finite size effects in a field theoretic model with long range exchange interaction we present a systematic approach to the calculation of finite size fs effects for ano n field theoretic model with both short range sr and long range lr exchange interactions the lr exchange interaction decays at large distances as 1 rd 2 2 0 0 renormalization group calculations ind du e are performed for a system with a fully finite block geometry under periodic boundary conditions we calculate the fs shift of the critical temperature and the fs renormalized coupling constant of the model to one loop order the universal scaling variable is obtained and the fs scaling hypothesis is verified

on finite size scaling in the presence of dangerous irrelevant variables a scaling hypothesis on finite size scaling in the presence of a dangerous irrelevant variable is formulated for systems with long range interaction and general geometryld d d a characteristic length which obeys a universal finite size scaling relation is defined the general conjectures are based on exact results for the mean spherical model with inverse power law interaction

first order transitions in spherical models finite size scaling finite size behavior near the first order phase boundary of ferromagnetic spherical models is investigated for block and cylinder shaped systems ind dimensions the bulk thermodynamic singularities are rounded and asymptotically for large size obey appropriate scaling laws both short range interactions and long range couplings decaying like 1 rd with 0 are analyzed the short range results agree precisely with a recently developed scaling theory foro n symmetric systems in the limitn more generally the scaling functions are universal depending only on explicit aspects of the shape and interactions enter only in the spin wave or goldstone mode contributions which appear technically as corrections to scaling an appendix analyzes the truncation error in the approximation by many fold sums of multivariate integrals with integrands diverging like jaj j2 as 0

finite size scaling investigations in the quantum varphi4 model with long range interaction in this paper we study in detail the critical behaviour of the n quantum 4 model with long range interaction decaying with distances r by a power law as r d in the large n limit the zero temperature critical behaviour is discussed its alteration by finite temperature and or finite sizes in the space is studied the scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead a number of results for the correlation length critical amplitudes and the finite size shift for different dimensionalities between the lower d 3 2 critical dimensions are calculated

lie algebra of anomalously scaled fluctuations for quantum lattice systems it is proven that anomalously scaled fluctuations have a natural lie algebra structure the harmonic lattice in the ground state is given as an illustration of the general theorem

finite size effects in a quantum exactly soluble model for structural phase transition abstract some consequences of finite size scaling are examined within an exactly soluble model of structural phase transition explicit expressions for the susceptibility for classical and quantum limits are derived it is shown that both the cases have the same scaling behaviour

non commutative central limits non commutative central limit theorems are derived the ccr c algebra of fluctuations is analyzed in detail the stability of the central limit is studied by means of the notion of relative entropy

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

algebraic structure of quantum fluctuations on the basis of the existence of second and third moments of fluctuations we prove a theorem about the lie algebraic structure of fluctuation operators this result gives insight into the quantum character of fluctuations we illustrate the presence of a lie algebra of fluctuation operators in a model of the anharmonic crystal and show the dependence of the lie algebra structure on the fine structure of the fluctuation operator algebra the result is also applied to construct the normal goldstone mode in the ideal bose gas for bose einstein condensation

on the finite size behaviour of systems with asymptotically large critical shift exact results of the finite size behaviour of the susceptibility in three dimensional mean spherical model films under dirichlet dirichlet dirichlet neumann and neumann neumann boundary conditions are presented the corresponding scaling functions are explicitly derived and their asymptotics close to above and below the bulk critical temperature tc are obtained the results can be incorporated in the framework of the finite size scaling theory where the exponent characterizing the shift of the finite size critical temperature with respect to tc is smaller than 1 with being the critical exponent of the bulk correlation length

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

t 0 finite size scaling for a quantum system with long range interaction abstract the general idea of finite size scaling are tested by the example of the pure quantum version of an exactly solvable model of structural phase transition with long range interaction decaying at large distances r as r d where d is the space dimensionality and 0 the finite size shift of the quantum parameter playing the same role as that of the temperature for classical systems is calculated for the general geometry ld d d with 0 0 2

explicit results for the correlation length of the finite sized spherical model of ferromagnetism we report explicit results for the zero field correlation length xi t l of a spherical model ferromagnet confined to geometry ld d infinity d d 2 d or 2 and subjected to twisted boundary conditions in the region of first order phase transition t tc xi under twisted boundary conditions obeys the same scaling law as under periodic boundary conditions though with a different amplitude in the core region t approximately tc the scaling behaviour changes radically as one moves from one set of boundary conditions to the other affected greatly by the pinning of the ground state wavevector k0 of the system

