stacs new active contour scheme for cardiac mr image segmentation the paper presents a novel stochastic active contour scheme stacs for automatic image segmentation designed to overcome some of the unique challenges in cardiac mr images such as problems with low contrast papillary muscles and turbulent blood flow stacs minimizes an energy functional that combines stochastic region based and edge based information with shape priors of the heart and local properties of the contour the minimization algorithm solves by the level set method the euler lagrange equation that describes the contour evolution stacs includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional three particularly attractive features of stacs are 1 ability to segment images with low texture contrast by modeling stochastically the image textures 2 robustness to initial contour and noise because of the utilization of both edge and region based information 3 ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors application of stacs to a set of 48 real cardiac mr images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures the left and right ventricles and the epicardium we compare stacs automatically generated contours with manually traced contours or the gold standard using both area and edge similarity measures this assessment demonstrates very good and consistent segmentation performance of stacs

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

the boundary caratheodory fejer interpolation problem abstract we give a new solvability criterion for the boundary caratheodory fejer problem given a point x r and a finite set of target values to construct a function f in the pick class such that the first few derivatives of f take on the prescribed target values at x we also derive a linear fractional parametrization of the set of solutions of the interpolation problem with real target values the proofs are based on a reduction method due to julia and nevanlinna

adjoint active surfaces for localization and imaging this paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries as opposed to imaging the entirety of the volume active surfaces are used to directly reconstruct the shape of the region of interest we describe the procedure for finding the optimal surface which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface in doing so we introduce the adjoint model to compute the sensitivity and in this respect the method shares common ground with several other disciplines such as optimal control finally we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar helmholtz equation potential applications include electromagnetics acoustics geophysics nondestructive testing and medical imaging

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

a variational model with hybrid images data fitting energies for segmentation of images with intensity inhomogeneity level set functions based variational image segmentation models provide reliable methods to capture boundaries of objects regions in a given image provided that the underlying intensity has homogeneity the case of images with essentially piecewise constant intensities is satisfactorily dealt with in the well known work of chan vese 2001 and its many variants however for images with intensity inhomogeneity or multiphases within the foreground of objects such models become inadequate because the detected edges and even phases do not represent objects and are hence not meaningful to deal with such problems in this paper we have proposed a new variational model with two fitting terms based on regions and edges enhanced quantities respectively from multiplicative and difference images tests and comparisons will show that our new model outperforms two previous models both synthetic and real life images are used to illustrate the reliability and advantages of our new model graphical abstractdisplay omitted highlightswe model image segmentation problem using product and difference images the convex formulation of the model is also presented the proposed model takes care of the minute details and inhomogeneity in an image this model is compared with lcv and fgm of the active contour model the competing energies are qualitatively tested by using jaccord similarity index

sobolev active contours all previous geometric active contour models that have been formulated as gradient flows of various energies use the same l 2 type inner product to define the notion of gradient recent work has shown that this inner product induces a pathological riemannian metric on the space of smooth curves however there are also undesirable features associated with the gradient flows that this inner product induces in this paper we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with sobolev type inner products we call the resulting flows sobolev active contours sobolev metrics induce favorable regularity properties in their gradient flows in addition sobolev active contours favor global translations but are not restricted to such motions they are also less susceptible to certain types of local minima in contrast to traditional active contours these properties are particularly useful in tracking applications we demonstrate the general methodology by reformulating some standard edge based and region based active contour models as sobolev active contours and show the substantial improvements gained in segmentation

threshold dynamics for the piecewise constant mumford shah functional we propose an efficient algorithm for minimizing the piecewise constant mumford shah functional of image segmentation it is based on the threshold dynamics of merriman bence and osher for evolving an interface by its mean curvature we show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

associative algebras and universal enveloping algebras associated to voas abstract for any vertex operator algebra v and any finite automorphism g of v we prove that the associative algebra a g n v is isomorphic to some sub quotient of the universal enveloping algebra of v with respect to g

