finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

accurate vessel segmentation with constrained b snake we describean active contour framework with accurate shape and size constraints on the vessel cross sectional planes to produce the vessel segmentation it starts with a multiscale vessel axis tracing in a 3d computed tomography ct data followed by vessel boundary delineation on the cross sectional planes derived from the extracted axis the vessel boundary surface is deformed under constrained movements on the cross sections and is voxelized to produce the final vascular segmentation the novelty of this paper lies in the accurate contour point detection of thin vessels based on the ct scanning model in the efficient implementation of missing contour points in the problematic regions and in the active contour model with accurate shape and size constraints the main advantage of our framework is that it avoids disconnected and incomplete segmentation of the vessels in the problematic regions that contain touching vessels vessels in close proximity to each other diseased portions pathologic structure attached to a vessel and thin vessels it is particularly suitable for accurate segmentation of thin and low contrast vessels our method is evaluated and demonstrated on ct data sets from our partner site and its results are compared with three related methods our method is also tested on two publicly available databases and its results are compared with the recently published method the applicability of the proposed method to some challenging clinical problems the segmentation of the vessels in the problematic regions is demonstrated with good results on both quantitative and qualitative experimentations our segmentation algorithm can delineate vessel boundaries that have level of variability similar to those obtained manually

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

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

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

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

robust nanoparticles detection from noisy background by fusing complementary image information this paper studies the problem of detecting the presence of nanoparticles in noisy transmission electron microscopic tem images and then fitting each nanoparticle with an elliptic shape model in order to achieve robustness while handling low contrast and high noise in the tem images we propose an approach to fuse two kinds of complementary image information namely the pixel intensity and the gradient the first derivative in intensity our approach entails two main steps 1 the first step is to after necessary pre processing employ both intensity based information and gradient based information to process the same tem image and produce two independent sets of results and 2 the subsequent step is to formulate a binary integer programming bip problem for conflict resolution among the two sets of results solving the bip problem determines the final nanoparticle identification we apply our method to a set of tem images taken under different microscopic resolutions and noise levels the empirical results show the merit of the proposed method it can process a tem image of 1024 times 1024 pixels in a few minutes and the processed outcomes appear rather robust

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

closed form grammians and model reduction for flexible space structures the author derives analytical expressions for the grammians of a model given in modal coordinates for the dynamics of a flexible space structure fss these expressions are then used as the basis for a new algorithm to compute a dominant reduced order model for such a system in an efficient manner the resulting reduced order model is obtained directly rather than by truncating a balanced model of the entire system thus giving rise to significant efficiency gains for the typical fss case where the reduced order model is of very much lower order than the original system

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

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 variational model for image segmentation in this paper we propose a new variational model for image segmentation our model is inspired by the complex ginzburg landau model and the semi norm defined by us this new model can detect both the convex and concave parts of images moreover it can also detect non closed edges as well as quadruple junctions compared with other methods the initialization is completely automatic and the segmented images obtained by using our new model could keep fine structures and edges of the original images very effectively finally numerical results show the effectiveness of our model

using prior shapes in geometric active contours in a variational framework in this paper we report an active contour algorithm that is capable of using prior shapes the energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape the model provides the segmentation and the transformation that maps the segmented contour to the prior shape the active contour is able to find boundaries that are similar in shape to the prior even when the entire boundary is not visible in the image i e when the boundary has gaps a level set formulation of the active contour is presented the existence of the solution to the energy minimization is also established we also report experimental results of the use of this contour on 2d synthetic images ultrasound images and fmri images classical active contours cannot be used in many of these images

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

an adaptive level set evolution equation for contour extraction level set evolution without re initialization is a novel variational level set method for edge contour extraction which has many advantages over the traditional level set formulations the resulting evolution equation is derived from the minimization of an energy functional which is a linear combination of a weighted length weighted area and deviation penalization energy however the zero level set always keeps evolving in only one direction during evolution depending on the sign of the scale parameter associated with the weighted area this inconvenient makes the evolution highly sensitive to the contour initializations in this paper we propose an adaptive level set evolution equation following this method wherein the scale parameter associated with the weighted area is modified as an adaptive variable sign function and one of two terms associated with the weighted length is removed to reduce computational cost the proposed equation avoids completely the intrinsic limitation mentioned above and offers many advantages over the original equation as illustrated by several examples of contour extraction such as robustness to noise and detection of objects with discontinuous boundaries

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

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

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

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

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

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

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

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

model order reduction of ion channel dynamics using approximate bisimulation we show that in the context of the iyer et al imw 67 variable cardiac myocycte model it is possible to replace the detailed 13 state probabilistic subsystem of the sodium channel dynamics with a much simpler hodgkin huxley hh like two state abstraction while only incurring a bounded approximation error we then extend our technique to the 10 state subsystem of the fast recovering calcium independent potassium channel the basis of our results is the construction of an approximate bisimulation between the hh type abstraction and the corresponding detailed ion channel model both of which are input controlled voltage in this case ctmcs the construction of the appropriate approximate bisimulation as well as the overall result regarding the behavior of this modified imw model involves 1 identification of the voltage dependent parameters of the m and h gates in the hh type models via a two step fitting process carried out over more than 20 000 representative observational traces of the detailed sodium and potassium ion channel models 2 proving that the distance between observations of the detailed models and their respective abstraction is bounded 3 exploring the sensitivity of the overall imw model to the hh type approximations our extensive simulation results experimentally validate our findings for varying imw type input stimuli

