well as the extension to models of polymer mixtures and solutions it is shown that using appropriate cluster algorithms even the scaling functions describing the crossover from the ising universality class to the mean field behavior with increasing interaction range can be described additionally the issue of finite size scaling in ising models above the marginal dimension d 4 is discussed

homogeneous stabilization for input affine homogeneous systems dilated homogeneous systems are local canonical forms of nonlinear control systems for input affine homogeneous systems existence of continuous homogeneous stabilizing controllers is equivalent to existence of differentiable homogeneous control lyapunov functions in this technical note we propose an homogeneous stabilizing controller and an homogeneous inverse optimal controller for multi input affine homogeneous systems with given homogeneous control lyapunov functions

nature of crossover from classical to ising like critical behavior we present an accurate numerical determination of the crossover from classical to ising like critical behavior upon approach of the critical point in three dimensional systems the possibility of varying the ginzburg number in our simulations allows us to cover the entire crossover region we employ these results to scrutinize several semiphenomenological crossover scaling functions that are widely used for the analysis of experimental results in addition we present strong evidence that the exponent relations do not hold between effective exponents

master singular behavior for the sugden factor of one component fluids near their gas liquid critical point we present the master i e unique behavior of the squared capillary length the so called sugden factor as a function of the temperaturelike field along the critical isochore asymptotically close to the gas liquid critical point of about twenty one component fluids this master behavior is obtained using the scale dilatation of the relevant physical fields of the one component fluids the scale dilatation method introduces the fluid dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the ising like universality class the master behavior for the sugden factor satisfies hyperscaling it can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory in the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the sugden factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one component fluid subclass

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

improved high temperature expansion and critical equation of state of three dimensional ising like systems high temperature series are computed for a generalized three dimensional ising model with arbitrary potential three specific improved potentials suppressing leading scaling corrections are selected by monte carlo computation critical exponents are extracted from high temperature series specialized to improved potentials achieving high accuracy our best estimates are gamma 1 2371 4 nu 0 630 02 23 alpha 0 1099 7 eta 0 0364 4 beta 0 326 48 18 by the same technique the coefficients of the small field expansion for the effective potential helmholtz free energy are computed these results are applied to the construction of parametric representations of the critical equation of state a systematic approximation scheme based on a global stationarity condition is introduced the lowest order approximation reproduces the linear parametric model this scheme is used for an accurate determination of universal ratios of amplitudes a comparison with other theoretical and experimental determinations of universal quantities is presented

controller design for nonlinear affine systems by control lyapunov functions abstract this paper addresses the stabilization problems for nonlinear affine systems first of all the explicit feedback controller is developed for a nonlinear multiple input affine system by assuming that there exists a control lyapunov function next based upon the homogeneous property sufficient conditions for the continuity of the derived controller are developed and then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems it is shown that under some homogeneous assumptions on control lyapunov functions and the interconnection term the cascaded system can be globally stabilized finally some interesting results of finite time stabilization for nonlinear affine systems are also obtained

on the crossover to universal criticality in dilute ising systems monte carlo simulations of the critical behaviour of disordered ising systems have led to concentration dependent critical exponents which seem to violate universality we apply the renormalization group to investigate the crossover effects which cause the observed behaviour we improve the three loop expansion of the callan symanzik and wilson functions by a pade borel approximation and solve the flow equations for various initial points the exponents found in the simulations can be related to regions in the space of coupling coefficients away from the fixed point

boundary finding with prior shape and smoothness models we propose a unified framework for boundary finding where a bayesian formulation based on prior knowledge and the edge information of the input image likelihood is employed the prior knowledge in our framework is based on principal component analysis of four different covariance matrices corresponding to independence smoothness statistical shape and combined models respectively indeed snakes modal analysis fourier descriptors and point distribution models can be derived from or linked to our approaches of different prior models when the true training set does not contain enough variability to express the full range of deformations a mixed covariance matrix uses a combined prior of the smoothness and statistical variation modes it adapts gradually to use more statistical modes of variation as larger data sets are available