higher level twisted zhu algebras the study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory in this paper we consider the general setup of a vertex algebra v graded by z for some subgroup of r containing z and with a hamiltonian operator h having real but not necessarily integer eigenvalues we construct the directed system of twisted level p zhu algebras zhup v and we prove the following theorems for each p there is a bijection between the irreducible zhup v modules and the irreducible twisted positive energy v modules and v is h rational if and only if all its zhu algebras zhup v are finite dimensional and semisimple the main novelty is the removal of the assumption of integer eigenvalues for h we provide an explicit description of the level p zhu algebras of a universal enveloping vertex algebra in particular of the virasoro vertex algebra virc and the universal affine kac moody vertex algebra vk g at non critical level we a

higher level zhu algebras are subquotients of universal enveloping algebras abstract we prove that higher level zhu algebras of a vertex operator algebra are isomorphic to subquotients of its universal enveloping algebra

a locally constrained watershed transform the watershed transform from mathematical morphology is a powerful and flexible tool for segmentation however it does not allow a priori knowledge relating to characteristics of region boundaries to be included in the way that other approaches do this paper introduces the locally constrained watershed transform which includes border constraints by modifying the underlying path definition upon which the watershed transform depends this approach maintains many of the desirable properties of the watershed transform such as well defined stopping conditions and efficient implementation while offering more stable segmentation in the presence of noisy or incomplete boundaries

geometric atlas modeling the cortex as an organized surface recent atlases of the cortical surface are based on a modelization of the cerebral cortex as a topological sphere this captures effectively its organization as a regular bidimensional sheet of layers parallel to the surface and with perpendicular cortical columns yet while in the vertical direction cortices are almost the same throughout phylia in the sense of its surface the cerebral cortex is one of the most variable and distinctive parts of the nervous system indeed gyri and sulci appear to have a crucial organizing role in an architectonic connectional and functional sense this organization is not explicitly captured by the surface model of the cortex we propose a geometric model of the cortical anatomy based on flat representations of principal sulci obtained from surface reconstructions of mri data and on neuroanatomical and theoretical considerations concerning the folding patterns of the cortex the cortex is modeled by a sphere where primary sulci are included as axes the arrangement of the axes is a simplification of the arrangement of principal sulci observed in flat stereographic representations of the whole cortical surface the position of secondary and tertiary sulci is then defined by a field of orientations parallel and orthogonal to the axes we consider the use of the geometric model as a synthetic reference cortex for addressing reconstructions of cortical surfaces we present a method which establishes a bijection between the geometric model and a cortical surface reconstruction by using the axes of the model as boundary conditions for a set of partial differential equations solved over both surfaces using the geometric model as atlas provides a natural parameterization of the cortical surface that unlike angular coordinates allows for a localization based on the surface distance to its main organizing landmarks and folding patterns

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

the nevanlinna pick problem on the closed unit disk minimal norm rational solutions of low degree for the nevanlinna pick interpolation problem with n interpolation conditions interior and boundary we construct a family of rational solutions of degree at most n 1 we also establish necessary and sufficient conditions for the existence and the uniqueness of a solution with the minimally possible h norm and construct a family of minimal norm rational solutions of degree at most n 1 in the indeterminate case finally we supplement a result of ruscheweyh and jones showing that in case the interpolation nodes and the target values are all unimodular any rational solution of degree at most n 1 is necessarily a finite blaschke product

three dimensional elastic matching of volumes registering volumes that have been deformed with respect to each other involves recovery of the deformation a 3 d elastic matching algorithm has been developed to use surface information for registering volumes surface extraction is performed in two steps extraction of contours in 2 d image planes using active contours and forming triangular patch surface models from the stack of 2 d contours one volume is modeled as being deformed with respect to another goal volume correspondences between surfaces in the two image volumes are used to warp the deformed volume towards its goal this process of contour extraction surface formation and matching and warping is repeated a number of times with decreasing image volume stiffness as the iterations continue the stretched volume is refined towards its goal volume registration examples of deformed volumes are presented

