aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

testing for effects on variance in experiments with factorial treatment structure and nested errors there is increased interest in industrial experiments aimed at improving quality by reducing the variability of a product characteristic while maintaining the desired mean level of the characteristic analysis of treatment effects on variability however is more difficult than analyzing the effects on mean performance in this article we extend the results of zelen to test for treatment effects on variance when there are two sources of variability that which exists between production runs or setups and variability within runs bootstrap critical values are developed to handle possibly nonnormal errors at either level of variability

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

d optimum designs for heteroscedastic linear models abstract the methods of optimum experimental design are applied to models in which the variance as well as the mean is a parametric function of explanatory variables extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions or the parameters of only one function are of interest the theory also applies whether the mean and variance are functions of the same variables or of different variables although the mathematical foundations differ the example studied is a second order two factor response surface for the mean with a parametric nonlinear variance function the theory is used both for constructing designs and for checking optimality a major potential for application is to experimental design in off line quality control

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

score tests for regression models abstract many score statistics used for testing trends in means either based on the observed values of the response variables or their ranks can be expressed in terms of quadratic forms this article explores systematically the robustness of optimality of these statistics as well as the optimal properties of the associated tests

an efficient method to determine the diagonal loading factor using the constant modulus feature the diagonal loading method is a simple and efficient method that improves the robustness of beamformers however determining an ideal diagonal loading factor dlf is not a trivial problem one that still has not been adequately addressed although beamformers are widely used in radar sonar and many other applications in this correspondence we consider a beamformer used only for digital communication applications in digital communications user information is coded into a sequence with the constant modulus cm in the baseband obviously if the beamformer can cancel interference sufficiently well the outputs of the beamformer should satisfy the cm condition more precisely therefore minimizing cm errors can act as a natural criterion for determining dlfs in this correspondence we present a cost function based on the criterion we also propose a direct search algorithm for dlf determination by minimizing the cost function numerical experiments show the effectiveness of the proposed method

maximal flow through a domain in place of flows on a discrete network we study flows described by a vector field x y in a plane domain the analogue of the capacity constraint is c x y and the strength of sources and sinks is n f on the boundary and div f in the interior we show that the largest the maximal flow is determined by the minimal cut as in the discrete case the dual problem has a 0 1 solution given by the characteristic function of the minimal cut for the continuous problem the argument depends on the coarea formula for functions of bounded variation

global minimization for continuous multiphase partitioning problems using a dual approach this paper is devoted to the optimization problem of continuous multi partitioning or multi labeling which is based on a convex relaxation of the continuous potts model in contrast to previous efforts which are tackling the optimal labeling problem in a direct manner we first propose a novel dual model and then build up a corresponding duality based approach by analyzing the dual formulation sufficient conditions are derived which show that the relaxation is often exact i e there exists optimal solutions that are also globally optimal to the original nonconvex potts model in order to deal with the nonsmooth dual problem we develop a smoothing method based on the log sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal dual model and suggests labelings with maximum entropy such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions an expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization numerical experiments also show that our method outperforms several competitive approaches in various aspects such as lower energies and better visual quality

an approximation for a continuous max flow problem we consider an approximation for the continuous max flow problem stated in 2 by a sequence of max flow problems in finite networks the used approximation scheme was introduced by gomory and hu in 6 chapter 12 but in 6 there is no definition of a continuous flow and therefore also no proof of a convergence of network flows to continuous flows in this sense this paper solves the central open problem of chapter 12 in 6

globally minimal surfaces by continuous maximal flows in this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction we present a solution simulating a continuous maximal flow by a novel system of partial differential equations existing methods are either grid biased graph based methods or suboptimal active contours and surfaces the solution simulates the flow of an ideal fluid with isotropic velocity constraints velocity constraints are defined by a metric derived from image data an auxiliary potential function is introduced to create a system of partial differential equations it is proven that the algorithm produces a globally maximal continuous flow at convergence and that the globally minimal surface may be obtained trivially from the auxiliary potential the bias of minimal surface methods toward small objects is also addressed an efficient implementation is given for the flow simulation the globally minimal surface algorithm is applied to segmentation in 2d and 3d as well as to stereo matching results in 2d agree with an existing minimal contour algorithm for planar images results in 3d segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias

continuous time flows in networks we consider a class of maximum flow problems formulated in a directed network where the arc flows vary as lebesgue measurable functions of time and storage is allowed at the nodes of the network a max flow min cut result of anderson nash and philpott 1 is extended to cover the case where each arc has a traversal time the ideas of the paper are then applied to derive some simple results on emptying networks at least cost

testing multiple dispersion effects in unreplicated fractional factorial designs in unreplicated 2k p designs the assumption of constant variance is commonly made when the variance of the response differs between the two levels of a column in the effect matrix that column produces a dispersion effect in this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column most existing methods for dispersion effect testing in unreplicated fractional factorial designs are subject to these spurious effects we propose a method of dispersion effect testing based on geometric means of residual sample variances we show through examples from the literature and simulations that the proposed test has many desirable properties that are lacking in other tests

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

characterization and optimization of a wave soldering process abstract a case study for improving the quality of a wave soldering process that produced printed circuit boards pcb s is presented a mixed level fractional factorial design was implemented in a high volume production system during normal operational hours the observed ordered categorical data from the bottom side soldered leads were weighted to formulate the average spatial uniformity and dispersion process performance measurements for lead classes like the integrated circuit and printed grid array a polynomial model was established using the least squares method with weights provided by a dispersion function the main effect and interaction model terms were selected by forward and all subsets regressions production quotas topside defects presoldering board temperature and variance models were used to set the constraints for simultaneously optimizing predictions from the average and the uniformity models of all leads a nonlinear optimization routine was used to determine the best and most ro

completely convex formulation of the chan vese image segmentation model the active contours without edges model of chan and vese ieee transactions on image processing 10 2 266 277 2001 is a popular method for computing the segmentation of an image into two phases based on the piecewise constant mumford shah model the minimization problem is non convex even when the optimal region constants are known a priori in siam journal of applied mathematics 66 5 1632 1648 2006 chan esedo lu and nikolova provided a method to compute global minimizers by showing that solutions could be obtained from a convex relaxation in this paper we propose a convex relaxation approach to solve the case in which both the segmentation and the optimal constants are unknown for two phases and multiple phases in other words we propose a convex relaxation of the popular k means algorithm our approach is based on the vector valued relaxation technique developed by goldstein et al ucla cam report 09 77 2009 and brown et al ucla cam report 10 43 2010 the idea is to consider the optimal constants as functions subject to a constraint on their gradient although the proposed relaxation technique is not guaranteed to find exact global minimizers of the original problem our experiments show that our method computes tight approximations of the optimal solutions particularly we provide numerical examples in which our method finds better solutions than the method proposed by chan et al siam journal of applied mathematics 66 5 1632 1648 2006 whose quality of solutions depends on the choice of the initial condition

a simple level set method for solving stefan problems a simple level set method for solving stefan problems is presented this method can be applied to problems involving dendritic solidification our method consists of an implicit finite difference scheme for solving the heat equation and a level set approach for capturing the front between solid and liquid phases of a pure substance our method is accurate with respect to some exact solutions of the stefan problem results indicate that this method can handle topology changes and complicated interfacial shapes and that it can numerically simulate many of the physical features of dendritic solidification

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

signal to noise ratios performance criteria and transformations for the analysis of designed experiments taguchi uses performance criteria that he calls signal to noise sn ratios three such criteria are here denoted by sn t sn l and sn s the criterion sn t was to be used in preference to the standard deviation for the problem of achieving for some quality characteristic y the smallest mean squared error about an operating target value leon shoemaker and kacker 1987 showed how sn t was appropriate to solve this problem only when y was proportional to y on that assumption the same result could be obtained more simply by conducting the analysis in terms of log y rather than y a more general transformation approach is here introduced for other commonly met kinds of dependence between y and y including no dependence and a lambda plot is presented that uses the data to suggest an appropriate transformation the criteria sn l and sn s were for problems in which the objective was to make the response as large or as small as possible it is arg