accurate segmentation of vertebral bodies and processes using statistical shape decomposition and conditional models detailed segmentation of the vertebrae is an important pre requisite in various applications of image based spine assessment surgery and biomechanical modeling in particular accurate segmentation of the processes is required for image guided interventions for example for optimal placement of bone grafts between the transverse processes furthermore the geometry of the processes is now required in musculoskeletal models due to their interaction with the muscles and ligaments in this paper we present a new method for detailed segmentation of both the vertebral bodies and processes based on statistical shape decomposition and conditional models the proposed technique is specifically developed with the aim to handle the complex geometry of the processes and the large variability between individuals the key technical novelty in this work is the introduction of a part based statistical decomposition of the vertebrae such that the complexity of the subparts is effectively reduced and model specificity is increased subsequently in order to maintain the statistical and anatomic coherence of the ensemble conditional models are used to model the statistical inter relationships between the different subparts for shape reconstruction and segmentation a robust model fitting procedure is used to exclude improbable inter part relationships in the estimation of the shape parameters segmentation results based on a dataset of 30 healthy ct scans and a dataset of 10 pathological scans show a point to surface error improvement of 20 and 17 respectively and the potential of the proposed technique for detailed vertebral modeling

mean crossover functions for uniaxial three dimensional ising like systems we give simple expressions for the mean of the max and min bounds of the critical to classical crossover functions previously calculated bagnuls and bervillier phys rev e 65 066132 2002 within the massive renormalization scheme of the phi d 4 n model in three dimensions d 3 and scalar order parameter n 1 of the ising like universality class the mean functions are determined relying on the properties of the theoretical functions in the two limiting three dimensional 3d ising like and mean field like descriptions close to the wilson fisher fixed point and to the gaussian fixed point respectively such descriptions correspond to the preasymptotic domains near each fixed point where a wegner expansion restricted to two terms leading and first confluent terms is valid the ising like preasymptotic domain description includes the correlations between parameters due to the error bar determination of the exponents and amplitude combinations very close to the wilson fisher fixed point adding the equivalent description of the mean field preasymptotic domain close to the gaussian fixed point leads to define each mean crossover function with three calculated parameters fixing a unique value of one parameter whatever the selected mean crossover function we use this parameter as a relative sensor to estimate the dominant nature either ising like critical or mean field like classical of the crossover behavior finally we obtain an explicit criterion to measure the extension of the ising like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite using a well controlled number of system dependent parameters like in the subclass of one component fluids

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

efficient energies and algorithms for parametric snakes parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity however they have a few drawbacks which limit their performance in this paper we identify some of these problems and propose efficient solutions to get around them the widely used gradient magnitude based energy is parameter dependent its use will negatively affect the parametrization of the curve and consequently its stiffness hence we introduce a new edge based energy that is independent of the parameterization it is also more robust since it takes into account the gradient direction as well we express this energy term as a surface integral thus unifying it naturally with the region based schemes the unified framework enables the user to tune the image energy to the application at hand we show that parametric snakes can guarantee low curvature curves but only if they are described in the curvilinear abscissa since normal curve evolution do not ensure constant arc length we propose a new internal energy term that will force this configuration the curve evolution can sometimes give rise to closed loops in the contour which will adversely interfere with the optimization algorithm we propose a curve evolution scheme that prevents this condition

model based deformable surface finding for medical images describes a new global shape parameterization for smoothly deformable three dimensional 3 d objects such as those found in biomedical images whose diversity and irregularity make them difficult to represent in terms of fixed features or parts this representation is used for geometric surface matching to 3 d medical image data such as from magnetic resonance imaging mri the parameterization decomposes the surface into sinusoidal basis functions four types of surfaces are modeled tori open surfaces closed surfaces and tubes this parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters extrinsic model based information is incorporated by introducing prior probabilities on the parameters surface finding is formulated as an optimization problem results of the method applied to synthetic images and 3 d medical images of the heart and brain are presented