divergence of gradient convolution deformable segmentation with arbitrary initializations in this paper we propose a unified approach to deformable model based segmentation the fundamental force field of the proposed method is based on computing the divergence of a gradient convolution field gcf which makes the full use of directional information of the image gradient vectors and their interactions across image domain however instead of directly using such a vector field for deformable segmentation as in the conventional approaches we derive a more salient representation for contour evolution and very importantly we demonstrate that this representation of image force field not only leads to global minimum through convex relaxation but also can achieve the same result using the conventional gradient descent with an intrinsic regularization thus the proposed method can handle arbitrary initializations the proposed external force field for deformable segmentation has both edge based properties in that the gcf is computed from image gradients and the region based attributes since its divergence can be treated as a region indication function moreover nonlinear diffusion can be conveniently applied to gcf to improve its performance in dealing with noise interference we also show the extension of gcf from 2d to 3d in comparison to the state of the art deformable segmentation techniques the proposed method shows greater flexibility in model initialization and optimization realization as well as better performance toward noise interference and appearance variation

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

local or global minima flexible dual front active contours most variational active contour models are designed to find local minima of data dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a desirable local minimum as opposed to an undesirable configuration due to noise or complex image structure as such there has been much research into the design of complex region based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge based energy functionals whose sensitivity to noise and texture is significantly worse unfortunately most of these more robust region based energy functionals are applicable to a much narrower class of imagery compared to typical edge based energies due to stronger global assumptions about the underlying image data devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima such implementations have been proposed for capturing global minima however sometimes the completely global minimum is just as undesirable as a minimum that is too local in this paper we propose a novel fast and flexible dual front implementation of active contours motivated by minimal path techniques and utilizing fast sweeping algorithms which is easily manipulated to yield minima with variable degrees of localness and globalness by simply adjusting the size of active regions the ability to gracefully move from capturing minima that are more local according to the initial placement of the active contour surface to minima that are more global allows this model to more easily obtain desirable minimizers which often are neither the most local nor the most global experiments on various 2d and 3d images and comparisons with some active contour models and region growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

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

stabilization of parametric active contours using a tangential redistribution term depending on implementation active contours have been classified as geometric or parametric active contours parametric contours irrespective of representation are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution in a spline based implementation of active contours this leads to occasional formation of loops locally and subsequently the curve blows up due to instabilities in this paper we analyze the reason for this problem and propose a solution to alleviate the same we propose an ordinary differential equation ode for controlling the curve parametrization during evolution by including a tangential force we show that the solution of the proposed ode is bounded we demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours

dense estimation and object based segmentation of the optical flow with robust techniques we address the issue of recovering and segmenting the apparent velocity field in sequences of images as for motion estimation we minimize an objective function involving two robust terms the first one cautiously captures the optical flow constraint while the second a priori term incorporates a discontinuity preserving smoothness constraint to cope with the nonconvex minimization problem thus defined we design an efficient deterministic multigrid procedure it converges fast toward estimates of good quality while revealing the large discontinuity structures of flow fields we then propose an extension of the model by attaching to it a flexible object based segmentation device based on deformable closed curves different families of curve equipped with different kinds of prior can be easily supported experimental results on synthetic and natural sequences are presented including an analysis of sensitivity to parameter tuning

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

image segmentation by map ml estimations image segmentation plays an important role in computer vision and image analysis in this paper image segmentation is formulated as a labeling problem under a probability maximization framework to estimate the label configuration an iterative optimization scheme is proposed to alternately carry out the maximum a posteriori map estimation and the maximum likelihood ml estimation the map estimation problem is modeled with markov random fields mrfs and a graph cut algorithm is used to find the solution to the map estimation the ml estimation is achieved by computing the means of region features in a gaussian model our algorithm can automatically segment an image into regions with relevant textures or colors without the need to know the number of regions in advance its results match image edges very well and are consistent with human perception comparing to six state of the art algorithms extensive experiments have shown that our algorithm performs the best

