finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media a numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented the method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield upon appropriate averaging of the fine scale velocity field the coarse scale or equivalent grid block permeability when the region over which this coarse scale permeability is computed constitutes a representative elementary volume rev the resulting equivalent permeability may be interpreted as the effective permeability of the region solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle based finite element numerical procedure which allows for the modeling of geometrically complex features the specification of periodic boundary conditions is shown to yield symmetric positive definite equivalent permeability tensors in all cases the method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields the applicability and limitations of the method for these more general heterogeneity fields are discussed

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

a synthesis of approaches to upscaling of hydraulic conductivities simulation of flow through heterogeneous media often requires discretizing the flow domain into blocks and assigning an equivalent block conductivity value to each one of them the process of defining block conductivities from point values is termed upscaling a number of approaches to upscaling are available most of which consider the uncertainty associated with any natural property so that they cast the problem in a stochastic frame recently indelman and dagan 1993a b provided a general stochastic methodology to upscaling in heterogeneous anisotropic formations by means of the dissipation energy function unfortunately they did not provide any practical method to compute block values from point ones the objective of this work is twofold first we analyze different practical approaches to compute block conductivities and find that all of them provide very similar results in terms of actual computed values second we check that all approaches verify approximately a number of conditions stated by indelman and dagan 1993a specifically we show analytically that for regular blocks the methodologies of both rubin and gomez hernandez 1990 and desbarats 1992 which we call practical methodologies satisfy the condition that the effective conductivity obtained from a field where the elementary conductivities are defined over a certain support we call this the actual formation is identical to that obtained from the same field with conductivities defined at a larger support upscaled formation the analysis is carried out by working with the logarithm of block conductivities and using a small perturbation expansion and thus is strictly valid for small variances on the other hand we show numerically that the two methodologies satisfy approximately an important condition stated in terms of the dissipation energy that block averaged dissipation values computed are indeed very close to the true dissipation values in each block the agreement is even better if we consider statistical moments instead of point values as an important conclusion we should note that all practical methodologies considered in this work perform equally well and more important constitute a simple way to treat an otherwise very complex problem

non linear analysis of shells with arbitrary evolving cracks using xfem a new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method the method is valid for completely non linear problems through the thickness cracks in sandwich shells are considered an exact shell kinematics is presented and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition to avoid locking an enhanced strain formulation is proposed for the 4 node cracked shell element a finite strain plane stress constitutive model based on the logarithmic corotational rate is employed a cohesive zone model is introduced which embodies the special characteristics of the shell kinematics stress intensity factors are calculated for selected problems and crack propagation problems are solved copyright 2004 john wiley sons ltd

scaling of constitutive relationships in unsaturated heterogeneous media a numerical investigation numerical models of groundwater flow in the unsaturated zone require relative conductivity and moisture retention curves at a discretization scale much larger than that at which these constitutive relationships are measured this study seeks to identify simple scaling laws linking parameters of block scale constitutive relationships with the parameters of their measurement scale counterparts represented here using gardner russo models the two parameters of these models saturated conductivity and pore size distribution parameter are viewed as cross correlated regionalized variables with isotropic or anisotropic spatial correlation structures and are simulated using the sequential gaussian method upscaled constitutive curves for steady gravity drainage through three dimensional heterogeneous domains are then constructed by repeating numerical flow experiments for a series of applied infiltration rates and plotting the resulting upscaled relative conductivities and average water saturations against average matric potentials the experiments reveal clear log linear relationships between upscaled relative conductivities and average matric potentials the slopes of which are used to define an upscaled pore size distribution parameter the reciprocal of this quantity which represents an upscaled characteristic capillary length is very well approximated by a spatial power average of its measurement scale values furthermore the averaging exponent is found to be the same as that associated with the upscaling of saturated conductivities over the same flow domains when average matric potentials are normalized using this upscaled characteristic capillary length relative conductivity and moisture saturation values for widely different flow field realizations collapse along well defined curves however for wet conditions the form of these curves differs from that of the models assumed at the measurement scale