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

bit threads and holographic entanglement the ryu takayanagi rt formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface using the max flow min cut principle a theorem from network theory we rewrite the rt formula in a way that does not make reference to the minimal surface instead we invoke the notion of a flow defined as a divergenceless norm bounded vector field or equivalently a set of planck thickness bit threads the entanglement entropy of a boundary region is given by the maximum flux out of it of any flow or equivalently the maximum number of bit threads that can emanate from it the threads thus represent entanglement between points on the boundary and naturally implement the holographic principle as we explain this new picture clarifies several conceptual puzzles surrounding the rt formula we give flow based proofs of strong subadditivity and related properties unlike the ones based on minimal surfaces these proofs correspond in a transparent manner to the properties information theoretic meanings we also briefly discuss certain technical advantages that the flows oer over minimal surfaces in a mathematical appendix we review the max flow min cut theorem on networks and on riemannian manifolds and prove in the network case that the set of max flows varies lipshitz continuously in the network parameters

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

divergence of gradient convolution deformable segmentation with arbitrary initializations in this paper we propose a unified approach to deformable model based segmentation the fundamental force field of the proposed method is based on computing the divergence of a gradient convolution field gcf which makes the full use of directional information of the image gradient vectors and their interactions across image domain however instead of directly using such a vector field for deformable segmentation as in the conventional approaches we derive a more salient representation for contour evolution and very importantly we demonstrate that this representation of image force field not only leads to global minimum through convex relaxation but also can achieve the same result using the conventional gradient descent with an intrinsic regularization thus the proposed method can handle arbitrary initializations the proposed external force field for deformable segmentation has both edge based properties in that the gcf is computed from image gradients and the region based attributes since its divergence can be treated as a region indication function moreover nonlinear diffusion can be conveniently applied to gcf to improve its performance in dealing with noise interference we also show the extension of gcf from 2d to 3d in comparison to the state of the art deformable segmentation techniques the proposed method shows greater flexibility in model initialization and optimization realization as well as better performance toward noise interference and appearance variation

least squares approach to blind channel equalization we present a least squares ls algorithm for blind channel equalization based on a reformulation of the godard algorithm a transformation for the equalizer parameters is considered to convert the nonlinear ls problem inherent in the godard algorithm to a linear ls problem unlike the godard 1980 algorithm the proposed ls approach does not suffer from ill convergence to closed eye local minima methods for extracting the equalizer parameters from their transformed version are developed offline and recursive implementations of the ls algorithm are presented the algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis a vis the godard algorithm the channel input correlation does not impose any restriction on the application of the algorithm as long as a weak sufficient excitation condition is satisfied simulation examples are presented to demonstrate the ls approach and to compare it with the godard algorithm

a spatially continuous max flow and min cut framework for binary labeling problems we propose and investigate novel max flow models in the spatially continuous setting with or without i priori defined supervised constraints under a comparative study of graph based max flow min cut we show that the continuous max flow models correspond to their respective continuous min cut models as primal and dual problems in this respect basic conceptions and terminologies from discrete max flow min cut are revisited under a new variational perspective we prove that the associated nonconvex partitioning problems unsupervised or supervised can be solved globally and exactly via the proposed convex continuous max flow and min cut models moreover we derive novel fast max flow based algorithms whose convergence can be guaranteed by standard optimization theories experiments on image segmentation both unsupervised and supervised show that our continuous max flow based algorithms outperform previous approaches in terms of efficiency and accuracy