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

adjoints of composition operators with rational symbol abstract building on techniques developed by cowen and gallardo gutierrez we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the hardy space h 2 we consider some specific examples comparing our formula with several results that were previously known

using an mri distortion transfer function to characterize the ghosts in motion corrupted images motion artefact suppression remains an active topic in mri in this paper the authors suggest that certain nonrigid or spatially variant characteristics of motion of an object can be represented by extending the work of mitsa et al 1989 this empirical extension uses a ghost distortion transfer function gtdf applied to the k space frequency domain data the authors demonstrate the variety of ghost characteristics that can be generated from various two dimensional 2 d gtdf s the distortion transfer function for periodic motion along the z axis can be determined from the nonoverlapped portions of the ghost and central image it required a gdtf with the shape of a belt bandpass filter to produce an image corresponding to the ghosts of a volunteer s abdomen image corrupted by unknown respiratory motion artefacts the preliminary results of a composite method of motion artefact suppression are presented the artefact suppression was successful for ghost images described by a gdtf have a low pass nature but less successful with ghosts have a gdtf of a bandpass nature

boundary vector field for parametric active contours snakes are widely used in the fields of computer vision and image processing there are a number of shortcomings of the traditional snakes including the capture range problem and the concave object extraction problem gradient vector flow snake enhances the concave object extraction capability however it suffers from high computational requirement in this paper we present a new external force which is generated by a novel interpolation scheme which reduces the computational requirement significantly and at the same time improves the capture range and concave object extraction capability

linear relations in the calkin algebra for composition operators we consider this and related questions when is a finite linear combination of composition operators acting on the hardy space or the standard weighted bergman spaces on the unit disk a compact operator

geodesic deformable models for medical image analysis in this paper implicit representations of deformable models for medical image enhancement and segmentation are considered the advantage of implicit models over classical explicit models is that their topology can be naturally adapted to objects in the scene a geodesic formulation of implicit deformable models is especially attractive since it has the energy minimizing properties of classical models the aim of this paper is twofold first a modification to the customary geodesic deformable model approach is introduced by considering all the level sets in the image as energy minimizing contours this approach is used to segment multiple objects simultaneously and for enhancing and segmenting cardiac computed tomography ct and magnetic resonance images second the approach is used to effectively compare implicit and explicit models for specific tasks this shows the complementary character of implicit models since in case of poor contrast boundaries or gaps in boundaries e g due to partial volume effects noise or motion artifacts they do not perform well since the approach is completely data driven

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

continuous global optimization in multiview 3d reconstruction in this article we introduce a new global optimization method to the field of multiview 3d reconstruction while global minimization has been proposed in a discrete formulation in form of the maxflow mincut framework we suggest the use of a continuous convex relaxation scheme specifically we propose to cast the problem of 3d shape reconstruction as one of minimizing a spatially continuous convex functional in qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution firstly geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner the continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased moreover memory requirements are reduced allowing for globally optimal reconstructions at higher resolutions we study three different energy models for multiview reconstruction which are based on a common variational template unifying regional volumetric terms and on surface photoconsistency the three models use data measurements at increasing levels of sophistication while the first two approaches are based on a classical silhouette based volume subdivision the third one relies on stereo information to define regional costs furthermore this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation all three models are compared on standard data sets demonstrating their advantages and shortcomings for the third one which gives the most accurate results a more exhaustive qualitative and quantitative evaluation is presented

2d segmentation using a robust active shape model with the em algorithm statistical shape models have been extensively used in a wide range of applications due to their effectiveness in providing prior shape information for object segmentation problems the most popular method is the active shape model asm however accurately fitting the shape model to an object boundary under a cluttered environment is a challenging task under such assumptions the model is often attracted toward invalid observations outliers leading to meaningless estimates of the object boundary in this paper we propose a novel algorithm that improves the robustness of asm in the presence of outliers the proposed framework assumes that both type of observations valid observations and outliers are detected in the image a new strategy is devised for treating the data in different ways depending on the observations being considered as valid or invalid the proposed algorithm assigns a different weight to each observation the shape parameters are recursively updated using the expectation maximization method allowing a correct and robust fit of the shape model to the object boundary in the image two estimation criteria are considered 1 the maximum likelihood criterion and 2 the maximum a posteriori criterion that use priors for the unknown parameters the methods are tested with synthetic and real images comprising medical images of the heart and image sequences of the lips the results are promising and show that this approach is robust in the presence of outliers leading to a significant improvement over the standard asm and other state of the art methods