generalized mittag leffler functions in the theory of finite size scaling for systems with strong anisotropy and or long range interaction the difficulties arising in the investigation of finite size scaling in d dimensional o n systems with strong anisotropy and or long range interaction decaying with the interparticle distance r as r d 0 2 are discussed some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries the analysis is simplified further by expressing this general form in terms of a generalization of the mittag leffler special functions this turned out to be very useful for the extraction of asymptotic finite size behaviours of the thermodynamic functions

game theoretic integration for image segmentation robust segmentation of structures from an image is essential for a variety of image analysis problems however the conventional methods of region based segmentation and gradient based boundary finding are often frustrated by poor image quality here we propose a method to integrate the two approaches using game theory in an effort to form a unified approach that is robust to noise and poor initialization this combines the perceptual notions of complete boundary information using edge data and shape priors with gray level homogeneity using two computational modules the novelty of the method is that this is a bidirectional framework whereby both computational modules improve their results through mutual information sharing a number of experiments were performed both on synthetic datasets and datasets of real images to evaluate the new approach and it is shown that the integrated method typically performs better than conventional gradient based boundary finding

phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal a complete description of the fluctuation operator algebra is given for a quantum crystal showing displacement structural phase transitions in the one phase region the fluctuations are normal and its algebra is non abelian in the two phase region and on the critical line t c 0 the momentum fluctuation is normal the displacement is critical and the algebra is abelian att c 0 quantum phase transition this algebra is non abelian with abnormal displacement and supernormal squeezed momentum fluctuation operators both being dimension dependent

scaling of fluctuations and critical exponents we present a new technique to describe the abnormal behavior of certain fluctuation observables in the critical regime of quantum statistical systems which undergo a phase transition the idea is to rescale the local fluctuation operators by a relevant external parameter of the system in addition to the usual scaling with the inverse square root of the volume the scaling indices used in this scaling procedure are directly related to the critical exponents furthermore it is explained that this new method of scaling preserves the ccr structure of the algebra of macroscopic fluctuations finally scaling indices are computed for the relevant microscopic observables at all temperatures in a mean field approximation for a quantum anharmonic crystal these indices yield the same critical exponents as predicted by mean field theory

finite size scaling for the mean spherical model with inverse power law interaction a new analytical technique based on integral transformations with mittag leffler type kernels is used to derive the finite size scaling function for the free energy per particle of the mean spherical model with inverse power law asymptotics of the interaction potential the asymptotic formation of the singularities in the specific heat and magnetic susceptibility at the bulk critical point is studied

active shape models with invariant optimal features application to facial analysis this work is framed in the field of statistical face analysis in particular the problem of accurate segmentation of prominent features of the face in frontal view images is addressed we propose a method that generalizes linear active shape models asms l which have already been used for this task the technique is built upon the development of a nonlinear intensity model incorporating a reduced set of differential invariant features as local image descriptors these features are invariant to rigid transformations and a subset of them is chosen by sequential feature selection for each landmark and resolution level the new approach overcomes the unimodality and gaussianity assumptions of classical asms regarding the distribution of the intensity values across the training set our methodology has demonstrated a significant improvement in segmentation precision as compared to the linear asm and optimal features asm a nonlinear extension of the pioneer algorithm in the tests performed on ar xm2vts and equinox databases

a probabilistic view on finite size scaling in infinitely coordinated spherical models abstract it is shown that the finite size scaling functions of the infinitely coordinated spherical model are closely related to the limit probability distribution of a triangular array of properly normalized block spin variables the triangular array is defined with the aid of a two parameter family of gibbs distributions which approach the critical point together with the increase of the size of the system our consideration confirms the modification of finite size for infinitely coordinated systems suggested by botet jullien and pfeuty and extends it to the nonzero field case the explicit results rigorously derived here manifest the ensemble dependence of the relevant statistical distributionss which in turn produce different finite size scaling functions we demonstrate how the finite size scaling functions of the free energy can be determined from the relations between its first derivatives with respect to the temprature and magnetic field and expectation values of block spin variables whose asymptotic behavior is given by the smooth limit distribution a general conjecture pertaining to other models is stated too