the impact of unidentified location effects on dispersion effects identification from unreplicated factorial designs there have been several publications on identifying dispersion effects from an unreplicated fractional or full factorial experiment some of these methods implicitly assume that unknown location effects are first identified correctly from the data in practice however an empirical location effects identification procedure may leave some small to moderate location effects undetected it is shown in this study that such unidentified location effects can cumulatively impair subsequent dispersione effects identification numerical evidence based on a welding experiment and results from a simulation study are provided a mathematical explanation of the impact of unidentified location effects on dispersion effects identification is given the dispersion effects identification methods initially proposed for unreplicated data can be naturally extended to replicated experiments with the impact of unidentified location effects eliminated a fluorescent lamp experiment is analyzed to illustrate these methods

fenchel duality and smoothness of solution of the optimal routing problem abstract a linear state and control constrained problem arising in optimal routing in communication networks is investigated by fenchel duality methods the problem reduces to a dual program having a particularly simple solution

a self adaptive oriented particles level set method for tracking interfaces a new method for tracking evolving interfaces by lagrangian particles in conjunction with a level set approach is introduced this numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the eulerian description given by a level set function f to the use of lagrangian massless particles the term oriented points out that the information advected by the particles not only concern the spatial location but also the local outward normal vector n to the interface c and the second fundamental tensor the shape operator n the particles are exactly located upon c and provide all the requested information for tracking the interface on their own in addition a self adaptive mechanism suitably modifies at each time step the markers distribution in the numerical domain each particle behaves both as a potential seeder of new markers on c so as to guarantee an accurate reconstruction of the interface and a de seeder to avoid any useless gathering of markers and to limit the computational effort the algorithm is conceived to avoid any transport equation for f and to confine the level set function to the role of a mere post processing tool thus all the numerical diffusion problems usually affecting the level set methodology are removed the method has been tested both on 2d and 3d configurations it carries out a fast reconstruction of the interface and its accuracy is only limited by the spatial resolution of the mesh

analyzing dispersion effects from replicated factorial experiments recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments a commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within replication variance bartlett and kendall 1946 box and meyer 1986 introduced a pooling technique for unreplicated two level experiments we extend this to replicated two level experiments and compare its performance with the least squares analysis we show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory the pooling technique is generally biased and is not recommended for model identification the least squares analysis performs well as a model identification tool but the estimators can be inefficient in such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood we derive some prop

mac magnetostatic active contour model we propose an active contour model using an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries the major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations weak edges and broken boundaries the proposed method is shown to achieve significant improvements when compared against six well known and state of the art shape recovery methods including the geodesic snake the generalized version of gradient vector flow gvf snake the combined geodesic and gvf snake and the charged particle model

topology optimization of steady navier stokes flow with body force abstract this paper presents the topology optimization of steady navier stokes flows with body forces that influence the optimal shape and topology of fluid flows based on the implicit expression of the fluid flow with the level set method an optimization problem is formulated and analyzed using the continuous adjoint method the shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem in the optimization procedure the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously three kinds of body forces that are commonly used in the design of fluid devices i e constant nonuniform and solution dependent body forces are considered in the two dimensional and three dimensional numerical examples numerical results demonstrate that this method can effectively achieve the topology optimization of the navier stokes flows with body forces

symmetry analysis of an equation for constrained optimal transport modelling the distribution of ants round a nest a second order nonlinear partial differential equation modelling the optimal transport of food into an ant nest is derived the lie group method is used to determine group invariant solutions admitted by the model equation two classes of solutions are obtained in the first case we are able to impose zero ant density on a circle which yields physically relevant solutions here the optimal transport of food into the ant nest occurs when the foraging region has a circular boundary in the second case we are only able to impose zero ant density at a point

checking for lack of fit in linear models with parametric variance functions i adapt near replicate lack of fit tests for checking the adequacy of a linear model for means to check for lack of fit in a standard log linear model for variances a graphical method for checking lack of fit in the variance model is also proposed in addition an overall test of lack of fit in means or variances is presented three examples are used to illustrate the techniques

