an optimization based approach to enforcing mass conservation in level set methods this paper presents a new conservative level set method for numerical simulation of evolving interfaces a pde constrained optimization problem is formulated and solved in an iterative fashion the proposed optimal control procedure constrains the level set function to satisfy a conservation law for the corresponding heaviside function the target value of the state variable is defined as the solution to the standard level set transport equation the gradient of the control variable corrects the convective flux in the nonlinear state equation so as to enforce mass conservation while minimizing deviations from the target state a relaxation term is added when it comes to the design of an iterative solver for the nonlinear system the potential of the optimization based approach is illustrated by two numerical examples

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

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

a high order elliptic pde based level set reinitialisation method using a discontinuous galerkin discretisation abstract in this paper an efficient high order accurate level set reinitialisation method is proposed based on the elliptic reinitialisation method basting and kuzmin 2013 1 which is discretised spatially using the discontinuous galerkin dg symmetric interior penalty method sipg in order to achieve this a number of improvements have been made to the elliptic reinitialisation method including reformulation of the underlying minimisation problem driving the solution adoption of a lagrange multiplier approach for enforcing a dirichlet boundary condition on the implicit level set interface and adoption of a narrow band approach numerical examples confirm the high order accuracy of the resultant method by demonstrating experimental orders of convergence congruent with optimal convergence rates for the sipg method that is h p 1 and h p in the l 2 and dg norms respectively furthermore the degree to which the level set function satisfies the eikonal equation improves proportionally to h p and the often ignored homogeneous dirichlet boundary condition on the interface is shown to be satisfied accurately with a rate of convergence of at least h 2 for all polynomial orders

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

fuzzy c means clustering with local information and kernel metric for image segmentation in this paper we present an improved fuzzy c means fcm algorithm for image segmentation by introducing a tradeoff weighted fuzzy factor and a kernel metric the tradeoff weighted fuzzy factor depends on the space distance of all neighboring pixels and their gray level difference simultaneously by using this factor the new algorithm can accurately estimate the damping extent of neighboring pixels in order to further enhance its robustness to noise and outliers we introduce a kernel distance measure to its objective function the new algorithm adaptively determines the kernel parameter by using a fast bandwidth selection rule based on the distance variance of all data points in the collection furthermore the tradeoff weighted fuzzy factor and the kernel distance measure are both parameter free experimental results on synthetic and real images show that the new algorithm is effective and efficient and is relatively independent of this type of noise

a simple iterative algorithm for generating selected eigenspaces of large matrices we propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations we also give convergence criteria for the iterative process and investigate its efficiency by evaluating computer storage and time requirements and by a few numerical tests

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

computing interior eigenvalues of nonsymmetric matrices application to three dimensional metamaterial composites we propose a numerical method to calculate interior eigenvalues and corresponding eigenvectors for nonsymmetric matrices based on the subspace projection technique onto expanded ritz subspace it becomes possible to obtain eigenvalues and eigenvectors with sufficiently high precision this method overcomes the difficulties of the traditional nonsymmetric lanczos algorithm and improves the accuracy of the obtained interior eigenvalues and eigenvectors using this algorithm we investigate three dimensional metamaterial composites consisting of positive and negative refractive index materials and it is demonstrated that the finite difference frequency domain algorithm is applicable to analyze these metamaterial composites

correntropy properties and applications in non gaussian signal processing the optimality of second order statistics depends heavily on the assumption of gaussianity in this paper we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure a close relationship between correntropy and m estimation is established connections and differences between correntropy and kernel methods are presented as such correntropy has vastly different properties compared with second order statistics that can be very useful in non gaussian signal processing especially in the impulsive noise environment examples are presented to illustrate the technique

improving level set method for fast auroral oval segmentation auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics compared with various existing image segmentation methods level set is a promising auroral oval segmentation method with satisfactory precision however the traditional level set methods are time consuming which is not suitable for the processing of large aurora image database for this purpose an improving level set method is proposed for fast auroral oval segmentation the proposed algorithm combines four strategies to solve the four problems leading to the high time complexity the first two strategies including our shape knowledge based initial evolving curve and neighbor embedded level set formulation can not only accelerate the segmentation process but also improve the segmentation accuracy and then the latter two strategies including the universal lattice boltzmann method and sparse field method can further reduce the time cost with an unlimited time step and narrow band computation experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time