critical crossover functions for simple fluids towards the crossover modelling uniqueness based on a single non universal temperature scaling factor present in a simple fluid case a detailed analysis of non universal parameters involved in different critical to classical crossover models is given for the infinite limit of the cutoff wave number a set of three scaling parameters is defined for each model such that it shows all the shapes of the theoretical crossover functions overlap on the mean crossover function shapes close to the non trivial fixed point the analysis of corresponding links between their fluid dependent parameters opens a route to define a parametric model of crossover equation of state closely satisfying the universal features calculated from the ising like limit in the massive renormalization scheme

static and dynamic critical behavior of thin magnetic ising films this work presents a study of the effect of film thickness on the static and dynamic critical behavior of thin magnetic ising films monte carlo simulations using the wolff algorithm were performed to determine the static and dynamic critical exponents of the films a dimensionality crossover from 2d to 3d due to the finiteness of the films in the static and dynamic critical behavior was observed as the film thickness increases in addition a slight increase in the effective dimension deff and a considerable increase in the critical temperature tc were found small values for the dynamic critical exponents were obtained indicating that the wolff algorithm is a very efficient method for these magnetic systems

remarks on asymptotic controllability and sampled data feedback stabilization for autonomous systems a weak concept of sampled data feedback stabilization for the case of autonomous systems is presented and its lyapunov characterization is established sufficient conditions are derived for the existence of a time varying sampled data feedback exhibiting global stabilization for certain class of nonlinear systems

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

improved model for mixtures of polymers and hard spheres extensive monte carlo simulations are used to investigate how model systems of mixtures of polymers and hard spheres approach the scaling limit we represent polymers as lattice random walks of length l with an energy penalty w for each intersection domb joyce model interacting with hard spheres of radius r c via a hard core pair potential of range where r mon is identified as the monomer radius we show that the mixed polymer colloid interaction gives rise to new confluent corrections the leading ones scale as where is the usual flory exponent finally we determine optimal values of the model parameters w and r mon that guarantee the absence of the two leading confluent corrections this improved model shows a significantly faster convergence to the asymptotic limit and is amenable for extensive and accurate numerical simulations at finite density with only a limited computational effort

convergence rates of stochastic homogeneous systems abstract this study considers stochastic homogeneous systems and focuses on the relation between their homogeneity and the convergence rates we give a definition of stochastic homogeneous systems with weighted dilations as an extension of deterministic homogeneous systems we also introduce the stability properties such as exponential rational and finite time stability with respect to homogeneous norms as a main result we show that their homogeneous degrees imply the convergence rates of asymptotically stable systems based on the result we also deal with the stabilization of stochastic homogeneous control systems we provide a design method of homogeneous feedback laws with homogeneous control lyapunov functions which guarantees the convergence rates

multiscale 3 d shape representation and segmentation using spherical wavelets this paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform this work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures such as the caudate nucleus or the hippocampus our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations enabling the construction of more descriptive nonglobal nonuniform shape probability priors to be included in the segmentation and shape analysis framework in particular this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine local variations in a population of shapes in the presence of a limited dataset specifically our technique defines a multiscale parametric model of surfaces belonging to the same population using a compact set of spherical wavelets targeted to that population we further refine the shape representation by separating into groups wavelet coefficients that describe independent global and or local biological variations in the population using spectral graph partitioning we then learn a prior probability distribution induced over each group to explicitly encode these variations at different scales and spatial locations based on this representation we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation additionally the optimization method can be applied in a coarse to fine manner we apply our algorithm to two different brain structures the caudate nucleus and the hippocampus of interest in the study of schizophrenia we show 1 a reconstruction task of a test set to validate the expressiveness of our multiscale prior and 2 a segmentation task in the reconstruction task our results show that for a given training set size our algorithm significantly improves the approximation of shapes in a testing set over the point distribution model which tends to oversmooth data in the segmentation task our validation shows our algorithm is computationally efficient and outperforms the active shape model algorithm by capturing finer shape details

crossover scaling from classical to non classical critical behaviour interacting physical systems in the neighborhood of criticality and massive continuum field theories can often be characterized by just two physical scales a macroscopic correlation length and a microscopic interaction range related to the coupling and measured by the ginzburg number g a critical crossover limit can be defined when both scales become large while their ratio stays finite the corresponding scaling functions are universal and they are related to the standard field theory renormalization group functions the critical crossover describes the unique flow from the gaussian to the nonclassical fixed point

technical communique stabilization via homogeneous feedback controls in this paper we provide an explicit homogeneous feedback control with the requirement that a control lyapunov function exists for an affine control system and satisfies an homogeneous condition we use a modified version of the sontag formula to achieve our main goal moreover we prove that the existence of an homogeneous control lyapunov function for an homogeneous affine system leads to an homogeneous closed loop system by using the previous feedback control