uniqueness of the cheeger set of a convex body abstract we prove that if c r n is an open bounded convex set then there is only one cheeger set inside c and it is convex a cheeger set of c is a set which minimizes the ratio perimeter over volume among all subsets of c

a semi lagrangian particle level set finite element method for interface problems we present a quasi monotone semi lagrangian particle level set qmsl pls method for moving interfaces the qmsl method is a blend of first order monotone and second order semi lagrangian methods the qmsl pls method is easy to implement efficient and well adapted for unstructured either simplicial or hexahedral meshes we prove that it is unconditionally stable in the maximum discrete norm parallel cdot parallel h infty and the error analysis shows that when the level set solution u t is in the sobolev space w r 1 infty d r geq 0 the convergence in the maximum norm is of the form kt delta t min 1 delta t parallel v parallel h infty h 1 alpha h p h q p min 2 r 1 and q min 3 r 1 where v is a velocity this means that at high cfl numbers that is when delta t h the error is o frac 1 alpha h p h q delta t whereas at cfl numbers less than 1 the error is o 1 alpha h p 1 h q 1 we have tested our method with satisfactory results i

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

flux maximizing geometric flows several geometric active contour models have been proposed for segmentation in computer vision and image analysis the essential idea is to evolve a curve in 2d or a surface in 3d under constraints from image forces so that it clings to features of interest in an intensity image recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented however it is still unclear how to apply these techniques to images of narrow elongated structures such as blood vessels where intensity contrast may be low and reliable region statistics cannot be computed to address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve in 2d or a surface in 3d the key idea is to exploit the direction of the vector field along with its magnitude the calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions we illustrate its advantages with several level set based segmentations of 2d and 3d angiography images of blood vessels

modified least squares algorithm incorporating exponential resetting and forgetting in this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation the analysis is carried out in a deterministic framework and stresses geometrical interpretations the core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor the algorithm is particularly suitable for tracking time varying parameters and is similar in computational complexity to the standard recursive least squares algorithm the superior performance of the algorithm is verified via simulation studies

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

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

optimal step size constant modulus algorithm the step size leading to the absolute minimum of the constant modulus cm criterion along the search direction can be obtained algebraically at each iteration among the roots of a third degree polynomial the resulting optimal step size cma os cma is compared with other cm based iterative techniques in terms of performance versus complexity trade off

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

model checking techniques for linear models with parametric variance functions we present graphical and numerical methods for assessing the adequacy of the log linear model for variances the proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor under the assumed model the cumulative residual process converges weakly to a 0 mean gaussian process whose distribution can be approximated via monte carlo simulation the observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution these comparisons enable one to examine the functional form of each covariate the link function as well as the overall model adequacy of the variance model simulation studies demonstrate that the proposed methods perform well in practical settings illustrations with three datasets are provided

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

k statistics and dispersion effects in regression on donne deux ensembles d estimateurs sans biais pour le cas ou la reponse moyenne depend lineairement de covariables connues

continuous global optimization in multiview 3d reconstruction in this article we introduce a new global optimization method to the field of multiview 3d reconstruction while global minimization has been proposed in a discrete formulation in form of the maxflow mincut framework we suggest the use of a continuous convex relaxation scheme specifically we propose to cast the problem of 3d shape reconstruction as one of minimizing a spatially continuous convex functional in qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution firstly geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner the continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased moreover memory requirements are reduced allowing for globally optimal reconstructions at higher resolutions we study three different energy models for multiview reconstruction which are based on a common variational template unifying regional volumetric terms and on surface photoconsistency the three models use data measurements at increasing levels of sophistication while the first two approaches are based on a classical silhouette based volume subdivision the third one relies on stereo information to define regional costs furthermore this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation all three models are compared on standard data sets demonstrating their advantages and shortcomings for the third one which gives the most accurate results a more exhaustive qualitative and quantitative evaluation is presented