finite size crossover in systems with slab geometry abstract a renormalization group study of the finite size dimensional crossover is carried out with the help pf e 4 d and e0 3 d expansion techniques the finite size crossover and the invariance relation for the length scale transformation are proven up to the two loop approximation the formal equivalence between the finite size crossover in classical systems and the quantum to classical dimensional crossover in certain quantum statistical models is emphasized and exploited the finite size corrections to the fluctuation shift of the critical temperature and the width of the critical region are investigated it is shown that the shift exponent describing the fractional rounding of the critical temperature obeys the relation d 2 where d is the dimensionality of the system

gaussian non gaussian critical fluctuations in the curie weiss model it is known that at the critical temperature the curie weiss mean field model has non gaussian fluctuations and that internal fluctuations can be gaussian here we compute the distribution of theq mode magnetization fluctuations as a function of the temperature the wave vectorq and a fading out external field we obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out we discuss also the susceptibility as the limitq tending to zero

soft mode in the class of exactly soluble models of phase transitions the temperature dependence of susceptibility of a class of exactly soluble models of phase transitions is discussed instead of a goldstone mode type behaviour found in earlier treatments it is shown that this function reveals a quite rich structure inverse susceptibility vanishes in the ordered phase for d dc 4 and has a singularity at t 0 but is a continuous function of temperature for d 4 with a classical critical index 1 such a characteristic behaviour is probably associated with a non ergodic behaviour in the former case d dc and an ergodic behaviour in the latter case d dc a similar singularity of the susceptibility function d dc is found for a spherical model

a shape based approach to the segmentation of medical imagery using level sets we propose a shape based approach to curve evolution for the segmentation of medical images containing known object types in particular motivated by the work of leventon grimson and faugeras 2000 we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data the parameters of this representation are then manipulated to minimize an objective function for segmentation the resulting algorithm is able to handle multidimensional data can deal with topological changes of the curve is robust to noise and initial contour placements and is computationally efficient at the same time it avoids the need for point correspondences during the training phase of the algorithm we demonstrate this technique by applying it to two medical applications two dimensional segmentation of cardiac magnetic resonance imaging mri and three dimensional segmentation of prostate mri

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

hierarchical lung field segmentation with joint shape and appearance sparse learning lung field segmentation in the posterior anterior pa chest radiograph is important for pulmonary disease diagnosis and hemodialysis treatment due to high shape variation and boundary ambiguity accurate lung field segmentation from chest radiograph is still a challenging task to tackle these challenges we propose a joint shape and appearance sparse learning method for robust and accurate lung field segmentation the main contributions of this paper are 1 a robust shape initialization method is designed to achieve an initial shape that is close to the lung boundary under segmentation 2 a set of local sparse shape composition models are built based on local lung shape segments to overcome the high shape variations 3 a set of local appearance models are similarly adopted by using sparse representation to capture the appearance characteristics in local lung boundary segments thus effectively dealing with the lung boundary ambiguity 4 a hierarchical deformable segmentation framework is proposed to integrate the scale dependent shape and appearance information together for robust and accurate segmentation our method is evaluated on 247 pa chest radiographs in a public dataset the experimental results show that the proposed local shape and appearance models outperform the conventional shape and appearance models compared with most of the state of the art lung field segmentation methods under comparison our method also shows a higher accuracy which is comparable to the inter observer annotation variation

on the limit gibbs states of the spherical model the effect of a class of hamiltonian perturbations vanishing in the thermodynamic limit on the limit gibbs states of the spherical and mean spherical models is studied the perturbation term is taken in the form of interaction energy with uniform magnetic field of strength h0n alpha where h0 in r1 and alpha 0 are parameters and n is the number of particles for fixed temperatures below the critical temperature in the absence of constant external magnetic fields and at alpha 1 the authors obtain convex sets of different mixed gibbs states parametrised by h0 a natural one parameter generalisation of the kac thompson transformation kernel which relates the states of the mean spherical model to the states of the spherical model is found when 0 alpha 1 and h0 not 0 or alpha 1 and h0 or infinity this kernel becomes a delta function even below the critical temperature then the states in both ensembles coincide with each other and with one of the two depending on the sign of h0 extreme points the case of alpha 1 is found to lead to the well known results corresponding to the absence of perturbation h0 0

