the asymmetric exclusion process and brownian excursions we consider the totally asymmetric exclusion process tasep in one dimension in its maximal current phase we show by an exact calculation that the non gaussian part of the fluctuations of density can be described in terms of the statistical properties of a brownian excursion numerical simulations indicate that the description in terms of a brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase

spectral gap of the totally asymmetric exclusion process at arbitrary filling we calculate the spectral gap of the markov matrix of the totally asymmetric simple exclusion process tasep on a ring of l sites with n particles our derivation is simple and self contained and extends a previous calculation that was valid only for half filling we use a special property of the bethe equations for tasep to reformulate them as a one body problem our method is closely related to the one used to derive exact large deviation functions of the tasep

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

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

parameter space warping shape based correspondence between morphologically different objects this paper presents a novel and comprehensive method for the automated determination of correspondences between two morphologically different two dimensional 2 d or three dimensional 3 d objects correspondences are determined by warping parametric representations of the objects to be matched the warp is guided by the minimization of a similarity criterion function that measures features related to structural correspondence including euclidian point to point distance and differences in normals and curvature the method uses a continuous harmonic parameterization for both the object and the warp which provides 1 a high degree of computational efficiency 2 robust extraction of differential features not subject to discretization errors or noise amplification in differentiation 3 direct formulation of constraints to avoid overlaps in the resulting correspondence set and 4 a scale space paradigm of object shape and warp the new method does not search for individual landmarks but operates with a complete integrated representation of the object geometry the method was tested on 2 d and 3 d objects with substantial shape differences results demonstrated substantial improvements of 2 33 in correspondence accuracy and 15 59 in correspondence quality compared with direct registration methods

building 3 d statistical shape models by direct optimization statistical shape models are powerful tools for image interpretation and shape analysis a simple yet effective way of building such models is to capture the statistics of sampled point coordinates over a training set of example shapes however a major drawback of this approach is the need to establish a correspondence across the training set in 2 d a correspondence is often defined using a set of manually placed landmarks and linear interpolation to sample the shape in between such annotation is however time consuming and subjective particularly when extended to 3 d in this paper we show that it is possible to establish a dense correspondence across the whole training set automatically by treating correspondence as an optimization problem the objective function we use for the optimization is based on the minimum description length principle which we argue is a criterion that leads to models with good compactness specificity and generalization ability we manipulate correspondence by reparameterizing each training shape we describe an explicit representation of reparameterization for surfaces in 3 d that makes it impossible to generate an illegal i e not one to one correspondence we also describe several large scale optimization strategies for model building and perform a detailed analysis of each approach finally we derive quantitative measures of model quality allowing meaningful comparison between models built using different methods results are given for several different training sets of 3 d shapes which show that the minimum description length models perform significantly better than other approaches

new algorithms for 2d and 3d point matching pose estimation and correspondence abstract a fundamental open problem in computer vision determining pose and correspondence between two sets of points in space is solved with a novel fast robust and easily implementable algorithm the technique works on noisy 2d or 3d point sets that may be of unequal sizes and may differ by non rigid transformations using a combination of optimization techniques such as deterministic annealing and the softassign which have recently emerged out of the recurrent neural network statistical physics framework analog objective functions describing the problems are minimized over thirty thousand experiments on randomly generated points sets with varying amounts of noise and missing and spurious points and on hand written character sets demonstrate the robustness of the algorithm

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

solving the kpz equation we introduce a new concept of solution to the kpz equation which is shown to extend the classical cole hopf solution this notion provides a factorisation of the cole hopf solution map into a universal measurable map from the probability space into an explicitly described auxiliary metric space composed with a new solution map that has very good continuity properties the advantage of such a formulation is that it essentially provides a pathwise notion of a solution together with a very detailed approximation theory in particular our construction completely bypasses the cole hopf transform thus laying the groundwork for proving that the kpz equation describes the uctuations of systems in the kpz universality class as a corollary of our construction we obtain very detailed new regularity results about the solution as well as its derivative with respect to the initial condition other byproducts of the proof include an explicit approximation to the stationary solution of the kpz equation a well posedness result for the fokker planck equation associated to a particle diusing in a rough space time dependent potential and a new periodic homogenisation result for the heat equation with a space time periodic potential one ingredient in our construction is an example of a non gaussian rough path such that the area process of its natural approximations needs to be renormalised by a diverging term for the approximations to converge