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

two parameter scaling of correlation functions near continuous phase transitions we discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two parameter scaling form g k k 2 c g k k k c where k is the wave vector and is the correlation length and the interaction dependent nonuniversal momentum scale k c remains finite at the critical fixed point the correlation function describes the entire critical regime and captures the classical to critical crossover one parameter scaling is recovered only in the limit k k c 0 we present an approximate calculation of g x y for the ising universality class using the functional renormalization group

cortical surface shape analysis based on spherical wavelets in vivo quantification of neuroanatomical shape variations is possible due to recent advances in medical imaging and has proven useful in the study of neuropathology and neurodevelopment in this paper we apply a spherical wavelet transformation to extract shape features of cortical surfaces reconstructed from magnetic resonance images mris of a set of subjects the spherical wavelet transformation can characterize the underlying functions in a local fashion in both space and frequency in contrast to spherical harmonics that have a global basis set we perform principal component analysis pca on these wavelet shape features to study patterns of shape variation within normal population from coarse to fine resolution in addition we study the development of cortical folding in newborns using the gompertz model in the wavelet domain which allows us to characterize the order of development of large scale and finer folding patterns independently given a limited amount of training data we use a regularization framework to estimate the parameters of the gompertz model to improve the prediction performance on new data we develop an efficient method to estimate this regularized gompertz model based on the broyden fletcher goldfarb shannon bfgs approximation promising results are presented using both pca and the folding development model in the wavelet domain the cortical folding development model provides quantitative anatomic information regarding macroscopic cortical folding development and may be of potential use as a biomarker for early diagnosis of neurologic deficits in newborns

the xy model and the three state antiferromagnetic potts model in three dimensions critical properties from fluctuating boundary conditions we present the results of a monte carlo study of the three dimensionalxy model and the three dimensional antiferromagnetic three state potts model in both cases we compute the difference of the free energies of a system with periodic and a system with antiperiodic boundary conditions in a neighborhood of the critical coupling from the finite size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponentv that are compatible with recent high statistics monte carlo studies of the models the results for the free energy difference at the critical temperature and for the exponentv confirm that both models belong to the same universality class

segmenting lung fields in serial chest radiographs using both population based and patient specific shape statistics this paper presents a new deformable model using both population based and patient specific shape statistics to segment lung fields from serial chest radiographs there are two novelties in the proposed deformable model first a modified scale invariant feature transform sift local descriptor which is more distinctive than the general intensity and gradient features is used to characterize the image features in the vicinity of each pixel second the deformable contour is constrained by both population based and patient specific shape statistics and it yields more robust and accurate segmentation of lung fields for serial chest radiographs in particular for segmenting the initial time point images the population based shape statistics is used to constrain the deformable contour as more subsequent images of the same patient are acquired the patient specific shape statistics online collected from the previous segmentation results gradually takes more roles thus this patient specific shape statistics is updated each time when a new segmentation result is obtained and it is further used to refine the segmentation results of all the available time point images experimental results show that the proposed method is more robust and accurate than other active shape models in segmenting the lung fields from serial chest radiographs

crossover from the dilute to the dense phase for self repelling polymer chains finite size effects and relation to zero component landau ginzburg wilson theory using a recently established perturbative approach we analyse a single polymer chain or a few chains floating in a good solvent contained in a finite box with periodic boundary conditions we calculate to one loop order the partition function and the equation of state relating segment concentration to segment chemical potential and we discuss in detail the chain length distribution for a field theoretic ensemble of chains characterized by fixed our results obey finite size scaling and cover the whole crossover from the dilute to the dense limit where is the critical chemical potential the different limits evolve smoothly from one another the theoretical results for the chain length distribution are compared with monte carlo simulations of self avoiding walks on a cubic lattice we find a good agreement between our results and the simulation data