finite size effects in the approximating hamiltonian method abstract the husimi temperley mean spherical model in which each two particles interact with equal strength is considered this model is shown to be equivalent to a d dimensional model with periodic boundary conditions and interaction potential j r where j r r d as r 0 being a parameter in the limit 0 it is found that the approximating hamiltonian method yields singular finite size scaling functions both in the neighbourhood of the critical point and near a first order phase transition a modification of this method is suggested which allows for all the essential configurations and reproduces the exact finite size scaling near a first order phase transition

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

canonical solution of classical magnetic models with long range couplings we study the canonical solution of a family of classical n vector spin models on a generic d dimensional lattice the couplings between two spins decay as the inverse of their distance raised to the power with d the control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy which makes the model extensive but not additive a detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables the properties of a class of functions related to the modified bessel functions had to be investigated for given n and for any d and lattice geometry the solution is equivalent to that of the 0 model where the dimensionality d and the geometry of the lattice are irrelevant

a generalized quasiaverage approach to the description of the limit states of then vector curie weiss ferromagnet a set of all limit gibbs states is constructed for the ferromagneticn vector curie weiss model by means of a generalized quasiaverage method

finite size scaling for systems with long range interactions abstract the present review is devoted to the fundamental problems of finite size scaling due to the presence of long range interactions the attention is focused on the precise formulation of critical finite size scaling in the case that the bulk correlation length is identically infinite the hypotheses based on the notion of a finite size scaling length are formulated in a way which treats the cases of short and long range interactions on equal grounds as well as the standard and modified above the upper critical dimensionality finite size scaling the general conjectures are tested on the exactly solvable mean spherical model with power law interaction special attention is paid to the adequate mathematical techniques the formulation of finite size scaling at first order phase transitions is also discussed since the finite size scaling length enters into the definition of the relevant scaled external field variable provided the system has d 0 infinite dimensions the review closes with a summary and short discussion of some open problems

fluctuation operators and spontaneous symmetry breaking we develop an alternative approach to this field which was to a large extent developed by verbeure et al it is meant to complement their approach which is largely based on a noncommutative central limit theorem and coordinate space estimates in contrast to that we deal directly with the limits of l point truncated correlation functions and show that they typically vanish for l 3 provided that the respective scaling exponents of the fluctuation observables are appropriately chosen this direct approach is greatly simplified by the introduction of a smooth version of spatial averaging which has a much nicer scaling behavior and the systematic development of fourier space and energy momentum spectral methods we both analyze the regime of normal fluctuations the various regimes of poor clustering and the case of spontaneous symmetry breaking or goldstone phenomenon

modified finite size scaling for anharmonic crystals with quantum fluctuations abstract the modified finite size scaling for dimensions d d where d is the upper critical dimensionality is verified in the closed vicinity of both the classical and the quantum multicritical points by the example of a quantum model for an anharmonic cyrstal confined to a fully finite block geometry under periodic boundary conditions unified scaling equations corresponding to the two kinds of correlation lengths related with the fixed dimensionless temperature t when the quantum parameter is varied and with fixed when t is varied are obtained

dynamics of fluctuations for quantum lattice systems for short range interactions and forl1 space clustering states it is proved that there exists a bonafide time evolution on the set of normal fluctuations this dynamics is applied to derive the notion of equilibrium state of the algebra of fluctuations

finite size effects in fluid interfaces abstract finite size effects in interfacial tensions of fluid interfaces are studied at the level of the gaussian model of capillary waves it had been suggested that such effects might play a significant role in surface tension measurements based on capillary rise between plates spaced a small distance d apart the finite size correction varying as 1 d a reconsideration of the thermodynamics of finite size effects followed by careful calculations for the gaussian model leads to a finite size correction varying as 1 d 2 with a universal coefficient the effect is too small to be noticeable in current experiments the calculations have been carried out for rectangular interfaces of arbitrary dimensionality and general shapes subject to many types of boundary conditions they also have implications for finite size effects in interfacial free energies in two and three dimensional ising models which are discussed in connection with recent exact and monte carlo calculations