high dimensional image registration using symmetric priors this paper is about warping a brain image from one subject the object image so that it matches another the template image a high dimensional model is used whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image bayesian statistics are used to obtain a maximum a posteriori map estimate of the deformation field the validity of any registration method is largely based upon the constraints or in this instance priors incorporated into the model describing the transformations in this approach we assume that the priors should have some form of symmetry in that priors describing the probability distribution of the deformations should be identical to those for the inverses i e warping brain a to brain b should not be different probabilistically from warping b to a the fundamental assumption is that the probability of stretching a voxel by a factor of n is considered to be the same as the probability of shrinking n voxels by a factor of n 1 in the bayesian framework adopted here the priors are assumed to have a gibbs form where the gibbs potential is a penalty function that embodies this symmetry the penalty function of choice is based upon the singular values of the jacobian having a lognormal distribution this enforces a continuous one to one mapping a gradient descent algorithm is presented that incorporates the above priors in order to obtain a map estimate of the deformations we demonstrate this approach for the two dimensional case but the principles can be extended to three dimensions a number of examples are given to demonstrate how the method works

fluctuations of tasep on a ring in relaxation time scale we consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions we assume that the size of the ring and the number of particles tend to infinity proportionally and evaluate the fluctuations of tagged particles and currents the crossover from the kpz dynamics to the equilibrium dynamics occurs when the time is proportional to the 3 2 power of the ring size we compute the limiting distributions in this relaxation time scale the analysis is based on an explicit formula of the finite time one point distribution obtained from the coordinate bethe ansatz method 2017 wiley periodicals inc

work fluctuations for a brownian particle in a harmonic trap with fluctuating locations we consider a brownian particle in a harmonic trap the location of the trap is modulated according to an ornstein uhlenbeck process we investigate the fluctuation of the work done by the modulated trap on the brownian particle in a given time interval in the steady state we compute the large deviation as well as the complete asymptotic form of the probability density function of the work done the theoretical asymptotic forms of the probability density function are in very good agreement with the numerics we also discuss the validity of the fluctuation theorem for this system

brownian gibbs property for airy line ensembles consider a collection of n brownian bridges b i n n to mathbb r b i n b i n 0 1 i n conditioned not to intersect the edge scaling limit of this system is obtained by taking a weak limit as n of the collection of curves scaled so that the point 0 21 2 n is fixed and space is squeezed horizontally by a factor of n 2 3 and vertically by n 1 3 if a parabola is added to each of the curves of this scaling limit an x translation invariant process sometimes called the multi line airy process is obtained we prove the existence of a version of this process which we call the airy line ensemble in which the curves are almost surely everywhere continuous and non intersecting this process naturally arises in the study of growth processes and random matrix ensembles as do related processes with wanderers and outliers we formulate our results to treat these relatives as well note that the law of the finite collection of brownian bridges above has the property called the brownian gibbs property of being invariant under the following action select an index 1 k n and erase b k on a fixed time interval a b n n then replace this erased curve with a new curve on a b according to the law of a brownian bridge between the two existing endpoints a b k a and b b k b conditioned to intersect neither the curve above nor the one below we show that this property is preserved under the edge scaling limit and thus establish that the airy line ensemble has the brownian gibbs property an immediate consequence of the brownian gibbs property is a confirmation of the prediction of m prahofer and h spohn that each line of the airy line ensemble is locally absolutely continuous with respect to brownian motion we also obtain a proof of the long standing conjecture of k johansson that the top line of the airy line ensemble minus a parabola attains its maximum at a unique point this establishes the asymptotic law of the transversal fluctuation of last passage percolation with geometric weights our probabilistic approach complements the perspective of exactly solvable systems which is often taken in studying the multi line airy process and readily yields several other interesting properties of this process

maximum distributions of bridges of noncolliding brownian paths one dimensional brownian motion starting from the origin at time t 0 conditioned to return to the origin at time t 1 and to stay positive during time interval 0 t 1 is called the bessel bridge with duration 1 we consider an n particle system of such bessel bridges conditioned never to collide with each other in 0 t 1 which is the continuum limit of the vicious walk model in watermelon configuration with a wall distributions of maximum values of paths attained in the time interval t epsilon 0 1 are studied to characterize the statistics of random patterns of the repulsive paths on the spatiotemporal plane for the outermost path the distribution function of maximum value is exactly determined for general n we show that the present n path system of noncolliding bessel bridges is realized as the positive eigenvalue process of the 2nx2n matrix valued brownian bridge in the symmetry class c using this fact computer simulations are performed and numerical results on the n dependence of the maximum value distributions of the inner paths are reported the present work demonstrates that the extreme value problems of noncolliding paths are related to random matrix theory the representation theory of symmetry and number theory

exact diffusion constant for the one dimensional partially asymmetric exclusion model we calculate exactly the diffusion constant associated with the fluctuations of the current for the partial asymmetric exclusion model on a ring with an arbitrary number of particles and holes we also give the diffusion constant of a tagged particle on that ring our approach extends using the deformed harmonic oscillator algebra a result already known for the fully asymmetric case in the limit of weak asymmetry we extract from our exact expression the crossover between the edwards wilkinson and the kardar parisi zhang equations in 1 1 dimensions

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

a multi layer extension of the stochastic heat equation motivated by recent developments on solvable directed polymer models we define a multi layer extension of the stochastic heat equation involving non intersecting brownian motions by developing a connection with darboux transformations and the two dimensional toda equations we conjecture a markovian evolution in time for this multi layer process as a first step in this direction we establish an analogue of the karlin mcgregor formula for the stochastic heat equation and use it to prove a special case of this conjecture

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

pre organizing shape instances for landmark based shape correspondence the major challenge in constructing a statistical shape model for a structure is shape correspondence which identifies a set of corresponded landmarks across a population of shape instances to accurately estimate the underlying shape variation both global or pairwise shape correspondence methods have been developed to automatically identify the corresponded landmarks for global methods landmarks are found by optimizing a comprehensive objective function that considers the entire population of shape instances while global methods can produce very accurate shape correspondence they tend to be very inefficient when the population size is large for pairwise methods all shape instances are corresponded to a given template independently therefore pairwise methods are usually very efficient however if the population exhibits a large amount of shape variation pairwise methods may produce very poor shape correspondence in this paper we develop a new method that attempts to address the limitations of global and pairwise methods in particular we first construct a shape tree to globally organize the population of shape instances by identifying similar shape instance pairs we then perform pairwise shape correspondence between such similar shape instances with high accuracy finally we combine these pairwise correspondences to achieve a unified correspondence for the entire population of shape instances we evaluate the proposed method by comparing its performance to five available shape correspondence methods and show that the proposed method achieves the accuracy of a global method with the efficiency of a pairwise method

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

probability distribution of the free energy of a directed polymer in a random medium we calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder by using the fact that the nth moment of the partition function is given by the ground state energy of a quantum problem of n interacting particles on a ring of length l we write an integral equation allowing to expand these moments in powers of the strength of the disorder gamma or in powers of n for n small and n approximately lgamma 1 2 the moments take a scaling form which allows us to describe all the fluctuations of order 1 l of the free energy per unit length of the directed polymer the distribution of these fluctuations is the same as the one found recently in the asymmetric exclusion process indicating that it is characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimensions

the use of three and four dimensional surface harmonics for rigid and nonrigid shape recovery and representation the use of spherical harmonics for rigid and nonrigid shape representation is well known this paper extends the method to surface harmonics defined on domains other than the sphere and to four dimensional spherical harmonics these harmonics enable us to represent shapes which cannot be represented as a global function in spherical coordinates but can be in other coordinate systems prolate and oblate spheroidal harmonics and cylindrical harmonics are examples of surface harmonics which we find useful nonrigid shapes are represented as functions of space and time either by including the time dependence as a separate factor or by using four dimensional spherical harmonics this paper compares the errors of fitting various surface harmonics to an assortment of synthetic and real data samples both rigid and nonrigid in all cases we use a linear least squares approach to find the best fit to given range data it is found that for some shapes there is a variation among geometries in the number of harmonics functions needed to achieve a desired accuracy in particular it was found that four dimensional spherical harmonics provide an improved model of the motion of the left ventricle of the heart

brownian bridges for late time asymptotics of kpz fluctuations in finite volume height fluctuations are studied in the one dimensional totally asymmetric simple exclusion process with periodic boundaries with a focus on how late time relaxation towards the non equilibrium steady state depends on the initial condition using a reformulation of the matrix product representation for the dominant eigenstate the statistics of the height at large scales is expressed for arbitrary initial conditions in terms of extremal values of independent standard brownian bridges comparison with earlier exact bethe ansatz asymptotics leads to explicit conjectures for some conditional probabilities of non intersecting brownian bridges with exponentially distributed distances between the endpoints

exact solutions for kpz type growth processes random matrices and equilibrium shapes of crystals abstract three models from statistical physics can be analyzed by employing space time determinantal processes 1 crystal facets in particular the statistical properties of the facet edge and equivalently tilings of the plane 2 one dimensional growth processes in the kardar parisi zhang universality class and directed last passage percolation 3 random matrices multi matrix models and dyson s brownian motion we explain the method and survey results of physical interest

modeling analysis and visualization of left ventricle shape and motion by hierarchical decomposition this paper presents an approach to the modeling analysis and visualization of left ventricle motion and deformation the authors modeling of left ventricle shape and motion as a hierarchical representation enables them to develop a promising noninvasive technique for monitoring heart dynamics where both image analysis and image synthesis are involved the proposed hierarchical motion model of left ventricle is constructed by combining several existing simple models and is able to capture major motion and deformation components of the left ventricle the hierarchical decomposition characterizes the left ventricle motion and deformation in a coarse to fine fashion and leads to computationally efficient estimation algorithms the authors estimate the global rigid motion of the left ventricle by establishing a time varying object centered coordinate system the global deformations of the left ventricle are obtained by fitting the given data to superquadric modeling primitives the local deformations are estimated by a tensor description approach that is based on the locally deformable surface obtained by constructing spherical harmonic local surface from the residues of global shape estimation the authors also describe in this paper methods of image synthesis and dynamic animation for visualizing the estimated results of the time varying left ventricle shape motion and deformations these animation results are consistent with the apparent motion pattern of the left ventricle and therefore show the success of the authors hierarchical decomposition based approach

non colliding brownian motions and the extended tacnode process we consider non colliding brownian motions with two starting points and two endpoints the points are chosen so that the two groups of brownian motions just touch each other a situation that is referred to as a tacnode the extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by delvaux kuijlaars and zhang the form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by adler ferrari and van moerbeke we also obtain the correlation kernel for a finite number of non colliding brownian motions starting at two points and ending at arbitrary points

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

accurate approximations to the sum of generalized random variables and applications in the performance analysis of diversity systems accurate closed form approximations to the sum of independent identically distributed eta mu and kappa mu random variables are provided the proposed approximations turn out to be simple precise and useful for obtaining important performance metrics of communications systems where sums of variates arise in particular average bit error rate and level crossing rate of multibranch equal gain combining receivers are attained to illustrate the applicability of the approximations some sample examples show that the intricate exact solution and the simple approximate expressions yield results that are almost indistinguishable from each other

brownian motion with a parabolic drift and airy functions let w t t be two sided brownian motion originating from zero and let v a be defined by v a sup t w t t a 2 is maximal then v a a is a markovian jump process running through the locations of maxima of two sided brownian motion with respect to the parabolas fa t t a 2 we give an analytic expression for the infinitesimal generators of the processes a in terms of airy functions in theorem 4 1 this makes it possible to develop asymptotics for the global behavior of a large class of isotonic estimators i e estimators derived under order restrictions an example of this is given in groeneboom 1985 where the asymptotic distribution of the standardized l1 distance between a decreasing density and the grenander maximum likelihood estimator of this density is determined on our way to theorem 4 1 we derive some other results for example we give an analytic expression for the joint density of the maximum and the location of the maximum of the process w t ct2 t where c is an aribrary positive constant we also determine the laplace transform of the integral over a brownian excursion these last results also have recently been derived by several other authors using a variety of methods

