decision analysis under states additive ssb preferences we survey fishburn s skew symmetric bilinear ssb theory of risky choice under nonlinear and potentially nontransitive preferences and apply the states additive special case in the context of decision analysis showing that tractable characterizations of optimal choices are obtainable via linear programming once the decision has been expressed in normal i e tabular form if preferences are transitive they are also linear and representable by von neumann morgenstern utility in which case optimal choices may be obtained by the familiar recursion analysis of the extensive i e tree form

a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

a polynomial piecewise constant approximation method based on dual constraint relaxation for segmenting images with intensity inhomogeneity abstract in the past decade several local region based level set models have been proposed to segment images with intensity inhomogeneity in general these models are designed based on one assumption i e intensity inhomogeneity is slowly varying in image domain however this assumption is not valid for those images with serious intensity inhomogeneity which inevitably leads to poor segmentation performance of existing models in this paper we propose a novel level set method named as polynomial piecewise constant approximation ppca to well segment images with serious intensity inhomogeneity the basic idea of the ppca method is to transform the original image to piecewise constant image so as to make piecewise constant segmentation criterion become applicable specially we firstly define an initial objective function with some constraint conditions to transform the original image then in order to obtain desirable piecewise constant image and highlight the anti noise performance the ppca method is used to realize the dual constraint relaxation for objective function the dual constraint relaxation reflects in two parts on one hand the objective function based on local region is exploited to replace the pointwise approximation method on the other hand considering the variance of local intensity distribution and the reliability of polynomial approximation we utilize a gaussian pyramid convolution strategy to devise polynomial fitting the ppca method relaxes the constraint condition of objective function so that the piecewise constant image is easily approximated according to piecewise constant segmentation criterion we obtain the partial differential equation based on polynomial piecewise constant approximation finally we utilize level set method to construct the energy functional the visual and quantitative experimental results demonstrate that the proposed ppca method can yield better results than existing classical local models for segmenting images with serious intensity inhomogeneity

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

the piecewise smooth mumford shah functional on an arbitrary graph the mumford shah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and despite being introduced over two decades ago it is still in widespread use present day optimization of the mumford shah functional is predominated by active contour methods until recently these formulations necessitated optimization of the contour by evolving via gradient descent which is known for its overdependence on initialization and the tendency to produce undesirable local minima in order to reduce these problems we reformulate the corresponding mumford shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast low energy solution in contrast to traditional optimization methods use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary requiring additionally the inclusion of regularization for generating these values the energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent based narrow band level set methods this comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time finally we demonstrate the usefulness of the graph formulation to apply the mumford shah functional to new applications such as point clustering and filtering of nonuniformly sampled images

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

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

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

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

on local region models and a statistical interpretation of the piecewise smooth mumford shah functional the mumford shah functional is a general and quite popular variational model for image segmentation in particular it provides the possibility to represent regions by smooth approximations in this paper we derive a statistical interpretation of the full piecewise smooth mumford shah functional by relating it to recent works on local region statistics moreover we show that this statistical interpretation comes along with several implications firstly one can derive extended versions of the mumford shah functional including more general distribution models secondly it leads to faster implementations finally thanks to the analytical expression of the smooth approximation via gaussian convolution the coordinate descent can be replaced by a true gradient descent

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

a modified chan vese model and its theoretical proof we present a modified chan vese functional and give its theoretical proof by using the geometric heat flow method to all the euler lagrange equations a system of evolution equations in level set formulation is derived we study the existence of solution to this system by schauder fixed point theorem and the implicit function theorem in banach space this variational formulation can detect interior and exterior boundaries of desired object s in color images

exact person fit indexes for the rasch model for arbitrary alternatives a new algorithm for obtaining exact person fit indexes for the rasch model is introduced which realizes most powerful tests for a very general family of alternative hypotheses including tests concerning dif as well as model deviating item correlations the method is also used as a goodness of fit test for whole data sets where the item parameters are assumed to be known for tests with 30 items at most exact values are obtained for longer tests a monte carlo algorithm is proposed simulated examples and an empirical investigation demonstrate test power and applicability to item elimination