elastic model based segmentation of 3 d neuroradiological data sets this paper presents a new technique for the automatic model based segmentation of three dimensional 3 d objects from volumetric image data the development closely follows the seminal work of taylor and cootes on active shape models but is based on a hierarchical parametric object description rather than a point distribution model the segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models geometric models are derived from a sample set of image data which have been segmented by experts the surfaces of these binary objects are converted into parametric surface representations which are normalized to get an invariant object centered coordinate system surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes it is shown that invariant object surface parametrization provides a good approximation to automatically determine object homology in terms of sets of corresponding sets of surface points gray level information near object boundaries is represented by 1 d intensity profiles normal to the surface considering automatic segmentation of brain structures as their driving application the authors choice of coordinates for object alignment was the well accepted stereotactic coordinate system major variation of object shapes around the mean shape also referred to as shape eigenmodes are calculated in shape parameter space rather than the feature space of point coordinates segmentation makes use of the object shape statistics by restricting possible elastic deformations into the range of the training shapes the mean shapes are initialized in a new data set by specifying the landmarks of the stereotactic coordinate system the model elastically deforms driven by the displacement forces across the object s surface which are generated by matching local intensity profiles elastical deformations are limited by setting bounds for the maximum variations in eigenmode space the technique has been applied to automatically segment left and right hippocampus thalamus putamen and globus pallidus from volumetric magnetic resonance scans taken from schizophrenia studies the results have been validated by comparison of automatic segmentation with the results obtained by interactive expert segmentation

a bayesian model of shape and appearance for subcortical brain segmentation automatic segmentation of subcortical structures in human brain mr images is an important but difficult task due to poor and variable intensity contrast clear well defined intensity features are absent in many places along typical structure boundaries and so extra information is required to achieve successful segmentation a method is proposed here that uses manually labelled image data to provide anatomical training information it utilises the principles of the active shape and appearance models but places them within a bayesian framework allowing probabilistic relationships between shape and intensity to be fully exploited the model is trained for 15 different subcortical structures using 336 manually labelled t1 weighted mr images using the bayesian approach conditional probabilities can be calculated easily and efficiently avoiding technical problems of ill conditioned covariance matrices even with weak priors and eliminating the need for fitting extra empirical scaling parameters as is required in standard active appearance models furthermore differences in boundary vertex locations provide a direct purely local measure of geometric change in structure between groups that unlike voxel based morphometry is not dependent on tissue classification methods or arbitrary smoothing in this paper the fully automated segmentation method is presented and assessed both quantitatively using leave one out testing on the 336 training images and qualitatively using an independent clinical dataset involving alzheimer s disease median dice overlaps between 0 7 and 0 9 are obtained with this method which is comparable or better than other automated methods an implementation of this method called first is currently distributed with the freely available fsl package

constructive nonsmooth stabilization of triangular systems the problem of local asymptotic continuous feedback stabilization of single input nonlinear systems is considered here the aim is to explicitly construct a continuous asymptotically stabilizing feedback for a class of nonlinear systems that is known to be continuous feedback asymptotically stabilizable but for which the known results do not provide an effective method to compute the stabilizer computer simulations are included to show practical applicability of our approach

two point correlation function of three dimensional o n models the critical limit and anisotropy in three dimensional o n models we investigate the low momentum behavior of the two point green s function g x in the critical region of the symmetric phase we consider physical systems whose criticality is characterized by a rotationally invariant fixed point several approaches are exploited such as strong coupling expansion of lattice n vector model and 1 n expansion field theoretical methods within the ensuremath varphi 4 continuum formulation non gaussian corrections to the universal low momentum behavior of g x are evaluated and found to be very small in nonrotationally invariant physical systems with o n invariant interactions the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent ensuremath rho which is universal and is related to the leading irrelevant operator breaking rotational invariance at n ensuremath infty one finds ensuremath rho 2 we show that for all values of ng 0 ensuremath rho ensuremath simeq 2