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

skeletal shape correspondence through entropy we present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points each object s interior is modeled by an s rep i e by a sampled folded two sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary the skeleton is divided into three parts the up side the down side and the fold curve the spokes on each part are treated separately and using spoke interpolation are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes geometric properties while sampling the object interior regularly as with the surface boundary based correspondence method of cates et al entropy is used to measure both the probability distribution tightness and the sampling regularity here of the spokes geometric properties evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions this improvement is greater than that achieved by an entropy based correspondence method on the boundary points

on matching brain volumes abstract to characterize the complex morphological variations that occur naturally in human neuroanatomy so that their confounding effect can be minimized in the identification of brain structures in medical images a computational framework has evolved in which individual anatomies are modeled as warped versions of a canonical representation of the anatomy known as an atlas to realize this framework the method of elastic matching was invented for determining the spatial mapping between a three dimensional image pair in which one image volume is modeled as an elastic continuum that is deformed to match the appearance of the second volume in this paper we review the seminal ideas underlying the elastic matching technique consider the practical implications of an integral formulation of the approach and explore a more general bayesian interpretation of the method in order to address issues that are less naturally resolved within a continuum mechanical setting such as the examination of a solution s reliability or the incorporation of empirical information that may be available about the spatial mappings into the analysis

a physics based coordinate transformation for 3 d image matching many image matching schemes are based on mapping coordinate locations such as the locations of landmarks in one image to corresponding locations in a second image a new approach to this mapping coordinate transformation called the elastic body spline ebs is described the spline is based on a physical model of a homogeneous isotropic three dimensional 3 d elastic body the model can approximate the way that some physical objects deform the ebs as well as the affine transformation the thin plate spline and the volume spline are used to match 3 d magnetic resonance images mri s of the breast that are used in the diagnosis and evaluation of breast cancer these coordinate transformations are evaluated with different types of deformations and different numbers of corresponding paired coordinate locations in all but one of the cases considered using the ebs yields more similar images than the other methods

exact distribution of the maximal height of p vicious walkers using path integral techniques we compute exactly the distribution of the maximal height hp of p nonintersecting brownian walkers over a unit time interval in one dimension both for excursions p watermelons with a wall and bridges p watermelons without a wall for all integer p or 1 for large p we show that approximately square root 2p excursions whereas approximately square root p bridges our exact results prove that previous numerical experiments only measured the preasymptotic behaviors and not the correct asymptotic ones in addition our method establishes a physical connection between vicious walkers and random matrix theory

robust point correspondence applied to two and three dimensional image registration accurate and robust correspondence calculations are very important in many medical and biological applications often the correspondence calculation forms part of a rigid registration algorithm but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time in this paper a new correspondence calculation algorithm csm correspondence by sensitivity to movement is described a robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched if the correspondence is reliable a perturbation in the position of this point should not result in a large movement of the correspondence a measure of reliability is also calculated this correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2d elastic registration algorithm for warping serial sections and a 3d rigid registration algorithm for registering pre and postoperative facial range scans these applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the csm method it is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondences

point tracked quantitative analysis of left ventricular surface motion from 3 d image sequences proposes and validates the hypothesis that one can use differential shape properties of the myocardial surfaces to recover dense field motion from standard three dimensional 3 d image sequences mri and ct quantitative measures of left ventricular regional function can be further inferred from the point correspondence maps the noninvasive algorithm derived results are validated on two levels first the motion trajectories are compared to those of implanted imaging opaque markers of a canine model in two imaging modalities where subpixel accuracy is achieved second the validity of using motion parameters path length and thickness changes for detecting myocardial injury area is tested by comparing algorithms derived results to postmortem analysis ttc staining of myocardial tissue where the achieved pearson product moment correlation value is 0 968