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

automatic active model initialization via poisson inverse gradient active models have been widely used in image processing applications a crucial stage that affects the ultimate active model performance is initialization this paper proposes a novel automatic initialization approach for parametric active models in both 2 d and 3 d the pig initialization method exploits a novel technique that essentially estimates the external energy field from the external force field and determines the most likely initial segmentation examples and comparisons with two state of the art automatic initialization methods are presented to illustrate the advantages of this innovation including the ability to choose the number of active models deployed rapid convergence accommodation of broken edges superior noise robustness and segmentation accuracy

segmentation of external force field for automatic initialization and splitting of snakes active contours or snakes have been extensively utilized in handling image segmentation and classification problems in traditional active contour models snake initialization is performed manually by users and topological changes such as splitting of the snake cannot be automatically handled in this paper we introduce a new method to solve the snake initialization and splitting problem based on an area segmentation approach the external force field is segmented first and then the snake initialization and splitting can be automatically performed by using the segmented external force field such initialization and splitting produces multiple snakes each of which is within the capture range associated to an object and will be evolved to the object boundary the external force used in this paper is a gradient vector flow with an edge preserving property epgvf which can prevent the snakes from passing over weak boundaries to segment the external force field we represent it with a graph and a graph theory approach can be taken to determine the membership of each pixel experimental results establish the effectiveness of the proposed approach

modeling the large scale dynamics of saturated groundwater flow using spatial filtering theory 1 theoretical development we develop a model and a framework for understanding the explicitly resolved large scale dynamics of groundwater flow in fully saturated heterogeneous porous media the approach is based upon the large eddy simulation les methodology from geophysical fluid dynamics the idea behind the les approach is to explicitly resolve the larger scales of flow and provide a closure model for the effect of subgrid scales upon resolved scales the technical foundation of the method rests on a spatial filtering operation which allows one to precisely define the scale of the model we spatially filter darcy s law and the continuity equation to produce a model for the resolved scale dynamics we develop les approximations for the resulting flow equations and a closure model for unresolved subgrid scale terms we model the subgrid terms using resolved scale quantities only and thus do not require subgrid scale information the accuracy of these closure models depends upon the scale at which hydraulic conductivity is measured by field tests we characterize the approximations used to model subgrid scale effects asymptotically with a small parameter the dimensionless filter width defined as the ratio of the filter width to the dominant length scale of the explicitly resolved variables

fast constrained surface extraction by minimal paths in this paper we consider a new approach for single object segmentation in 3d images our method improves the classical geodesic active surface model it greatly simplifies the model initialization and naturally avoids local minima by incorporating user extra information into the segmentation process the initialization procedure is reduced to introducing 3d curves into the image these curves are supposed to belong to the surface to extract and thus also constitute user given information hence our model finds a surface that has these curves as boundary conditions and that minimizes the integral of a potential function that corresponds to the image features our goal is achieved by using globally minimal paths we approximate the surface to extract by a discrete network of paths furthermore an interpolation method is used to build a mesh or an implicit representation based on the information retrieved from the network of paths our paper describes a fast construction obtained by exploiting the fast marching algorithm and a fast analytical interpolation method moreover a level set method can be used to refine the segmentation when higher accuracy is required the algorithm has been successfully applied to 3d medical images and synthetic images

upscaling of permeability of anisotropic heterogeneous formations 1 the general framework in numerical simulations of flow through heterogeneous formations the domain is partitioned into numerical elements the solution requires assigning physical properties to each numerical block the process of transferring information from the scale of actual heterogeneity to that of the numerical elements is known as upscaling we consider steady one phase flow and the only property of interest is the permeability which is regarded as a random space function and the same is true for the upscaled conductivity in this paper we establish the necessary and sufficient conditions to be satisfied by upscaling the necessary conditions are expressed with the aid of the global response of the formation e g the total flux caused by a constant pressure head drop applied on the boundaries the requirement is that the expected value and the variance of the total flux are the same in the actual and upscaled domains these are supplemented by local conditions which stipulate that space averages of flow variables over the numerical blocks in the upscaled domain tend to those in the actual formation when the elements size tends to 0 the result of this analysis is that the upscaled permeability must be such as to ensure the equality in a statistical sense between the space averaged dissipation in the two media by assuming an unbounded domain average uniform flow and stationarity simplified relationships between the moments of the dissipation in the upscaled and actual media are derived it is shown that the effective permeability of the two media is the same the approach is illustrated for stratified formations for which exact composition rules are possible even in this simple case the upscaled permeability is a tensor characterized at second order by two mean components and three covariance functions