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

discrete time norms of flexible structures abstract the paper presents and analyses the h 2 h and hankel norms of flexible structures the analysis is conducted for the discrete time models of structures and compared with the continuous time results the structural state space models are presented in modal co ordinates closed form expressions for norms of structural modes are obtained and norms of a structure are determined from the modal norms the relationships between the hankel h and h 2 modal norms are derived in addition the paper shows that the discrete time hankel and h norms converge to the continuous time counterparts when the sampling time approaches zero however the h 2 norm does not

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

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

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

geometric flow approach for region based image segmentation geometric flows have been successfully used for surface modeling and designing largely because they are inherently good at controlling geometric shape evolution variational image segmentation approaches on the other hand detect objects of interest by deforming certain given shapes this motivates us to revisit the minimal partition problem for segmentation of images and propose a new geometric flow based formulation and solution to it our model intends to derive a mapping that will evolve given contours or piecewise constant regions toward objects in the image the mapping is approximated by b spline basis functions and the positions of the control points are to be determined starting with the energy functional based on intensity averaging we derive a euler lagrange equation and then a geometric evolution equation the linearized system of equations is efficiently solved via a special matrix vector multiplication technique furthermore we extend the piecewise constant model to a piecewise smooth model which effectively handles images with intensity inhomogeneity

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

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

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

principal component analysis of flexible systems open loop case a generic class of flexible systems characterized by finitely many lightly damped harmonic oscillators is analyzed by means of the open loop principal component analysis that is singular value analysis and gramian balancing as the main result it is shown that as the damping ratio goes to zero the balanced state coordinates are decoupled and coincide with the modal coordinates further simple formulas expressing the asymptotic singular values as functions of the modal parameters are derived

probability density difference based active contour for ultrasound image segmentation because of its low signal noise ratio low contrast and blurry boundaries ultrasound us image segmentation is a difficult task in this paper a novel level set based active contour model is proposed for breast ultrasound bus image segmentation at first an energy function is formulated according to the differences between the actual and estimated probability densities of the intensities in different regions the actual probability densities are calculated directly for calculating the estimated probability densities the probability density estimation method and background knowledge are utilized the energy function is formulated with level set approach and a partial differential equation is derived for finding the minimum of the energy function for performing numerical computation the derived partial differential equation is approximated by the central difference and non re initialization approach the proposed method was operated on both the synthetic images and clinical bus images for studying its characteristics and evaluating its performance the experimental results demonstrate that the proposed method can model the bus images well be robust to noise and segment the bus images accurately and reliably

a fast segmentation method based on constraint optimization and its applications intensity inhomogeneity and texture segmentation we propose a new constraint optimization energy and an iteration scheme for image segmentation which is connected to edge weighted centroidal voronoi tessellation ewcvt we show that the characteristic functions of the edge weighted voronoi regions are the minimizers may not unique of the proposed energy at each iteration we propose a narrow banding algorithm to accelerate the implementation which makes the proposed method very fast we generalize the cvt segmentation to hand intensity inhomogeneous and texture segmentation by incorporating the global and local image information into the energy functional compared with other approaches such as level set method the experimental results in this paper have shown that our approach greatly improves the calculation efficiency without losing segmentation accuracy

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

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

vcells simple and efficient superpixels using edge weighted centroidal voronoi tessellations vcells the proposed edge weighted centroidal voronoi tessellations ewcvts based algorithm is used to generate superpixels i e an oversegmentation of an image for a wide range of images the new algorithm is capable of generating roughly uniform subregions and nicely preserving local image boundaries the undersegmentation error is effectively limited in a controllable manner moreover vcells is very efficient with core computational cost at o k nc n in which k nc and n are the number of iterations superpixels and pixels respectively extensive qualitative discussions are provided together with the high quality segmentation results of vcells on a wide range of complex images the simplicity and efficiency of our model are demonstrated by complexity analysis time and accuracy evaluations

a level set method based on the bayesian risk for medical image segmentation this paper proposes an alternative criterion derived from the bayesian risk classification error for image segmentation the proposed model introduces a region based force determined through the difference of the posterior image densities for the different classes a term based on the prior probability derived from kullback leibler information number and a regularity term adopted to avoid the generation of excessively irregular and small segmented regions compared with other level set methods the proposed approach relies on the optimum decision of pixel classification and the estimates of prior probabilities thus the approach has more reliability in theory and practice experiments show that the proposed approach is able to extract the complicated shapes of targets and robust for various types of medical images moreover the algorithm can be easily extendable for multiphase segmentation

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