numerical conditioning problems and solutions for nonparametric i i d statistical active contours in this paper we propose an active contour model based on nonparametric independent and identically distributed i i d statistics of the image that can segment an image without any a priori information about the intensity distributions of the region of interest or the background this is not however the first active contour model proposed to solve the segmentation problem under these same assumptions in contrast to prior active contour models based on nonparametric i i d statistics we do not formulate our optimization criterion according to any distance measure between estimated probability densities inside and outside the active contour instead treating the segmentation problem as a pixel wise classification problem we formulate an active contour to minimize the unbiased pixel wise average misclassification probability amp this not only simplifies the problem by avoiding the need to arbitrarily select among many sensible distance measures to measure the difference between the probability densities estimated inside and outside the active contour but it also solves a numerical conditioning problem that arises with such prior active contour models as a result the amp model exhibits faster convergence with higher accuracy and robustness when compared to active contour models previously formulated to solve the same nonparametric i i d statistical segmentation problem via probability distances to discuss this improved numerical behavior more precisely we introduce the notion of x201c conditioning ratio x201d and demonstrate that the proposed amp active contour is numerically better conditioned i e exhibits a much smaller conditioning ratio than prior probability distance based active contours

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

localizing region based active contours in this paper we propose a natural framework that allows any region based segmentation energy to be re formulated in a local way we consider local rather than global image statistics and evolve a contour based on local information localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method the presented technique is versatile enough to be used with any global region based active contour energy and instill in it the benefits of localization we describe this framework and demonstrate the localization of three well known energies in order to illustrate how our framework can be applied to any energy we then compare each localized energy to its global counterpart to show the improvements that can be achieved next an in depth study of the behaviors of these energies in response to the degree of localization is given finally we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models

robust model for segmenting images with without intensity inhomogeneities intensity inhomogeneities and different types levels of image noise are the two major obstacles to accurate image segmentation by region based level set models to provide a more general solution to these challenges we propose a novel segmentation model that considers global and local image statistics to eliminate the influence of image noise and to compensate for intensity inhomogeneities in our model the global energy derived from a gaussian model estimates the intensity distribution of the target object and background the local energy derived from the mutual influences of neighboring pixels can eliminate the impact of image noise and intensity inhomogeneities the robustness of our method is validated on segmenting synthetic images with without intensity inhomogeneities and with different types levels of noise including gaussian noise speckle noise and salt and pepper noise as well as images from different medical imaging modalities quantitative experimental comparisons demonstrate that our method is more robust and more accurate in segmenting the images with intensity inhomogeneities than the local binary fitting technique and its more recent systematic model our technique also outperformed the region based chan vese model when dealing with images without intensity inhomogeneities and produce better segmentation results than the graph based algorithms including graph cuts and random walker when segmenting noisy images

exploiting information geometry to improve the convergence of nonparametric active contours this paper presents a fast converging riemannian steepest descent method for nonparametric statistical active contour models with application to image segmentation unlike other fast algorithms the proposed method is general and can be applied to any statistical active contour model from the exponential family which comprises most of the models considered in the literature this is achieved by first identifying the intrinsic statistical manifold associated with this class of active contours and then constructing a steepest descent on that manifold a key contribution of this paper is to derive a general and tractable closed form analytic expression for the manifold s riemannian metric tensor which allows computing discrete gradient flows efficiently the proposed methodology is demonstrated empirically and compared with other state of the art approaches on several standard test images a phantom positron emission tomography scan and a b mode echography of in vivo human dermis

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

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

an active contour model and its algorithms with local and global gaussian distribution fitting energies in this paper we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation in the proposed model the local and global region fitting energies are described by the combination of the local and global gaussian distributions with different means and variances respectively in this combination we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies then we present an algorithm for implementing the proposed model directly considering that in practice the selection of the weighting coefficient is troublesome we present a modified algorithm in order to overcome this problem and increase the flexibility by adaptively updating the weighting coefficient and the time step with the contour evolution this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate besides it is robust to the noise and can be used to extract the desired objects experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real world images