upscaling of permeability of anisotropic heterogeneous formations 3 applications the general results of indelman and dagan this issue a b are applied to some cases of interest in applications the exact solution of upscaling of stratified formations is used in order to assess the range of applicability of the first order analysis the explicit expressions of the two first moments of the upscaled permeability are derived for media of two dimensional isotropic and three dimensional axisymmetric actual log permeability of gaussian covariance and for parallelepipedic rectangular for two dimensional averaging elements the effects of the actual log permeability covariance and of the anisotropy of partition elements on the upscaled permeability statistics are analyzed the asymptotic behavior of the upscaled permeability for large and small blocks is discussed for general heterogeneity the strong dependence of the small element limit on the properties of actual heterogeneity and on the shape of the elements is illustrated by typical examples in contrast the homogenization of the upscaled media by large blocks depends primarily on the volume area for two dimensions of the partition element relative to the one based on the correlation scale of the log permeability

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

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

dynamic directional gradient vector flow for snakes snakes or active contour models have been widely used in image segmentation however most present snake models do not discern between positive and negative step edges in this paper a new type of dynamic external force for snakes named dynamic directional gradient vector flow ddgvf is proposed that uses this information for better performance it makes use of the gradients in both x and y directions and deals with the external force field for the two directions separately in snake deformation the ddgvf field is utilized dynamically according to the orientation of snake in each iteration experimental results demonstrate that the ddgvf snake provides a much better segmentation than gvf snake in situations when edges of different directions are present which pose confusion for segmentation

a stochastic approach to the problem of upscaling of conductivity in disordered media theory and unconditional numerical simulations a general problem in groundwater modeling is how to assign conductivity values to blocks of a numerical model in this study a method is proposed to upscale the conductivity measurements observed at a given scale to block conductivity values for arbitrary block size assuming a multilognormal distribution for the point conductivities the block conductivity appears as a random function whose distribution conditional to point measurements can be derived this conditional distribution allows filling the flow simulator blocks with equiprobable realizations of block conductivities locally conditioned to actual data these realizations could also be conditioned to conductivity values measured at any scale if the size of the measurement support is known the analytical results are compared to results obtained through a monte carlo analysis and a good agreement was found even for variances of ln t larger than 1

effective groundwater model parameter values influence of spatial variability of hydraulic conductivity leakance and recharge a stochastic simulation approach was used to inspect the influence of spatial variability in aquifer and recharge properties on effective averaged groundwater model parameters a two dimensional unconfined aquifer model was set up for an area similar to that near livermore california monte carlo simulations were generated for different sets of spatial correlation structures assuming stationarity and an exponential semivariogram for each monte carlo realization groundwater flow was simulated and estimates of the means and standard deviations of the hydraulic head were obtained nine different cases were studied involving different correlation lengths of hydraulic conductivity conditional simulations parameter zonation and spatial recharge distributions results indicate that there is no single uniform value of the hydraulic conductivity that reproduces the expected head values spatial averaging to obtain effective values was based on the p norm power norm which ranges from 1 for the arithmetic mean to 1 for the harmonic mean with 0 representing the geometric mean for the unconditional case the 0 4 p norm seems to best reproduce the expected values the 0 2 p norm gave the best result for the conditional simulation case if the geometric mean were used instead the heads would deviate from the expected heads by about 2 m near the wells some value between the arithmetic and the geometric means of riverbed leakance will give results close to the expected head values the arithmetic mean of aerially distributed recharge produced results with small deviations from the expected head values these particular results may only apply to this modeled system as the pumping pattern and magnitudes exhibited strong influences on zones of maximum head deviation the implication of this work is that if an effective hydraulic conductivity is used in a simulation model it must be selected for a particular set of wells and pumping rates in an aquifer with significant pumping centers the best effective value for a two dimensional unconfined flow model is most likely between the geometric and harmonic mean if the wells are turned off the effective hydraulic conductivity for that flow model reverts to the geometric mean

analysis of variance method for the equivalent conductivity of rectangular blocks we use an analysis of variance anova decomposition of the log hydraulic conductivity f x ln k x as the sum of an average value f plus main effects and interactions of various orders to evaluate the equivalent conductivity of rectangular blocks in d dimensional space some of the anova components are dealt with exactly the effect of the other components is approximated through calibration to the effective conductivity keff under ergodic conditions our analysis applies to both isotropic and anisotropic lognormal k fields we evaluate the theoretical findings through analytical and numerical comparisons with exact results and previously proposed approximations we find that the anova formula is nearly unbiased although its performance is generally inferior to numerical renormalization advantages of the anova formula are that it is less computationally demanding and explicitly shows the dependence of the block conductivity kb on the various components of fluctuation of f inside the block such dependence is more complex than previously assumed considering the anova formula to be unbiased we derive the bias of the geometric mean of the cardwell parsons bounds for three dimensional rectangular blocks

a smoothed finite element method for plate analysis a quadrilateral element with smoothed curvatures for mindlin reissner plates is proposed the curvature at each point is obtained by a non local approximation via a smoothing function the bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells numerical results show that the proposed element is robust computational inexpensive and simultaneously very accurate and free of locking even for very thin plates the most promising feature of our elements is their insensitivity to mesh distortion

second fundamental measure of geometric sets and local approximation of curvatures using the theory of normal cycles we associate with each geometric subset of a riemannian manifold a tensor valued curvature measure which we call its second fundamental measure this measure provides a finer description of the geometry of singular sets than the standard curvature measures moreover we deal with approximation of curvature measures we get a local quantitative estimate of the difference between curvature measures of two geometric subsets when one of them is a smooth hypersurface

constraining active contour evolution via lie groups of transformation we present a novel approach to constraining the evolution of active contours used in image analysis the proposed approach constrains the final curve obtained at convergence of curve evolution to be related to the initial curve from which evolution begins through an element of a desired lie group of plane transformations constraining curve evolution in such a way is important in numerous tracking applications where the contour being tracked in a certain frame is known to be related to the contour in the previous frame through a geometric transformation such as translation rotation or affine transformation for example it is also of importance in segmentation applications where the region to be segmented is known up to a geometric transformation our approach is based on suitably modifying the euler lagrange descent equations by using the correspondence between lie groups of plane actions and their lie algebras of infinitesimal generators and thereby ensures that curve evolution takes place on an orbit of the chosen transformation group while remaining a descent equation of the original functional the main advantage of our approach is that it does not necessitate any knowledge of nor any modification to the original curve functional and is extremely straightforward to implement our approach therefore stands in sharp contrast to other approaches where the curve functional is modified by the addition of geometric penalty terms we illustrate our algorithm on numerous real and synthetic examples

multigrid geometric active contour models geometric active contour models are very popular partial differential equation based tools in image analysis and computer vision we present a new multigrid algorithm for the fast evolution of level set based geometric active contours and compare it with other established numerical schemes we overcome the main bottleneck associated with most numerical implementations of geometric active contours namely the need for very small time steps to avoid instability by employing a very stable fully 2 d implicit explicit time integration numerical scheme the proposed scheme is more accurate and has improved rotational invariance properties compared with alternative split schemes particularly when big time steps are utilized we then apply properly designed multigrid methods to efficiently solve the occurring sparse linear system the combined algorithm allows for the rapid evolution of the contour and convergence to its final configuration after very few iterations image segmentation experiments demonstrate the efficiency and accuracy of the method

a general discrete contour model in two three and four dimensions for topology adaptive multichannel segmentation we present a discrete contour model for the segmentation of image data with any dimension of image domain and value range the model consists of a representation using simplex meshes and a mechanical formulation of influences that drive an iterative segmentation the object s representation as well as the influences are valid for any dimension of the image domain the image influences introduced here can combine information from independent channels of higher dimensional value ranges additionally the topology of the model automatically adapts to objects contained in images noncontextual tests have validated the ability of the model to reproducibly delineate synthetic objects in particular images with a signal to noise ratio of snr spl les 0 5 are delineated within two pixels of their ground truth contour contextual validations have shown the applicability of the model for medical image analysis in image domains of two three and four dimensions in single as well as multichannel value ranges

upscaling of permeability of anisotropic heterogeneous formations 2 general structure and small perturbation analysis the general methodology developed in part 1 indelman and dagan this issue of this study is applied to the detailed analysis of upscaled permeability first the structure of the dissipation function for the general conductivity a tensor of stationary random components is examined with the aid of dimensional analysis it is shown that for arbitrary shapes of the numerical elements the upscaled permeability has also this general structure and the numbers of unknown parameters and equations match this result suggests that the upscaling problem has an unique solution in the particular case of scalar permeability of isotropic covariance of the actual formation it is shown that a similar upscaled permeability is possible only for spherical circular numerical elements otherwise the upscaled permeability has to be a tensor of anisotropic covariance if the actual formation has a scalar permeability of axisymmetric covariance upscaling preserves the last property only for axisymmetric partition elements i e for a sphere cylinder and ellipsoid explicit expressions for the first moments of the upscaled permeability mean covariance are derived at first order in the log permeability variance the detailed computations for a scalar permeability of axisymmetric covariance and for axisymmetric numerical elements lead to simple results the upscaled permeability expected values are components of an axisymmetric tensor whereas the fluctuations are determined by a scalar random space function of anisotropic covariance the general case of upscaling by a first order approximation is examined in appendix b these results will be applied to a few particular cases in part 3 indelman this issue

representation of grid block permeability in coarse scale models of randomly heterogeneous porous media the two basic approaches for the assignment of coarse scale grid block permeabilities from highly detailed permeability descriptions are sampling where the permeability of the coarse scale grid block is simply specified as the fine scale permeability evaluated at the grid block center no averaging is performed and scaleup or homogenization where the coarse scale permeability is determined through some procedure which appropriately averages the fine scale data the intent of this paper is to quantitatively compare these two approaches through extensive numerical calculations for the modeling of single phase flow through two dimensional realizations of randomly heterogeneous porous media with heterogeneity quantified through the correlation length and the variance of the log of permeability 2 several different flow scenarios and two scaleup techniques local and global are considered over a range of l and it is seen that for flows driven by smoothly varying boundary conditions a sampling procedure is more accurate than global scaleup when the length scale of a typical grid block is less than l independent of for flows driven by source terms by contrast more resolution is required for a sampling approach to be preferable to global scaleup particularly at high variances local scaleup is shown to be preferable to either sampling or global scaleup in essentially all cases though its use for more general permeability fields requires additional numerical calculations

image segmentation based on the poincare map method active contour models acms integrated with various kinds of external force fields to pull the contours to the exact boundaries have shown their powerful abilities in object segmentation however local minimum problems still exist within these models particularly the vector field s equilibrium issues different from traditional acms within this paper the task of object segmentation is achieved in a novel manner by the poincare map method in a defined vector field in view of dynamical systems an interpolated swirling and attracting flow isaf vector field is first generated for the observed image then the states on the limit cycles of the isaf are located by the convergence of newton raphson sequences on the given poincare sections meanwhile the periods of limit cycles are determined consequently the objects boundaries are represented by integral equations with the corresponding converged states and periods experiments and comparisons with some traditional external force field methods are done to exhibit the superiority of the proposed method in cases of complex concave boundary segmentation multiple object segmentation and initialization flexibility in addition it is more computationally efficient than traditional acms by solving the problem in some lower dimensional subspace without using level set methods

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

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

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

adapting geostatistical transmissivity simulations to finite difference flow simulators the validity of hydrogeological studies is often dependant on the correct estimation of the flux or equivalently the equivalent transmissivity of the field however depending on the level of fine scale heterogeneity of the porous media considered flow simulators based on the finite differences algorithm can be shown to underestimate the equivalent transmissivity this result is shown to depend on the value on the intermesh transmissivities and not the mesh transmissivities when working with geostatistically simulated point support transmissivities intermesh transmissivities can be directly calculated so that the finite differences result obtained is consistent with the spatial transmissivity distribution

active contour external force using vector field convolution for image segmentation snakes or active contours have been widely used in image processing applications typical roadblocks to consistent performance include limited capture range noise sensitivity and poor convergence to concavities this paper proposes a new external force for active contours called vector field convolution vfc to address these problems vfc is calculated by convolving the edge map generated from the image with the user defined vector field kernel we propose two structures for the magnitude function of the vector field kernel and we provide an analytical method to estimate the parameter of the magnitude function mixed vfc is introduced to alleviate the possible leakage problem caused by choosing inappropriate parameters we also demonstrate that the standard external force and the gradient vector flow gvf external force are special cases of vfc in certain scenarios examples and comparisons with gvf are presented in this paper to show the advantages of this innovation including superior noise robustness reduced computational cost and the flexibility of tailoring the force field

variational segmentation of vector valued images with gradient vector flow in this paper we extend the gradient vector flow field for robust variational segmentation of vector valued images rather than using scalar edge information we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4d gradient vector flow equation to reduce the contribution of noise in the structure tensor image channels are weighted according to a blind estimator of contrast the method is applied to biological volume delineation in dynamic pet imaging and validated on realistic monte carlo simulations of numerical phantoms as well as on real images

a fast algorithm for the estimation of the equivalent hydraulic conductivity of heterogeneous media fast upscaling of hydraulic conductivity is a recurrent problem in modeling flow through heterogeneous porous media we propose a new renormalization technique it is based on the iterative application of the cardwell and parsons 1945 bounds on elementary groups of cells the combination of the bounds with a heuristic formula allows anisotropy to be taken into account the new technique is tested and compared with other fast techniques among the tested techniques the two most reliable ones are the tensorial renormalization and the new simplified renormalization the numerical efficiency of the simplified renormalization leads us to recommend it when a diagonal tensor of equivalent conductivity is sufficient

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

statistics of block conductivity through a simple bounded stochastic medium a monte carlo approach is employed to estimate the distribution of an equivalent conductivity measure the block conductivity which characterizes the total flow rate through a two dimensional bounded domain and which is itself a random variable chi square goodness of fit tests indicate that the lognormal distribution is an appropriate choice for the block conductivity distribution for square domains the mean and variance of the block conductivity are seen to be closely approximated using the statistics of local averages of log conductivity

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

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

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

upscaling transport with mass transfer models mean behavior and propagation of uncertainty 1 the choice of an adequate large scale conceptual transport model constitutes a major challenge associated with the upscaling of solute transport among the different alternatives to the classical advection dispersion model the multirate mass transfer model has been proposed as a valuable and convenient alternative to model the large scale behavior of solute transport this paper evaluates the use of mass transfer models as a constitutive equation for upscaling solute transport to achieve this we compare monte carlo simulations of solute transport at two different support scales transport simulations performed at the smallest scale represent a set of reference transport solutions described at a high resolution which are contrasted against transport simulations obtained using an upscaled model low resolution several formulations of the multirate mass transfer model which differ in the type of memory function single rate double rate and truncated power law are used as a constitutive transport equation the large scale scenario represents a simplified model obtained by partially homogenizing the reference solution results show that the double rate and the truncated power law mass transfer models are capable of properly describing the ensemble average behavior of the main features associated with the integrated breakthrough curves however the uncertainty associated with the upscaled mass transfer models was substantially smaller than that attributed to the reference solution importantly the cumulative distribution function of concentrations associated with the upscaled model follows a distribution similar to the reference solution but with smaller statistical dispersion the reason is that while appropriate memory functions can be used to preserve the residence time distribution of mass particles during upscaling the lack of memory in space prevents the model from reproducing mass fluxes in all directions specifically the reproduction of mass fluxes taking place at the interface between two homogenized blocks of the upscaled model is not satisfied thus providing a poor description of the spatial distribution of mass particles in a given realization