free surface flows under impacting droplets a numerical method which fulfils the free surface boundary conditions and extrapolates the fluid velocity into empty grid cells outside the fluid region on a fixed cartesian grid system is presented the complex three dimensional vortex structures formed via surface vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level set method for both vertical and oblique droplet impacts in incompressible fluids the present results have been validated through numerical tests which confirm zero tangential shear at the free surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location in some cases transitions from a concentric vortex ring to a fully three dimensional vortex structure has been confirmed whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact resulting in axial counter rotating vorticity between the cavity and descending vortex ring underlying mechanisms which induce local deformation of the free surface creating a so called scar due to the sub surface vortices at the oblique impacts are also discussed

an active contour model for image segmentation based on elastic interaction the task of image segmentation is to partition an image into non overlapping regions based on intensity or textural information the active contour methods provide an effective way for segmentation in which the boundaries of the objects are detected by evolving curves in this paper we propose a new edge based active contour method which uses a long range and orientation dependent interaction between image boundaries and the moving curves while maintaining the edge fidelity as a result this method has a large capture range and is able to detect sharp features of the images the velocity field for the moving curves generated by this elastic interaction is calculated using the fast fourier transform fft method level set representation is used for the moving curves so that the topological changes during the evolution are handled automatically this new method is derived based on the elastic interaction between line defects in solids dislocations although it is derived originally for two dimensional segmentation we also extend it to three dimensions the features of the new method are examined by experiments on both synthetic images and medical images of blood vessels comparisons are made with the existing active contour methods

dispersion effects from 7 unreplicated designs in the 2 k p series quality improvement requires reduction of undesired variation design of experiments haa become a useful tool for discovering such minimum variance conditions but most existing techniques require a large experimental effort involving replicated experiments in this article we develop a method for significance testing of dispersion effects from unreplicated two level fractional factorial experiments using principles close to those for identifying location effects the method provides an f distributed test statistic and appears to be useful for identification of dispersion effects as early as the screening stage when fractionated unreplicated experiments are frequently employed

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

methods for identifying dispersion effects in unreplicated factorial experiments a critical analysis and proposed strategies there has been considerable interest recently in the use of statistically designed experiments to identify both location and dispersion effects for quality improvement analysis of dispersion effects usually requires replications that can be expensive or time consuming several recent articles have considered identification of both location and dispersion effects from unreplicated fractional factorial experiments in this article we provide a systematic study of various methods that are commonly used or have been proposed recently both theoretical and simulation results are used to characterize the properties although all methods suffer from some degree of bias some have serious problems when the bias remains large even as the design run size increases to infinity based on these analyses we propose some iterative strategies for model selection and estimation of the dispersion effects a real example and simulations as well are used to illustrate the results

discrete and continuous models for partitioning problems recently variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention since they introduce significantly less artifacts than established graph cut based techniques this work is concerned with the sources of such artifacts we discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples moreover we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method since the employed regularizer is quite tight the considered relaxation generally involves a large computational cost we propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics thus generalizing a method recently proposed by strekalovskiy and cremers ieee conference on computer vision and pattern recognition pp 1905 1911 2011

joint identification of location and dispersion effects in unreplicated two level factorials most procedures that have been proposed to identify dispersion effects in unreplicated factorial designs assume that location effects have been identified correctly incorrect identification of location effects may impair subsequent identification of dispersion effects we develop a method for joint identification of location and dispersion effects that can reliably identify active effects of both types a normal based model containing parameters for effects in both the mean and variance is used parameters are estimated using maximum likelihood and subsequent effect selection is done using a specially derived information criterion an exhaustive search through a limited version of the space of possible models is conducted both a single model output and model averaging are considered the method is shown to be capable of identifying sensible location dispersion models that are missed by methods that rely on sequential estimation of location and dispersion effects supplementary materials for this articl

shapes from pixels continuous domain visual signals are usually captured as discrete digital images this operation is not invertible in general in the sense that the continuous domain signal cannot be exactly reconstructed based on the discrete image unless it satisfies certain constraints e g bandlimitedness in this paper we study the problem of recovering shape images with smooth boundaries from a set of samples thus the reconstructed image is constrained to regenerate the same samples consistency as well as forming a shape bilevel image we initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes next we relax the non convex shape constraint to transform the problem into minimizing the total variation over consistent non negative valued images we also introduce a requirement called reducibility that guarantees equivalence between the two problems we illustrate that the reducibility property effectively sets a requirement on the minimum sampling density we also evaluate the performance of the relaxed alternative in various numerical experiments