an efficient bi convex fuzzy variational image segmentation method abstract image segmentation is an important and well known ill posed inverse problem in computer vision it is a process of assigning a label to each pixel in a digital image so that pixels with the same label have similar characteristics chan vese model which belongs to partial differential equation approaches has been widely used in image segmentation tasks chan vese model has to optimize a non convex problem it usually converges to local minima furthermore the length penalty item which is critical to the final results of chan vese model makes the model be sensitive to parameter settings and costly in computation in order to overcome these drawbacks a novel bi convex fuzzy variational image segmentation method is proposed it is unique in two aspects 1 introducing fuzzy logic to construct a bi convex object function in order to simplify the procedure of finding global optima and 2 efficiently combining the length penalty item and the numerical remedy method to get better results and to bring robustness to parameter settings and greatly reduce computation costs experiments on synthetic natural medical and radar images have visually or quantitatively validated the superiorities of the proposed method compared with five state of the art algorithms

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

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost

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

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

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

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

the spectra of large toeplitz band matrices with a randomly perturbed entry this paper is concerned with the union sp j k tn a of all possible spectra that may emerge when perturbing a large n n toeplitz band matrix tn a in the j k site by a number randomly chosen from some set the main results give descriptive bounds and in several interesting situations even provide complete identifications of the limit of sp j k tn a as n also discussed are the cases of small and large sets as well as the discontinuity of the infinite volume case which means that in general sp j k tn a does not converge to something close to sp j k tn a as n where t a is the corresponding infinite toeplitz matrix illustrations are provided for tridiagonal toeplitz matrices a notable special case

active contours driven by local image fitting energy a new region based active contour model that embeds the image local information is proposed in this paper by introducing the local image fitting lif energy to extract the local image information our model is able to segment images with intensity inhomogeneities moreover a novel method based on gaussian filtering for variational level set is proposed to regularize the level set function it can not only ensure the smoothness of the level set function but also eliminate the requirement of re initialization which is very computationally expensive experiments show that the proposed method achieves similar results to the lbf local binary fitting energy model but it is much more computationally efficient in addition our approach maintains the sub pixel accuracy and boundary regularization properties

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

on some inequalities for the gamma and psi functions we present new inequalities for the gamma and psi functions and we provide new classes of completely monotonic star shaped and superadditive functions which are related to and

radial basis functions and level set method for image segmentation using partial differential equation combining nonlinear evolution equations which arise from image segmentation using partial differential equation based level set method using radial basis functions a meshless numerical algorithm is presented for image segmentation in this paper both globally supported and compactly supported radial basis functions are used to interpolate the level set function of the evolution equation with a high level of accuracy and smoothness the nonlinear evolution equation is finally cast into ordinary differential equations and euler s scheme is employed compared with traditional level set approaches the presented algorithm is robust to initialization or even free of manual initialization and avoids the complex and costly re initialization of the level set function the capability of the presented algorithm is demonstrated through some numerical experiments

exponential gamma and polygamma functions simple proofs of classical and new inequalities abstract some inequalities for the exponential gamma and polygamma functions are established by means of the mean value theorem of differential calculus in particular the cases of the ratio of gamma and polygamma functions are considered in some cases the results are new in some others classical results are recovered or extended

structural topology and shape optimization using a level set method with distance suppression scheme abstract in level set methods for structural topology and shape optimization the level set function gradients at the design interface need to be controlled in order to ensure stability of the optimization process one popular way to do this is to enforce the level set function to be a signed distance function by periodically using initialization schemes which is commonly known as re initialization however such re initialization schemes are time consuming as additional partial differential equations need to be solved in every iteration step furthermore the use of re initialization brings some undesirable problems for example it may move the zero level set away from the expected position this paper presents a level set method with distance suppression scheme for structural topology and shape optimization an energy functional is introduced into the level set equation to maintain the level set function to close to a signed distance function near the structural boundaries meanwhile forcing the level set function to be a constant at locations far away from the structural boundaries as a result the present method not only can avoid the need for re initialization but also can simplify the setting of the initial level set function the validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem different aspects of the proposed method are demonstrated on a number of benchmarks from the literature of structural optimization

b spline based globally optimal segmentation combining low level and high level information abstract image segmentation is an important step for large scale image analysis and object recognition variational based segmentation methods are widely studied due to their good performance but they still suffer from incapability to deal with images bearing weak contrast overlapped noise and cluttered texture to tackle this problem we propose a new statistical information analysis based multi scale and global optimization method for image segmentation this multi scale processing which is consistent with human s cognition mechanism enables us identify target at coarse scale the high level prior is obtained by the multiple gaussian kernel gray equalization and used as shape constraint in following fine scale an efficient energy functional is proposed with convexity and improved tv regularization in order to segment inhomogeneous target from noisy background a convex relaxation function is explicitly represented by cubic b spline basis for fast convergence and intrinsic smooth segmentation finally the energy functional is minimized by standard methods of split bregman gradient descent flow and the corresponding euler lagrange equation experimental results on synthetic and real world images validate the robustness and high accuracy boundaries detection for low contrast noisy and texture images