hierarchical active shape models using the wavelet transform active shape models asms are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability this paper presents a method that overcomes this limitation by using a hierarchical formulation of active shape models using the wavelet transform the statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis and used as priors in the contour s deformation some of these priors reflect relatively global shape characteristics of the object boundaries whereas some of them capture local and high frequency shape characteristics and thus serve as local smoothness constraints this formulation achieves two objectives first it is robust when only a limited number of training samples is available second by using local statistics as smoothness constraints it eliminates the need for adopting ad hoc physical models such as elasticity or other smoothness models which do not necessarily reflect true biological variability examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved even with as few as five training samples

off equilibrium scaling behaviors driven by time dependent external fields in three dimensional o n vector models we consider the dynamical off equilibrium behavior of the three dimensional o n vector model in the presence of a slowly varying time dependent spatially uniform magnetic field h t h t e where e is an n dimensional constant unit vector h t t t s and t s is a time scale at fixed temperature t t c where t c corresponds to the continuous order disorder transition the dynamic evolutions start from equilibrium configurations at h i 0 with h t f 0 or vice versa we show that the magnetization displays an off equilibrium scaling behavior close to the transition line h t 0 it arises from the interplay among the time t the time scale t s and the finite size l the scaling behavior can be parametrized in terms of the scaling variables t s l and t t s t where 0 and t 0 are appropriate universal exponents which differ at the critical point and for t t c in the latter case and t also depend on the shape of the lattice and on the boundary conditions we present numerical results for the heisenberg n 3 model under a purely relaxational dynamics they confirm the predicted off equilibrium scaling behaviors at and below t c we also discuss hysteresis phenomena in round trip protocols for the time dependence of the external field we define a scaling function for the hysteresis loop area of the magnetization that can be used to quantify how far the system is from equilibrium

on the corrections to scaling in three dimensional ising models the leading correction to scaling amplitudes for the spin 1 2 nearest neighbor sc bcc and fee ising models are considered with the particular aim of determining their signs on the basis of previous two variable series analyses by chen fisher and nickel and renormalization group 4 d expansions it is concluded that the correction amplitudes for the susceptibility correlation length specific heat and spontaneous magnetization arenegative for all three lattices thus for example the effective exponent eff t asymptotically approaches the true susceptibility exponent fromabove other earlier and more recent high temperature series and field theoretic analyses are seen to be consistent with this result however the usual nonasymptotic perturbative field theoretic approaches are essentially committed to positive correction amplitudes the question of the signs therefore relates directly to the applicability of these non asymptotic field theoretic calculations to three dimensional ising models as well as to different experimental systems

crossover scaling in two dimensions we determine the scaling functions describing the crossover from ising like critical behavior to classical critical behavior in two dimensional systems with a variable interaction range since this crossover spans several decades in the reduced temperature as well as in the finite size crossover variable it has up to now largely evaded a satisfactory numerical determination using a dedicated monte carlo method we could obtain accurate results for sufficiently large interaction ranges our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal also the so called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region

high precision monte carlo study of the 3d xy universality class we present a monte carlo study of the two component 4 model on the simple cubic lattice in three dimensions by suitable tuning of the coupling constant we eliminate leading order corrections to scaling high statistics simulations using finite size scaling techniques yield 0 6723 3 8 and 0 0381 2 2 where the statistical and systematical errors are given in the first and second bracket respectively these results are more precise than any previous theoretical estimate of the critical exponents for the 3d xy universality class

sign of corrections to scaling amplitudes field theoretic considerations and results for self repelling walks i discuss the application of renormalized field theory to such critical systems where the renormalized coupling approaches the fixed point from the wrong strong coupling side in contrast to a belief sometimes expressed in the literature i find that also this situation can be described within the standard formalism only the interpretation of the strong coupling branch relies on the existence of a finite cutoff i illustrate these considerations with an analysis of monte carlo data for self avoiding walks finding that the data support the theory in all respects however it is stressed that the nonuniversal parameters of the renormalized theory in general have no simple relation to the parameters of the underlying bare model

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality