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

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

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

fast and robust image segmentation with active contours and student s t mixture model abstract in this paper a novel active contours method which combines with the student s t mixture model via expectaton maximizaton em algorithm is proposed to segment complicated two phase images firstly we rewrite the cost function and derive a novel updating of level set function based on probabilistic principles secondly we put forward two novel geometric priors from the level set based curve evolution and both of them have advantages the suitable one is selected by personalized need to obtain level set function in em framework with the aim of reducing the computational cost therefore the level set function is derived from latent variables and served as a feedback to the estimation of the latent variables in next iteration finally in order to enhance the robustness to the outliers student s t mixture model with heavy tail has been applied in our algorithm experimental results obtained by employing the proposed method on many synthetic medical and real world images to demonstrate its robustness accuracy and effectiveness

active contours for tracking distributions a new approach to tracking using active contours is presented the class of objects to be tracked is assumed to be characterized by a probability distribution over some variable such as intensity color or texture the goal of the algorithm is to find the region within the current image such that the sample distribution of the interior of the region most closely matches the model distribution two separate criteria for matching distributions are examined and the curve evolution equations are derived in each case the flows are shown to perform well in experiments

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

local histogram based segmentation using the wasserstein distance we propose and analyze a nonparametric region based active contour model for segmenting cluttered scenes the proposed model is unsupervised and assumes pixel intensity is independently identically distributed our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region based image term that uses histograms of pixel intensity to distinguish different regions more specifically the region data encourages segmentation so that local histograms within each region are approximately homogeneous an advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem we use wasserstein distance with exponent 1 to determine the dissimilarity between two histograms the wasserstein distance is a metric and is able to faithfully measure the distance between two histograms compared to many pointwise distances moreover it is insensitive to oscillations and therefore our model is robust to noise a fast global minimization method based on chan et al in siam j appl math 66 5 1632 1648 2006 bresson et al in j math imaging vis 28 2 151 167 2007 is employed to solve the proposed model the advantages of using this method are two fold first the computational time is less than that of the method by gradient descent of the associated euler lagrange equation chan et al in proc of ssvm pp 697 708 2007 second it is able to find a global minimizer finally we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes

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 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

a novel level set method for image segmentation by incorporating local statistical analysis and global similarity measurement this paper presents a novel level set method for complex image segmentation where the local statistical analysis and global similarity measurement are both incorporated into the construction of energy functional the intensity statistical analysis is performed on local circular regions centered in each pixel so that the local energy term is constructed in a piecewise constant way meanwhile the bhattacharyya coefficient is utilized to measure the similarity between probability distribution functions for intensities inside and outside the evolving contour the global energy term can be formulated by minimizing the bhattacharyya coefficient to avoid the time consuming re initialization step the penalty energy term associated with a new double well potential is constructed to maintain the signed distance property of level set function the experiments and comparisons with four popular models on synthetic and real images have demonstrated that our method is efficient and robust for segmenting noisy images images with intensity inhomogeneity texture images and multiphase images the intensity statistical analysis is performed on local circular regions the global energy term is formulated by minimizing the bhattacharyya coefficient the penalty energy term associated with a new double well potential is proposed the proposed method is efficient and robust for segmenting complex images

active walker models tracks and landscapes abstract the track patterns from the active walker models awms are compared with experimental retinal neuron and dielectric breakdown of liquid patterns respectively excellent qualitative and quantitative agreements are obtained the landscapes from the boltzmann awm in 1 1 dimensions form rough surfaces with a first order phase transition as the height of the landscaping function w0 is varied landscapes and statistics of the tracks from the probabilistic awm in 2 1 dimensions are presented

image segmentation and selective smoothing by using mumford shah model recently chan and vese developed an active contour model for image segmentation and smoothing by using piecewise constant and smooth representation of an image tsai et al also independently developed a segmentation and smoothing method similar to the chan and vese piecewise smooth approach these models are active contours based on the mumford shah variational approach and the level set method in this paper we develop a new hierarchical method which has many advantages compared to the chan and vese multiphase active contour models first unlike previous works the curve evolution partial differential equations pdes for different level set functions are decoupled each curve evolution pde is the equation of motion of just one level set function and different level set equations of motion are solved in a hierarchy this decoupling of the motion equations of the level set functions speeds up the segmentation process significantly second because of the coupling of the curve evolution equations associated with different level set functions the initialization of the level sets in chan and vese s method is difficult to handle in fact different initial conditions may produce completely different results the hierarchical method proposed in this paper can avoid the problem due to the choice of initial conditions third in this paper we use the diffusion equation for denoising this method therefore can deal with very noisy images in general our method is fast flexible not sensitive to the choice of initial conditions and produces very good results

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

global existence of classical solutions to the vlasov poisson system in a three dimensional cosmological setting the initial value problem for the vlasov poisson system is by now well understood in the case of an isolated system where by definition the distribution function of the particles as well as the gravitational potential vanish at spatial infinity here we start with homogeneous solutions which have a spatially constant non zero mass density and which describe the mass distribution in a newtonian model of the universe these homogeneous states can be constructed explicitly and we consider deviations from such homogeneous states which then satisfy a modified version of the vlasov poisson system we prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states

level set based bimodal segmentation with stationary global minimum in this paper we propose a new level set based partial differential equation pde for the purpose of bimodal segmentation the pde is derived from an energy functional which is a modified version of the fitting term of the chan vese model the energy functional is designed to obtain a stationary global minimum i e the level set function which evolves by the euler lagrange equation of the energy functional has a unique convergence state the existence of a global minimum makes the algorithm invariant to the initialization of the level set function whereas the existence of a convergence state makes it possible to set a termination criterion on the algorithm furthermore since the level set function converges to one of the two fixed values which are determined by the amount of the shifting of the heaviside functions an initialization of the level set function close to those values can result in a fast convergence

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

on scene segmentation and histograms based curve evolution we consider curve evolution based on comparing distributions of features and its applications for scene segmentation in the first part we promote using cross bin metrics such as the earth mover s distance emd instead of standard bin wise metrics as the bhattacharyya or kullback leibler metrics to derive flow equations for minimizing functionals involving the emd we employ a tractable expression for calculating emd between one dimensional distributions we then apply the derived flows to various examples of single image segmentation and to scene analysis using video data in the latter we consider the problem of segmenting a scene to spatial regions in which different activities occur we use a nonparametric local representation of the regions by considering multiple one dimensional histograms of normalized spatiotemporal derivatives we then obtain semisupervised segmentation of regions using the flows derived in the first part of the paper our results are demonstrated on challenging surveillance scenes and compare favorably with state of the art results using parametric representations by dynamic systems or mixtures of them

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

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

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

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

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