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

front propagation and phase field theory the connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction diffusion equations is rigorously established two different scalings are studied in the first the limiting geometric equation is a first order equation in the second it is a generalization of the mean curvature equation intrinsic definitions for the geometric equations are obtained and uniqueness under a geometric condition on the initial surface is proved in particular in the case of the mean curvature equation this condition is satisfied by surfaces that are strictly starshaped that have positive mean curvature or that satisfy a condition that interpolates between the positive mean curvature and the starshape conditions

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

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

a monolithic conservative level set method with built in redistancing abstract we introduce a new level set method for representing evolving interfaces in the case of divergence free velocity fields the new method satisfies a conservation principle conservation is important for many applications such as modeling two phase incompressible flow in the present implementation the conserved quantity is defined as the integral of a smoothed characteristic function the new approach embeds level sets into a volume of fluid formulation the evolution of an approximate signed distance function is governed by a conservation law for its smoothed sign the non linear level set transport equation is regularized by adding a flux correction term that assures a non singular jacobian and penalizes deviations from a distance function the result is a locally conservative level set method with built in elliptic redistancing the continuous model is monolithic in the sense that the level set transport model the volume of fluid law of mass conservation and the minimization problem that preserves the approximate distance function property are incorporated into a single equation there is no need for any extra stabilization artificial compression flux limiting redistancing mass correction and other numerical fixes which are commonly used in level set or volume of fluid methods in addition there is just one free parameter that controls the strength of regularization and penalization in the model the accuracy and conservation properties of the monolithic finite element level set method are illustrated by the results of numerical studies for passive advection of free interfaces

reinitialization free level set evolution via reaction diffusion this paper presents a novel reaction diffusion rd method for implicit active contours that is completely free of the costly reinitialization procedure in level set evolution lse a diffusion term is introduced into lse resulting in an rd lse equation from which a piecewise constant solution can be derived in order to obtain a stable numerical solution from the rd based lse we propose a two step splitting method to iteratively solve the rd lse equation where we first iterate the lse equation then solve the diffusion equation the second step regularizes the level set function obtained in the first step to ensure stability and thus the complex and costly reinitialization procedure is completely eliminated from lse by successfully applying diffusion to lse the rd lse model is stable by means of the simple finite difference method which is very easy to implement the proposed rd method can be generalized to solve the lse for both variational level set method and partial differential equation based level set method the rd lse method shows very good performance on boundary antileakage the extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed rd lse approach

multi layer graph constraints for interactive image segmentation via game theory the combination of pixels and superpixels has been widely used for image segmentation where the pixels and superpixels are segmented together these combination methods can obtain more robust results by using more informative superpixel features however since the superpixel may not accurately capture the details for the small and slender regions the results of these combination methods are often label inconsistent with the objects furthermore these methods also fall into expensive time cost due to introducing more interactions between pixels and superpixels to overcome the above problems in this paper we propose an interactive image segmentation method based on multi layer graph constraints the relationships between pixels superpixels and labels are introduced into the conventional combination framework to further improve the segmentation accuracy the segmentation model is constructed based on the estimation of probabilities of pixels and superpixels by a nonparametric learning framework then the probabilities of pixels and superpixels are updated iteratively by utilizing the game theory based optimization strategy experiments on challenging data sets demonstrate that the proposed method can obtain better segmentation results than the state of the art methods multi layer graph constraints are utilized for the interactive image segmentation labeling information is introduced into the conventional pixel superpixel combinational model the optimization based on game theory is proposed for the combinational energy functions the proposed method can obtain better performance than the state of the art methods

