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

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

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

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

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

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

codimensions of newton strata for sl3 f in the iwahori case we study the newton stratification on sl 3 f where f is a laurent power series field we provide a formula for the codimensions of the newton strata inside each component of the affine bruhat decomposition on sl 3 f these calculations are related to the study of certain affine deligne lusztig varieties in particular we describe a method for determining which of these varieties is non empty in the case of sl 3 f

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

an improved region based model with local statistical features for image segmentation in this paper we propose a new region based active contour model acm for image segmentation in particular this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour by this improved region fitting term images with noise intensity non uniformity and low contrast boundaries can be well segmented integrated with the duality theory and the anisotropic diffusion process based on structure tensor a new regularization term is defined through the duality formulation to penalize the length of active contour by this new regularization term the structural information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps from a numerical point of view we minimize the energy function of our model by an efficient dual algorithm which avoids the instability and the non differentiability of traditional numerical solutions e g the gradient descent method experiments on medical and natural images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy

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

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

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

rapid and brief communication gacv geodesic aided c v method a novel algorithm for image segmentation is proposed the proposed method incorporates geodesic curves and c v method to raise active contours performance on image segmentation moreover we extend our method to color images by practical experiments it is verified that our model obtains better results than original methods especially with respect to images within holes complex background weak edges and noise

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

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

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

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

level set evolution with locally linear classification for image segmentation this paper presents a novel local region based level set model for image segmentation in each local region we define a locally weighted least squares energy to fit a linear classifier with level set representation these local energy functions are then integrated over the whole image domain to develop a global segmentation model the objective function in this model is thereafter minimized via level set evolution in this process the parameters related to the locally linear classifier are iteratively estimated by introducing the locally linear functions to separate background and foreground in local regions our model not only achieves accurate segmentation results but also is robust to initialization extensive experiments are reported to demonstrate that our method holds higher segmentation accuracy and more initialization robustness compared with the classical region based and local region based methods

a new fast multiphase image segmentation algorithm based on nonconvex regularizer we present a new variational model for the soft multiphase image segmentation in the model we introduce a nonconvex regularizer on the membership functions which are used as indicators of different homogeneous regions the nonconvex regularizer performs better than the usual convex ones in that i it well preserves geometric shapes of the homogeneous regions and ii it protects edges from oversmoothing which is a common drawback of the convex regularizer to solve the nonconvex minimization problem we design a new fast alternative iteration algorithm which is robust to the setting of the parameters in the model we conduct comprehensive experiments to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for image segmentation the algorithm achieves more accurate results compared to other well known convex variational methods for image segmentation

one dimensional δ function potential and the radiation boundary condition in a recent paper 1 datta and jayannavar d j suggest a g function potential model to describe a single imperfect trap in one dimension as an alternative to the traditional radiation boundary condition rbc approach 2 using their model they re study some of the statistical properties of nearest neighbor distance at the trap this distance is one of the possible measures of self segregation in trapping reactions a topic of current great interest 3 10 in the rbc description actual particles are restricted to one side of the trap of which some are absorbed at the trap while others are reflected back as dj point out such a constraint is removed in their treatment diffusing particles impinging on the trap can partially be absorbed and partially move away to either side of the trap dj obtain different results for the nearest neighbor distance statistics when particles are initially distributed along the positive semi infinite space but for initial uniform distribution throughout the infinite line their results are equivalent to those obtained using the rbc 5 with redefined parameters although dj do explain this similarity by physical symmetry arguments they claim that the equivalence is a coincidence in this paper we show how this equivalence can be obtained explicitly we also address the question of the appropriateness of the two approaches to describe partial absorbing traps in various physical systems

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