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

generalizing mumford shah model for multiphase piecewise smooth image segmentation this paper concerns multiphase piecewise smooth image segmentation with intensity inhomogeneities traditional methods based on the mumford shah ms model require solving complicated diffusion equations evolving in irregular subdomains leading to significant difficulties in efficient and accurate segmentation especially in multiphase scenarios in this paper we propose a general framework to modify the ms model by using smoothing operators that can avoid the complicated implementation and inaccurate segmentation of traditional approaches a detailed analysis connecting the smoothing operators and the diffusion equations is given to justify the modification in addition we present an efficient algorithm based on the direct augmented lagrangian method which requires fewer parameters than the commonly used augmented lagrangian method typically the smoothing operator in the general model is chosen to be gaussian kernel the bilateral kernel and the directional diffusion kernel respectively ample numerical results are provided to demonstrate the efficiency and accuracy of the modified model and the proposed minimization algorithm through various comparisons with existing approaches

disjunctive normal parametric level set with application to image segmentation level set methods are widely used for image segmentation because of their convenient shape representation for numerical computations and capability to handle topological changes however in spite of the numerous works in the literature the use of level set methods in image segmentation still has several drawbacks these shortcomings include formation of irregularities of the signed distance function sensitivity to initialization lack of locality and expensive computational cost which increases dramatically as the number of objects to be simultaneously segmented grows in this paper we propose a novel parametric level set method called disjunctive normal level set dnls and apply it to both two phase single object and multiphase multiobject image segmentations dnls is a differentiable model formed by the union of polytopes which themselves are created by intersections of half spaces we formulate the segmentation algorithm in a bayesian framework and use a variational approach to minimize the energy with respect to the parameters of the model the proposed dnls can be considered as an open framework that allows the use of different appearance models and shape priors compared with the conventional level sets available in the literature the proposed dnls has the following major advantages it requires significantly less computational time and memory it naturally keeps the level set function regular during the evolution it is more suitable for multiphase and local region based image segmentations and it is less sensitive to noise and initialization the experimental results show the potential of the proposed method

a variational model for image classification and restoration we present a variational model devoted to image classification coupled with an edge preserving regularization process the discrete nature of classification i e to attribute a label to each pixel has led to the development of many probabilistic image classification models but rarely to variational ones in the last decade the variational approach has proven its efficiency in the field of edge preserving restoration we add a classification capability which contributes to provide images composed of homogeneous regions with regularized boundaries a region being defined as a set of pixels belonging to the same class the soundness of our model is based on the works developed on the phase transition theory in mechanics the proposed algorithm is fast easy to implement and efficient we compare our results on both synthetic and satellite images with the ones obtained by a stochastic model using a potts regularization

on a nonlocal phase separation model abstract an alternative to the cahn hilliard model of phase separation for two phase systems in a simplified isothermal case is given the model is derived from a free energy with a nonlocal interacting term and allows reasonable bounds for the concentrations using the free energy as lyapunov functional the asymptotic state of the system is investigated and characterized by a variational principle

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

split bregman method for minimization of improved active contour model combining local and global information dynamically abstract this paper presents an improved active contour model by combining the chan vese model the region scalable fitting energy model the globally convex segmentation method and the split bregman method a weight function that varies with the location of a given image is used to control the influence of the local and global information dynamically we first present our model in a 2 phase level set formulation and then extend it to a multi phase formulation by taking the local and global information into consideration together our model can segment more general images especially images with intensity inhomogeneity our model has been applied to synthetic and real images with promising results numerical results show the advantages of our model compared with other models the accuracy and efficiency are demonstrated by the numerical results besides our model is robust in the presence of noise

an active contour model based on local fitted images for image segmentation active contour models are popular and widely used for a variety of image segmentation applications with promising accuracy but they may suffer from limited segmentation performances due to the presence of intensity inhomogeneity to overcome this drawback a novel region based active contour model based on two different local fitted images is proposed by constructing a novel local hybrid image fitting energy which is minimized in a variational level set framework to guide the evolving of contour curves toward the desired boundaries the proposed model is evaluated and compared with several typical active contour models to segment synthetic and real images with different intensity characteristics experimental results demonstrate that the proposed model outperforms these models in terms of accuracy in image segmentation