optimum image thresholding via class uncertainty and region homogeneity thresholding is a popular image segmentation method that converts a gray level image into a binary image the selection of optimum thresholds has remained a challenge over decades besides being a segmentation tool on its own often it is also a step in many advanced image segmentation techniques in spaces other than the image space we introduce a thresholding method that accounts for both intensity based class uncertainty a histogram based property and region homogeneity an image morphology based property a scale based formulation is used for region homogeneity computation at any threshold intensity based class uncertainty is computed by fitting a gaussian to the intensity distribution of each of the two regions segmented at that threshold the theory of the optimum thresholding method is based on the postulate that objects manifest themselves with fuzzy boundaries in any digital image acquired by an imaging device the main idea here is to select that threshold at which pixels with high class uncertainty accumulate mostly around object boundaries to achieve this a threshold energy criterion is formulated using class uncertainty and region homogeneity such that at any image location a high energy is created when both class uncertainty and region homogeneity are high or both are low finally the method selects that threshold which corresponds to the minimum overall energy the method has been compared to a maximum segmented image information method superiority of the proposed method was observed both qualitatively on clinical medical images as well as quantitatively on 250 realistic phantom images generated by adding different degrees of blurring noise and background variation to real objects segmented from clinical images

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

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

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

robust level set image segmentation via a local correntropy based k means clustering it is still a challenging task to segment real world images since they are often distorted by unknown noise and intensity inhomogeneity to address these problems we propose a novel segmentation algorithm via a local correntropy based k means lck clustering due to the correntropy criterion the clustering algorithm can decrease the weights of the samples that are away from their clusters as a result lck based clustering algorithm can be robust to the outliers the proposed lck clustering algorithm is incorporated into the region based level set segmentation framework the iteratively re weighted algorithm is used to solve the lck based level set segmentation method extensive experiments on synthetic and real images are provided to evaluate our method showing significant improvements on both noise sensitivity and segmentation accuracy as compared with the state of the art approaches

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

gpu accelerated edge region based level set evolution constrained by 2d gray scale histogram due to its intrinsic nature which allows to easily handle complex shapes and topological changes the level set method lsm has been widely used in image segmentation nevertheless lsm is computationally expensive which limits its applications in real time systems for this purpose we propose a new level set algorithm which uses simultaneously edge region and 2d histogram information in order to efficiently segment objects of interest in a given scene the computational complexity of the proposed lsm is greatly reduced by using the highly parallelizable lattice boltzmann method lbm with a body force to solve the level set equation lse the body force is the link with image data and is defined from the proposed lse the proposed lsm is then implemented using an nvidia graphics processing units to fully take advantage of the lbm local nature the new algorithm is effective robust against noise independent to the initial contour fast and highly parallelizable the edge and region information enable to detect objects with and without edges and the 2d histogram information enable the effectiveness of the method in a noisy environment experimental results on synthetic and real images demonstrate subjectively and objectively the performance of the proposed method

accurate cervical cell segmentation from overlapping clumps in pap smear images accurate segmentation of cervical cells in pap smear images is an important step in automatic pre cancer identification in the uterine cervix one of the major segmentation challenges is overlapping of cytoplasm which has not been well addressed in previous studies to tackle the overlapping issue this paper proposes a learning based method with robust shape priors to segment individual cell in pap smear images to support automatic monitoring of changes in cells which is a vital prerequisite of early detection of cervical cancer we define this splitting problem as a discrete labeling task for multiple cells with a suitable cost function the labeling results are then fed into our dynamic multi template deformation model for further boundary refinement multi scale deep convolutional networks are adopted to learn the diverse cell appearance features we also incorporated high level shape information to guide segmentation where cell boundary might be weak or lost due to cell overlapping an evaluation carried out using two different datasets demonstrates the superiority of our proposed method over the state of the art methods in terms of segmentation accuracy

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

parametric structural shape topology optimization with a variational distance regularized level set method abstract the signed distance function sdf gives the shortest distance from a given point to the boundary and the sign indicates whether this point is inside or outside the closed boundary or enclosed region the sdf property is highly preferred in classical level set methods to maintain the numerical stability during the topology optimization process and provide a metric for the distance based interpolation of different material properties in conventional level set methods a common way of achieving a level set function with the signed distance property is to periodically implement the so called reinitialization scheme by solving an additional hamilton jacobi partial differential equation however such reinitialization scheme is implemented outside the optimization loop with the optimization process suspended which may shift the optimization result and bring convergence issues in this paper a double well potential functional is employed for distance regularization inside the topology optimization loop which can enforce the signed distance property of the level set function in a narrow band along the design boundaries while keeping the level set function flat in the rest area of the computational domain the radial basis function rbf based parameterization technique is combined with mathematical programming to improve the performance of the proposed distance regularized topology optimization method in handling problems with non convex objective functions and multiple constraints the flatness of the level set function in the material region also enables easy creation of new holes to the design in the topology optimization process both 2d and 3d benchmark examples are employed to demonstrate the validity of the proposed method