imposing semi local geometric constraints for accurate correspondences selection in structure from motion a game theoretic perspective most structure from motion pipelines are based on the iterative refinement of an initial batch of feature correspondences typically this is performed by selecting a set of match candidates based on their photometric similarity an initial estimate of camera intrinsic and extrinsic parameters is then computed by minimizing the reprojection error finally outliers in the initial correspondences are filtered by enforcing some global geometric property such as the epipolar constraint in the literature many different approaches have been proposed to deal with each of these three steps but almost invariably they separate the first inlier selection step which is based only on local image properties from the enforcement of global geometric consistency unfortunately these two steps are not independent since outliers can lead to inaccurate parameter estimation or even prevent convergence leading to the well known sensitivity of all filtering approaches to the number of outliers especially in the presence of structured noise which can arise for example when the images present several repeated patterns in this paper we introduce a novel stereo correspondence selection scheme that casts the problem into a game theoretic framework in order to guide the inlier selection towards a consistent subset of correspondences this is done by enforcing geometric constraints that do not depend on full knowledge of the motion parameters but rather on some semi local property that can be estimated from the local appearance of the image features the practical effectiveness of the proposed approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques

finite size shift of the critical temperature in the spherical model the finite size shift of the critical temperature is calculated by the example of the spherical model with short and long range interactions confined to the general geometryld d d subject to periodic boundary conditions the derived formula unifies in some sense all results found up to now

hierarchical ferromagnetic vector spin model possessing the lee yang property thermodynamic limit at the critical point and above the hierarchical ferromagneticn dimensional vector spin model as a sequence of probability measures onrn is considered the starting element of this sequence is chosen to belong to the lee yang class of measures that is defined in the paper and includes most known examples 4 measures gaussian measures and so on for this model we probe two thermodynamic limit theorems one of them is just the classical central limit theorem for weakly dependent random vectors it describes the convergence of classically normed sums of spins when temperature is sufficiently high the other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature it corresponds to the strong dependence of spins which appears at the critical point of the model

finite size scaling for the correlation function of the spherical model with long range interactions finite size scaling for the effective correlation length and the pair correlation function of the mean spherical model is studied in the case of general geometry ld d d periodic boundary conditions and long range interactions decaying like r d at large distances r with arbitrary real parameters 0 2 d 2 d 0 the analytical technique used is based on integral transformations with kernels of mittag leffler type it makes it possible to easily generalize a number of results available only for short range interactions or in special cases of the ld d d geometry the effective correlation length is identified at arbitrary temperatures from the finite size large distance asymptotic behavior of the pair correlation function it is explicitly shown that the finite size scaling functions are not singular in the e expansion when e 0 neither at d e nor at d 2 e moreover the applicability of the e expansion is tested in the specific finite size case of d e the definition of the scaled fiel

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

on the finite size scaling in quantum critical phenomena abstract an exactly solvable d dimentional model of a structural phase transition confined to a geometry ld d d are subjected to periodic boundary conditions is considered in the low temperature region it is shown that in this region quantum effects are essential and that borderline dimensionalities between which finite size scaling holds do not coincide with the lower and upper critical dimensionalities for the bulk system a generalized version of the dimensional cross over rule is established i e the finite size scaling behaviour of a d dimensional system finite in d d d directions in the quantum limit is equivalent to the finite size scaling behaviour of the classical d 1 dimensional system also finite in d directions

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

universal amplitudes in finite size scaling for an anharmonic crystal abstract we consider an exactly solvable d dimensional lattice model of an anharmonic crystal confined to a geometry l d d d and subject to periodic boundary conditions the general idea of finite size scaling on the whole phase diagram is tested and the universal amplitudes of the correlation length near the upper and lower critical dimensions in both the classifical and the quantum multicritical points are computed a detailed analysis is given in terms of the dimensions d and d of the lattice and parameter of the harmonic force decreasing at long distances as 1 r d 0 2