nonparametric goodness of fit tests for the rasch model a monte carlo algorithm realizing a family of nonparametric tests for the rasch model is introduced which are conditional on the item and subject marginals the algorithm is based on random changes of elements of data matrices without changing the marginals most powerful tests against all alternative hypotheses are given for which a monotone characteristic may be computed from the data matrix alternatives may also be composed computation times are long but exactp values are approximated with the quality of approximation only depending on calculation time but not on the number of persons the power and the flexibility of the procedure is demonstrated by means of an empirical example where among others indicators for increased item similarities the existence of subscales violations of sufficiency of the raw score as well as learning processes were found many of the features described are implemented in the program t rasch 1 0 by ponocny and ponocny seliger 1999

active contour model driven by global and local intensity information for ultrasound image segmentation abstract due to the abundant noise blurry boundaries and intensity inhomogeneities present in ultrasound us images it is a difficult task to segment us images accurately in this paper we propose a novel active contour method that combines global and local region information to achieve this task the global information can segment us images with noise and blurry boundaries while the local information can settle the intensity homogeneities of images the proposed method can be directly applied to synthetic real and us images segmentation results demonstrate the superiority of the proposed method over other representative algorithms moreover we also extend the proposed method to vector valued images experiments are performed to testify the feasibility of the method and the proposed vector valued idea can be applied to the medical co segmentation in the future

weighted level set evolution based on local edge features for medical image segmentation level set methods have been widely used to implement active contours for image segmentation applications due to their good boundary detection accuracy in the context of medical image segmentation weak edges and inhomogeneities remain important issues that may hinder the accuracy of any segmentation method based on active contours implemented using level set methods this paper proposes a method based on active contours implemented using level set methods for segmentation of such medical images the proposed method uses a level set evolution that is based on the minimization of an objective energy functional whose energy terms are weighted according to their relative importance in detecting boundaries this relative importance is computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour the local edge features employed are the edge intensity and the degree of alignment between the image s gradient vector flow field and the evolving contour s normal we evaluate the proposed method for segmentation of various regions in real mri and ct slices x ray images and ultra sound images evaluation results confirm the advantage of weighting energy forces using local edge features to reduce leakage these results also show that the proposed method leads to more accurate boundary detection results than the state of the art edge based level set segmentation methods particularly around weak edges

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

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

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

image segmentation using active contours calculus of variations or shape gradients we consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals we show that one can go from one class to the otherby solving poisson s orhelmholtz s equation with well chosen boundar y conditions using this equivalence we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding euler lagrange equations we revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals we also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding gateaux derivatives and euler lagrange equations finally we apply this new functional to the problem of regions segmentation in sequences of color images we briefly describe our numerical scheme and show some experimental results

the many null distributions of person fit indices this paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of rasch contrary to the standard analysis of the rasch model where all persons are kept in the analysis and badly fittingitems may be removed this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the rasch model such persons are called anomalous or aberrant from the response vectors consisting ofk symbols each equal to 0 or 1 it is desired to classify each respondent as either anomalous or as conforming to the model as this model is probabilistic such a classification will possibly involve false positives and false negatives both for the rasch model and for other item response models the literature contains several proposals for a person fit index which expresses for each individual the plausibility that his her behavior follows the model the present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model this distribution however turns out to be rather different for different values of the person s latent trait value this value will be called ability parameter although our results are equally valid for rasch scales measuring other attributes

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

nonlinear optimization by successive linear programming successive linear programming slp which is also known as the method of approximation programming solves nonlinear optimization problems via a sequence of linear programs this paper reports on promising computational results with slp that contrast with the poor performance indicated by previously published comparative tests the paper provides a detailed description of an efficient reliable slp algorithm along with a convergence theorem for linearly constrained problems and extensive computational results it also discusses several alternative strategies for implementing slp the computational results show that slp compares favorably with the generalized reduced gradient code grg2 and with minos grg it appears that slp will be most successful when applied to large problems with low degrees of freedom