stochastic modeling of groundwater flow by unconditional and conditional probabilities 1 conditional simulation and the direct problem mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated the formation properties hydraulic conductivity transmissivity as well as flow variables head specific discharge solute concentration are regarded as random variables subjected to uncertainty the main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables the unconditional probability density functions are supposed to be stationary multivariate normal while conditioning accounts for the measured values at a few points of the formation two problems of groundwater flow are discussed in part 1 conditional simulation and the direct problem for steady flow analytical results are obtained by using perturbation approximations average uniform head gradient flows as well as recharge and flow to wells are discussed in unconditional modeling the input variable the conductivity or transmissivity log is regarded as stationary and is represented by its constant mean and variogram the ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions in conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points consequently statistical computations are performed for the subensemble of aquifers which preserve the measured values and as a result both input and output variables are nonstationary the main effect of conditioning is to reduce the variance i e the uncertainty of these variables this effect is particularly important in the case of flow toward wells application of the modeling method to field problems is outlined

transmissivity upscaling in numerical models of steady aquifer flow conditional statistics 1 numerical solution of regional scale aquifer flow requires discretizing the transmissivity t for spatially varying t and by the stochastic approach t is modeled as a random field typically both the numerical element scale r and the log transmissivity integral scale i are of order of hundreds to thousands meters consequently the upscaled block transmissivity is random and its statistical moments depend on those of the fine scale t on flow conditions and on r i modeling y ln t as a two dimensional normally distributed stationary random field we have derived dagan and lessoff water resources research 43 w05431 doi 10 1029 2006wr005235 2007 the unconditional statistics of the upscaled ln accurate to the first order in y2 the log transmissivity variance both cases of mean uniform flow solved previously by indelman and dagan transport in porous media 12 161 183 1993 and of strongly nonuniform flow in a circular block of radius r centered at a well of radius rw were considered such upscaling applies either to elements in regions of natural gradient flow or those surrounding a projected well respectively which are sufficiently far from points of measurement of t the present article extends the analysis to account for the presence of a measurement removed in the center of the element e g result of a pumping test the fine scale conditional log transmissivity yc is modeled as multi gaussian of nonstationary mean and of two point covariance which depend on the measured value and distance from the measurement location upscaling in mean uniform flow is related for instance to the case of a pumping well which is not operative but served to determine t while natural gradient flow conditions prevail in the area it was found that upscaling has a significant effect upon the mean upscaled log transmissivity that changes from the measured value for r i 1 to the effective one y ln tg for r i 6 similarly the conditional log transmissivity variance is greatly reduced compared to the unconditional case it tends to zero for r i 0 or r i and it reaches a maximal value of around 0 15 y2 for r i 1 the second case of upscaling in well flow applies to an element with an operative well at its center which was used to determine the transmissivity tw unlike mean uniform flow it is found that upscaling has a very small effect for the realistic values of rw i 0 10 3 and r i 5 in this case the upscaled transmissivity is practically deterministic and equal to the given tw a summary of the two articles dagan and lessoff 2007 and the present one concludes the paper

rags region aided geometric snake an enhanced region aided geometric active contour that is more tolerant toward weak edges and noise in images is introduced the proposed method integrates gradient flow forces with region constraints composed of image region vector flow forces obtained through the diffusion of the region segmentation map we refer to this as the region aided geometric snake or rags the diffused region forces can be generated from any reliable region segmentation technique greylevel or color this extra region force gives the snake a global complementary view of the boundary information within the image which along with the local gradient flow helps detect fuzzy boundaries and overcome noisy regions the partial differential equation pde resulting from this integration of image gradient flow and diffused region flow is implemented using a level set approach we present various examples and also evaluate and compare the performance of rags on weak boundaries and noisy images