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

active contouring based on gradient vector interaction and constrained level set diffusion this paper presents an extension of our recently introduced mac model to deal with the initialization dependency problem that commonly appears in edge based approaches its dynamic force field unique bidirectionality and constrained diffusion based level set evolution provide great freedom in contour initialization and show significant improvements in initialization independency compared to other edge based techniques it can handle more sophisticated topological changes than splitting and merging it provides new potentials for edge based active contour methods particularly when detecting and localizing objects with unknown location geometry and topology

a generalized linear modeling approach to robust design this article presents an extension of the response surface approach to taguchi s parameter design by accommodating generalized linear modeling the approach of myers khuri and vining is taken as a starting point treating noise variables as fixed effects it is however assumed that process variability is caused not only by the presence of noise factors but also by residual variation therefore in addition to a model with a linear link function that relates the process mean to design and noise factors a second model with a log link function is proposed that relates the variance to a linear predictor in the design factors the conditional response model with noise factors taken as fixed is fitted by iteratively reweighted least squares unconditionally response surfaces for the process mean and process variance are produced through the use of a mean and variance operator on the conditional response model as an illustration data from an injection molding experiment are reanalyzed and residual disp

blind and semi blind equalization based on the constant power criterion this paper focuses on the constant power cp criterion for blind linear equalization of digital communication channels this recently proposed criterion is specially designed for the extraction of q ary phase shift keying q psk signals using finite impulse response equalizers when zero forcing equalizers exist the cp cost function accepts exact analytic solutions that are unaffected by undesired local extrema and spare costly iterative optimization a subspace based method exploiting the toeplitz like structure of the solution space is put forward to recover the minimum length equalizer impulse response from the overestimated length solutions the proposed method is more robust to the relative weights of the minimum length equalizer taps than existing techniques in less ideal scenarios where the analytic solutions are only approximate minimizers of the criterion a gradient descent algorithm is proposed to minimize the cost function to reduce the detrimental effects of suboptimal equilibria and accelerate convergence the iterative algorithm is initialized with the approximate closed form solution and an optimal step size is incorporated into its updating rule this optimal step size which globally minimizes the cost function along the search direction can be computed algebraically a semi blind implementation which is useful when training data are available further reduces the impact of undesired local extrema and enhances the convergence characteristics particularly the robustness to the equalizer initialization of the iterative algorithm from just a few pilot symbols all these beneficial features are demonstrated with an experimental study of the proposed cp based methods in a variety of channels and simulation conditions

examples of max flow and min cut problems with duality gaps in continuous networks strang mathematical programming 26 1983 gave a method to establish a max flow min cut theorem in a domain of a euclidean space the method can be applied also to max flow min cut problems defined by iri survey of mathematical programming north holland 1979 whenever the capacity functions of max flow problems are bounded and continuous this paper deals with max flow min cut problems of strang and iri with unbounded or noncontinuous capacity functions it is proved that in such problems max flow min cut theorems may fail to hold

gradient vector flow fast geometric active contours in this paper we propose an edge driven bidirectional geometric flow for boundary extraction to this end we combine the geodesic active contour flow and the gradient vector flow external force for snakes the resulting motion equation is considered within a level set formulation can deal with topological changes and important shape deformations an efficient numerical schema is used for the flow implementation that exhibits robust behavior and has fast convergence rate promising results on real and synthetic images demonstrate the potentials of the flow