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

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

active contour model based on improved fuzzy c means algorithm and adaptive functions abstract distance regularized level set evolution drlse model which solves the re initialization problem in early active contours is a ground breaking edge based model for image segmentation however it has the disadvantages of unsatisfactory robustness to initialization and noise unidirectional movement slow convergence and poor stability in this paper we propose an active contour model driven by improved fuzzy c means algorithm fcm and adaptive functions an adaptive sign function based on image clustering information not only increases stability but also solves the problem of unidirectional movement furthermore it gives our model the ability to selectively segment targets in image an adaptive edge indicator function accelerates convergence with better function performance to further increase stability a novel double well potential function and the corresponding evolution speed function are proposed due to the improved fcm the proposed model is robust to initialization and noise in addition our model exhibits an edge based and region based characteristic experimental results have proved that the proposed model can not only effectively segment images with intensity inhomogeneity but also show a good robustness to initialization moreover it has shorter time spent and higher segmentation accuracy compared with other models

active contours driven by local likelihood image fitting energy for image segmentation accurate image segmentation is an essential step in image analysis and understanding where active contour models play an important part due to the noise low contrast and intensity inhomogeneity in images many segmentation algorithms suffer from limited accuracy this paper presents a novel region based active contour model for image segmentation by using the variational level set formulation in this model we construct the local likelihood image fitting llif energy functional by describing the neighboring intensities with local gaussian distributions the means and variances of local intensities in the llif energy functional are spatially varying functions which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries to address diverse image segmentation needs we also expand this model to the multiphase level set multi scale gaussian kernels and narrowband formulations the proposed model has been compared with several state of the art active contour models on images with different modalities our results indicate that the proposed llif model achieves superior performance in image segmentation

mesh free alternate directional implicit method based three dimensional super diffusive model for benign brain tumor segmentation abstract the brain tumor is one of the life threatening diseases it has been classified into the malignant and benign brain tumor benign tumor cells have very similar characteristics to its surrounding healthy cells hence its accurate detection and segmentation are one of the difficult and challenging tasks existing state of the art methods used for detection and segmentation of such tumor cells are unable to locate such benign tumor region in this manuscript a novel fractional partial differential equation fpde based super diffusive models is being proposed the fractional nature enables to detect and segment such low variational of benign brain tumor region more accurately it is also found that these partial differential models are computationally inefficient due to dependence on the mesh hence the fpde is being solved using the mesh free method both qualitative and quantitative evaluation has been done it is found that the proposed model is superior in benign brain tumor detection and segmentation

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

active contours driven by the salient edge energy model in this brief we present a new indicator i e salient edge energy for guiding a given contour robustly and precisely toward the object boundary specifically we define the salient edge energy by exploiting the higher order statistics on the diffusion space and incorporate it into a variational level set formulation with the local region based segmentation energy for solving the problem of curve evolution in contrast to most previous methods the proposed salient edge energy allows the curve to find only significant local minima relevant to the object boundary even in the noisy and cluttered background moreover the segmentation performance derived from our new energy is less sensitive to the size of local windows compared with other recently developed methods owing to the ability of our energy function to suppress diverse clutters the proposed method has been tested on various images and experimental results show that the salient edge energy effectively drives the active contour both qualitatively and quantitatively compared to various state of the art methods

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

a nonparametric statistical method for image segmentation using information theory and curve evolution in this paper we present a new information theoretic approach to image segmentation we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities subject to a constraint on the total length of the region boundaries we assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori and we formulate the problem based on nonparametric density estimates due to the nonparametric structure our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic we solve the information theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques we use level set methods to implement the resulting evolution the experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems furthermore our method which does not require any training performs as good as methods based on training