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

glauber dynamics of fluctuations we derive the time evolution of the normal fluctuations of a classical lattice spin system induced by a generalized glauber dynamics the canonical form of this dynamics is derived we prove that it is asymptotically i e after the central limit free the results are applied to give a rigorous proof of the macroscopic reciprocity relations and the linear theory for small deviations from equilibrium

euclidean gibbs measures of interacting quantum anharmonic oscillators a rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting dimensional quantum anharmonic oscillators is given the oscillators are indexed by the elements of a countable set mathbb l subset mathbb r d possibly irregular the anharmonic potentials vary from site to site and the interaction has infinite range the description is based on the representation of the gibbs states in terms of path measures the so called euclidean gibbs measures it is proven that a the set of such measures mathcal g rm t is non void and compact b every mu in mathcal g rm t obeys an exponential integrability estimate the same for the whole set mathcal g rm t c every mu in mathcal g rm t has a lebowitz presutti type support d mathcal g rm t is a singleton at high temperatures the case of attractive interaction and nu 1 is studied in more detail we prove that a mathcal g rm t 1 at low temperatures b mathcal g rm t 1 due to quantum effects and at a nonzero external field thereby a qualitative theory of phase transitions and quantum effects which interprets most important experimental data known for the corresponding physical objects is developed

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

small mass implies uniqueness of gibbs states of a quantum crystal a model of interacting quantum particles performing one dimensional anharmonic oscillations around their equilibrium positions which form a lattice d is considered for this model it is proved that the set of tempered euclidean gibbs measures is a singleton provided the particle mass is less than a certain bound m which is independent of the temperature 1 this settles a problem that was open for a long time and is an essential improvement of a similar result proved before by the same authors 5 where the bound m depended on in such a way that m ast beta rightarrow 0 as beta rightarrow infty

the influence of external boundary conditions on the spherical model of a ferromagnet i magnetization profiles the spherical model of a ferromagnet is investigated for various external boundary conditions it is shown that besides the well known critical point a second one can be produced by the boundary conditions although the main asymptotic of the free energy is analytic at the new critical point theo n1 2 d asymptotic possesses a singularity here a natural order parameter of the model has singularities at both critical points the magnetization profile is studied for the whole range of the model s parameters and at different scales it is shown that in an appropriate regime below the second critical temperature the magnetization profile freezes that is becomes temperature independent distributions of the single spin variables and some macroscopic observables including normalized total spin are studied for the whole temperature range including the critical points

an investigation of finite size scaling for systems with long range interaction the spherical model a method is suggested for the derivation of finite size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr d whered is the space dimensionality and 0 it allows for a unified treatment of short range 2 and long range 2 interaction the asymptotic analysis is illustrated by the mean spherical model of general geometryld d d subject to periodic boundary conditions the fisher privman equation of state is generalized to arbitrary real values ofd 0 d it is shown that thee expansion may be used to study the breakdown of standard finite size scaling at the borderline dimensionalities

classical dipoles on a finite triangular lattice the spherical model approximation abstract in the framework of the spherical model it is shown that a phase transition at finite temperature to a ferromagnetic phase in a two dimensional system with dipole dipole and exchange interactions on a lattice with arbitrary rhombicity angle exists if the ferromagnetic ground state is not continuously degenerate in spin direction when the degeneracy exists the system exhibits essential singularities in the thermodynamic functions at t 0 finite size effects in such systems are investigated in the example of the triangular latice under periodic boundary conditions the existence of only one relevant variable determining the crossover from infinite to finite size behavior is found as t 0 is approached despite that there are two characteristic lengths determining the scale of variation of the correlation function the validity of the general finite size scalling relations in terms of this variable is established

automatic model based segmentation of the heart in ct images automatic image processing methods are a pre requisite to efficiently analyze the large amount of image data produced by computed tomography ct scanners during cardiac exams this paper introduces a model based approach for the fully automatic segmentation of the whole heart four chambers myocardium and great vessels from 3 d ct images model adaptation is done by progressively increasing the degrees of freedom of the allowed deformations this improves convergence as well as segmentation accuracy the heart is first localized in the image using a 3 d implementation of the generalized hough transform pose misalignment is corrected by matching the model to the image making use of a global similarity transformation the complex initialization of the multicompartment mesh is then addressed by assigning an affine transformation to each anatomical region of the model finally a deformable adaptation is performed to accurately match the boundaries of the patient s anatomy a mean surface to surface error of 0 82 mm was measured in a leave one out quantitative validation carried out on 28 images moreover the piecewise affine transformation introduced for mesh initialization and adaptation shows better interphase and interpatient shape variability characterization than commonly used principal component analysis