clustering based denoising with locally learned dictionaries in this paper we propose k lld a patch based locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure in order to effectively perform such clustering we employ as features the local weight functions derived from our earlier work on steering kernel regression these weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise next we model each region or cluster which may not be spatially contiguous by ldquolearningrdquo a best basis describing the patches within that cluster using principal components analysis this learned basis or ldquodictionaryrdquo is then employed to optimally estimate the underlying pixel values using a kernel regression framework an iterated version of the proposed algorithm is also presented which leads to further performance enhancements we also introduce a novel mechanism for optimally choosing the local patch size for each cluster using stein s unbiased risk estimator sure we illustrate the overall algorithm s capabilities with several examples these indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods

erratum distance regularized level set evolution and its application to image segmentation ieee transactions on image processingvol 2010 19 12 3243 3254

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

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

some extensions of w gautschi s inequalities for the gamma function it has been shown by w gautschi that if 0 i xi s f x exp i s x 1 the following closer bounds are proved exp i s 4 x 12 f exp i s x s i f x s 2 and x 2 t x 2 s 4 these are compared with each other and with inequalities given by t erber and j d keckic and p m vasic

multi view stereo reconstruction of dense shape and complex appearance we address the problem of estimating the three dimensional shape and complex appearance of a scene from a calibrated set of views under fixed illumination our approach relies on a rank condition that must be satisfied when the scene exhibits specular diffuse reflectance characteristics this constraint is used to define a cost functional for the discrepancy between the measured images and those generated by the estimate of the scene rather than attempting to match image to image directly minimizing such a functional yields the optimal estimate of the shape of the scene represented by a dense surface as well as its radiance represented by four functions defined on such a surface these can be used to generate novel views that capture the non lambertian appearance of the scene

a novel active contour model for image segmentation using distance regularization term abstract in this paper a novel active contour model r drlse model based on level set method is proposed for image segmentation the r drlse model is a variational level set approach that utilizes the region information to find image contours by minimizing the presented energy functional to avoid the time consuming re initialization step the distance regularization term is used to penalize the deviation of the level set function from a signed distance function the numerical implementation scheme of the model can significantly reduce the iteration number and computation time the results of experiments performed on some synthetic and real images show that the r drlse model is effective and efficient in particular our method has been applied to mr kidney image segmentation with desirable results

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

inequalities for zero balanced hypergeometric functions the authors study certain monotoneity and convexity properties of the gaussian hypergeometric function and those of the euler gamma function

a novel active contour model for medical images via the hessian matrix and eigenvalues abstract this paper presents a new level set formulation for active contour models acm we propose the idea of integrating the eigenvalue information of hessian matrix into the level set function by this new level set function the principal curvature information of images is used to enhance the ability of segmenting boundary regions the advantages of our model are as follows firstly the interior and exterior object boundaries can be segmented with the initial contour being anywhere in the input image secondly this method can work with heterogeneous images thirdly the proposed model can produce smooth and right boundaries of objects having vital importance in medical operations extensive experiments demonstrate that the proposed model can obtain better segmentation results

the anderson model of localization a challenge for modern eigenvalue methods we present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics namely the computation of a few interior eigenvalues and their associated eigenvectors for the large sparse real symmetric and indefinite matrices of the anderson model of localization we compare the lanczos algorithm in the 1987 implementation of cullum and willoughby with the implicitly restarted arnoldi method coupled with polynomial and several shift and invert convergence accelerators as well as with a sparse hybrid tridiagonalization method we demonstrate that for our problem the lanczos implementation is faster and more memory efficient than the other approaches this seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms

fractal eigenstates in disordered systems abstract the wave functions of the non interacting electrons in disordered systems described by a tight binding model with site diagonal disorder are investigated by means of the inverse participation ratio the wave functions are shown to be fractal objects in three dimensional samples a critical fractal dimension can be defined for the mobility edge in the band centre which yields the mobility edge trajectory in the whole energy range in good agreement with previous calculations based on the investigation of the exponentially decaying transmission coefficient