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

a global and local active contour model based on dual algorithm for image segmentation most of local region based active contour models in terms of the level set approach are able to segment images with intensity inhomogeneity however these models do not utilize global statistical information and are quite sensitive to the initial placement of the contour this paper presents a new global and local region based active contour model to segment images with intensity inhomogeneity first in order to reduce number of iterations the global energy functional of the chanvese cv model is used as the global term then the local term is proposed to incorporate both local spatial information and local intensity information to handle intensity inhomogeneity moreover to increase robustness of the initialization of the contour and reduce number of iterations a convex energy functional and the dual algorithm are designed in the numerical implementation experimental results for synthetic and medical images have shown the efficiency and robustness of the proposed method

nearest neighbor clutter removal for estimating features in spatial point processes abstract we consider the problem of detecting features in spatial point processes in the presence of substantial clutter one example is the detection of minefields using reconnaissance aircraft images that identify many objects that are not mines our solution uses kth nearest neighbor distances of points in the process to classify them as clutter or otherwise the observed kth nearest neighbor distances are modeled as a mixture distribution the parameters of which are estimated by a simple em algorithm this method allows for detection of generally shaped features that need not be path connected in the minefield example this method yields high detection and low false positive rates another application to outlining seismic faults is considered with some success the method works well in high dimensions the method can also be used to produce very high breakdown point robust estimators of a covariance matrix

automatic ultrasound image segmentation based on local entropy and active contour model abstract it is still a challenging task to segment ultrasound medical images automatically and accurately because of the poor quality of images to address these problems a two stage automatic segmentation scheme based on local entropy and a proposed active contour model for ultrasound images are put forward in this paper first a new region based active contour model in the level set formulation driven by global and local intensity information is established for the segmentation furthermore for automatically segmenting the ultrasound images a coarse segmentation is performed utilizing local entropy information of the ultrasound images then the coarse segmentation result is used as the initial value of the explicit segmentation based on the proposed model several experiments on real ultrasound images demonstrate that the proposed method outperforms other methods on both visual perception and objective evaluation metrics

area and length minimizing flows for shape segmentation a number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation such as snakes the essential idea is to evolve a curve in two dimensions or a surface in three dimensions under constraints from image forces so that it clings to features of interest in an intensity image the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional tailored to features such as edges however because the flow may be slow to converge in practice a constant hyperbolic term is added to keep the curve surface moving in the desired direction we derive a modification of this term based on the gradient flow derived from a weighted area functional with image dependent weighting factor when combined with the earlier modified length gradient flow we obtain a partial differential equation pde that offers a number of advantages as illustrated by several examples of shape segmentation on medical images in many cases the weighted area flow may be used on its own with significant computational savings

approximating the conditional distribution of person fit indexes for checking the rasch model we present a simple approximation to the conditional distribution of goodness of fit statistics for the rasch model assuming that the item difficulties are known the approximation is easily programmed and gives relatively accurate assessments of conditionalp values for tests of length 10 or more a few generalizations are discussed

combination of piecewise geodesic paths for interactive segmentation minimum cost paths have been extensively studied theoretical tools for interactive image segmentation the existing geodesically linked active contour glac model which basically consists of a set of vertices connected by paths of minimal cost blends the benefits of minimal paths and region based active contours this results in a closed piecewise smooth curve over which an edge or region energy functional can be formulated as an important shortcoming the glac in its initial formulation does not guarantee the curve to be simple consistent with respect to the purpose of segmentation in this paper we draw our inspiration from the glac and other boundary based interactive segmentation algorithms in the sense that we aim to extract a contour given a set of user provided points by connecting these points using paths the key idea is to select a combination among a set of possible paths such that the resulting structure represents a relevant closed curve instead of considering minimal paths only we switch to a more general formulation which we refer to as admissible paths these basically correspond to the roads travelling along the bottom of distinct valleys between given endpoints we introduce a novel term to favor the simplicity of the generated contour as well as a local search method to choose the best combination among possible paths

asymptotically correct standardization of person fit statistics beyond dichotomous items the l z statistic drasgow et al in br j math stat psychol 38 67 86 1985 is one of the most popular person fit statistics armstrong et al in pract assess res eval 12 16 1 10 2007 snijders psychometrika 66 331 342 2001 derived the asymptotic null distribution of l z when the examinee ability parameter is estimated he also suggested the l z statistic which is the asymptotically correct standardized version of l z however snijders psychometrika 66 331 342 2001 only considered tests with dichotomous items in this paper the asymptotic null distribution of l z is derived for mixed format tests those that include both dichotomous and polytomous items the asymptotically correct standardized version of l z which can be considered as the extension of l z to such tests is suggested the type i error rate and power of the suggested statistic are examined from several simulated datasets the suggested statistic is computed using a real dataset the suggested statistic appears to be a satisfactory tool for assessing person fit for mixed format tests

does rolling back decision trees really require the independence axiom in a recent article lavalle and wapman argue that the recursion analysis of decision trees in extensive form requires the herstein milnor independence axiom i claim that most extensive form analyses are perfectly proper in the absence of independence but that the transformation from extensive to normal form is impermissible

level set segmentation with multiple regions the popularity of level sets for segmentation is mainly based on the sound and convenient treatment of regions and their boundaries unfortunately this convenience is so far not known from level set methods when applied to images with more than two regions this communication introduces a comparatively simple way how to extend active contours to multiple regions keeping the familiar quality of the two phase case we further suggest a strategy to determine the optimum number of regions as well as initializations for the contours

automated segmentation of overlapped nuclei using concave point detection and segment grouping abstract nuclei assessment and segmentation are essential in many biological research applications but it is a challenge to segment overlapped nuclei in this paper a new automatic method is proposed to segment overlapped nuclei robustly and efficiently the proposed method mainly contains four steps contour extraction concave point detection contour segment grouping and ellipse fitting blurry nuclei splitting and unobvious concave point detection are always difficult problems in nuclei segmentation contour extraction algorithm provides a smooth contour result and it is employed to estimate the blurriness degree of the image the blurry level determines parameters in subsequent steps which improves the accuracy of blurry nuclei splitting different methods to extract obvious and unobvious concave points from candidate points are proposed in addition grouping rules are proposed to assign segments divided by concave points into groups comparison study is performed and experimental results showed the effectiveness of the proposed method

spatially varying color distributions for interactive multilabel segmentation we propose a method for interactive multilabel segmentation which explicitly takes into account the spatial variation of color distributions to this end we estimate a joint distribution over color and spatial location using a generalized parzen density estimator applied to each user scribble in this way we obtain a likelihood for observing certain color values at a spatial coordinate this likelihood is then incorporated in a bayesian map estimation approach to multiregion segmentation which in turn is optimized using recently developed convex relaxation techniques these guarantee global optimality for the two region case foreground background and solutions of bounded optimality for the multiregion case we show results on the grabcut benchmark the recently published graz benchmark and on the berkeley segmentation database which exceed previous approaches such as grabcut 32 the random walker 15 santner s approach 35 tv seg 39 and interactive graph cuts 4 in accuracy our results demonstrate that taking into account the spatial variation of color models leads to drastic improvements for interactive image segmentation

approximation of functional depending on jumps by elliptic functional via t convergence we show how it is possible to approximate the mumford shah see 29 image segmentation functional by elliptic functionals defined on sobolev spaces the heuristic idea is to consider functionals h u z with z ranging between 0 and 1 and related to the set k the minimizing zh are near to 1 in a neighborhood of the set k and far from the neighborhood they are very small the neighborhood shrinks as h for a similar approach to the problem compare kulkarni see 25 the approximation of h to takes place in a variational sense the de giorgi f convergence

an exact and optimal standardized person test for assessing consistency with the rasch model the rasch model predicts that an individual s ability level is invariant over subtests of the total test and thus all subtests measure the same latent trait a person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic given a particular level of ability does not depend on the absolute value of the examinee s ability parameter the test can be routinely performed by applying a computer program designed by and obtainable from the author finally a suboptimal test is derived that is extremely easy to use and an overall group test of the invariance hypothesis discussed all tests considered do not rely on asymptotic approximations hence they may be applied when the test is of only moderate length and the group of examinees is small

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

minimization of region scalable fitting energy for image segmentation intensity inhomogeneities often occur in real world images and may cause considerable difficulties in image segmentation in order to overcome the difficulties caused by intensity inhomogeneities we propose a region based active contour model that draws upon intensity information in local regions at a controllable scale a data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour this energy is then incorporated into a variational level set formulation with a level set regularization term from which a curve evolution equation is derived for energy minimization due to a kernel function in the data fitting term intensity information in local regions is extracted to guide the motion of the contour which thereby enables our model to cope with intensity inhomogeneity in addition the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function experimental results for synthetic and real images show desirable performances of our method

a global minimization hybrid active contour model with applications to oil spill images active contour model is popularly and widely used in the field of image segmentation which is based on superior theoretical properties and efficient numerical methods nevertheless one of the prominent disadvantages of this kind of model is the existence of local minima in its functional energy in this paper we propose a novel global minimization hybrid active contour model this model effectively integrates the edge information the local region information and the global region information of the image which is relatively sufficient to extract the object boundaries furthermore we introduce an efficient and fast numerical approach to globally minimize the proposed model which is through a dual formulation of the minimization problem and easy to implement the proposed model is robust enough to the initial condition and does not need to initialize the contour in a distance function and re initialize it periodically during the evolution process specially we applied the proposed model to segment oil spill images in which there usually exist the noise blurry boundaries and intensity inhomogeneity compared with the state of the art models experiment results demonstrate the performance and effectiveness of the proposed model with applications to synthetical and real images especially for oil spill images

incorporating patch subspace model in mumford shah type active contours in this paper we propose a unified energy minimization model for segmentation of non smooth image structures e g textures based on mumford shah functional and linear patch model we consider that image patches of a non smooth image structure can be modeled by a patch subspace and image patches of different non smooth image structures belong to different patch subspaces which leads to a computational framework for segmentation of non smooth image structures motivated by the mumford shah model we show that this segmentation framework is equivalent to minimizing a piecewise linear patch reconstruction energy we also prove that the error of segmentation is bounded by the error of the linear patch reconstruction meaning that improving the linear patch reconstruction for each region leads to reduction of the segmentation error in addition we derive an algorithm for the linear patch reconstruction with proven global optimality and linear rate of convergence the segmentation in our method is achieved by minimizing a single energy functional without requiring predefined features hence compared with the previous methods that require predefined texture features our method can be more suitable for handling general textures in unsupervised segmentation as a by product our method also produces a dictionary of optimized orthonormal descriptors for each segmented region we mainly evaluate our method on the brodatz textures the experiments validate our theoretical claims and show the clear superior performance of our methods over other related methods for segmentation of the textures

higher order asymptotics and its application to testing the equality of the examinee ability over two sets of items in educational and psychological measurement researchers and or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items such problems can arise in measurement of change detection of cheating on unproctored tests erasure analysis detection of item preknowledge etc traditional frequentist approaches that are used in such problems include the wald test the likelihood ratio test and the score test e g fischer appl psychol meas 27 3 26 2003 finkelman weiss kim kang appl psychol meas 34 238 254 2010 glas dagohoy psychometrika 72 159 180 2007 guo drasgow int j sel assess 18 351 364 2010 klauer rettig br j math stat psychol 43 193 206 1990 sinharay j educ behav stat 42 46 68 2017 this paper shows that approaches based on higher order asymptotics e g barndorff nielsen cox inference and asymptotics springer london 1994 ghosh higher order asymptotics institute of mathematical statistics hayward 1994 can also be used to test for the equality of the examinee ability over two sets of items the modified signed likelihood ratio test e g barndorff nielsen biometrika 73 307 322 1986 and the lugannani rice approximation lugannani rice adv appl prob 12 475 490 1980 both of which are based on higher order asymptotics are shown to provide some improvement over the traditional frequentist approaches in three simulations two real data examples are also provided

a curve evolution approach for unsupervised segmentation of images with low depth of field in this paper we describe a novel algorithm for unsupervised segmentation of images with low depth of field dof first of all a multi scale reblurring model is used to detect the object of interest ooi in saliency space then to determine the boundary of ooi an active contour model based on hybrid energy function is proposed in this model a global energy item related with the saliency map is adopted to find the global minimum and a local energy term regarding the low dof image is used to improve the segmentation precision in addition an adaptive parameter is attached to this model to balance the weight of global and local energy furthermore an unsupervised curve initialization method is designed to reduce the number of evolution iterations finally we conduct experiments on various low dof images and the results demonstrate the high robustness and precision of the proposed approach