facial age estimation based on label sensitive learning and age oriented regression this paper provides a new age estimation approach which distinguishes itself with the following three contributions first we combine distance metric learning and dimensionality reduction to better explore the connections between facial features and age labels second to exploit the intrinsic ordinal relationship among human ages and overcome the potential data imbalance problem a label sensitive concept and several imbalance treatments are introduced in the system training phase finally an age oriented local regression is presented to capture the complicated facial aging process for age determination the simulation results show that our approach achieves the lowest estimation error against existing methods

which linear fractional composition operators are essentially normal abstract we characterize the essentially normal composition operators induced on the hardy space h2 by linear fractional maps they are either compact normal or the nontrivial case induced by parabolic nonautomorphisms these parabolic maps induce the first known examples of nontrivially essentially normal composition operators in addition we characterize those linear fractionally induced composition operators on h2 that are essentially self adjoint and present a number of results for composition operators induced by maps that are not linear fractional

image segmentation by iterated region merging with localized graph cuts this paper presents an iterated region merging based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions however the extraction of objects in a complex background often requires a lot of user interaction the proposed algorithm starts from the user labeled sub graph and works iteratively to label the surrounding un segmented regions in each iteration only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced meanwhile the data models of the object and background are updated iteratively based on high confident labeled regions the sub graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the grabcut methods in either qualitative or quantitative evaluation

a wavelet frame based image force model for active contouring algorithms this paper proposes a directional image force dif for active contouring dif is the inner product of the zero crossing strength zcs of wavelet frame coefficients and the normal of a snake by representing strength and orientation of edges at multiple resolution levels dif markedly improves the immunity of snakes to noise and convexity

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

a framework for multiple snakes and its applications we present a framework for segmentation of multiple objects whose shapes are similar but image qualities are different our framework is based on the snake or active contour method in which a new kind of energy called group energy is introduced the group energy is used to handle the sharing of properties across multiple objects and also to allow contours of objects with good image qualities to be used as reference contours for remaining objects during optimization in this framework we also deal with rotations among similar objects by applying group energy after removing the rotation offset comprehensive testing has been performed on synthetic and real images demonstrating that our framework has significantly better performance of segmentation compared to the original individual snake

essentially normal composition operators on h2 abstract we prove a simple criterion for essential normality of composition operators on the hardy space induced by maps in a reasonably large class s of analytic self maps of the unit disk by combining this criterion with boundary caratheodory fejer interpolation theory we exhibit a parametrization for all rational self maps of the unit disk which induce essentially normal composition operators

vertex operator algebras and associative algebras letvbe a vertex operator algebra we construct a sequence of associative algebrasan v n 0 1 2 such thatan v is a quotient ofan 1 v and a pair of functors between the category ofan v modules which are notan 1 v modules and the category of admissiblev modules these functors exhibit a bijection between the simple modules in each category we also show thatvis rational if and only if allan v are finite dimensional semisimple algebras

boundary nevanlinna pick interpolation via reduction and augmentation we give an elementary proof of sarason s solvability criterion for the nevanlinna pick problem with boundary interpolation nodes and boundary target values we also give a concrete parametrization of all solutions of such a problem the proofs are based on a reduction method due to julia and nevanlinna reduction of functions corresponds to schur complementation of the corresponding pick matrices

a new class of operators and a description of adjoints of composition operators abstract starting with a general formula precise but difficult to use for the adjoint of a composition operator on a functional hilbert space we compute an explicit formula on the classical hardy hilbert space for the adjoint of a composition operator with rational symbol to provide a foundation for this formula we study an extension to the definitions of composition weighted composition and toeplitz operators to include symbols that are multiple valued functions these definitions can be made on any banach space of analytic functions on a plane domain but in this work our attention is focused on the basic properties needed for the application to operators on the standard hardy and bergman hilbert spaces on the unit disk

an interacting multiple model probabilistic data association filter for cavity boundary extraction from ultrasound images this paper presents a novel segmentation technique for extracting cavity contours from ultrasound images the problem is first discretized by projecting equispaced radii from an arbitrary seed point inside the cavity toward its boundary the distance of the cavity boundary from the seed point is modeled by the trajectory of a moving object the motion of this moving object is assumed to be governed by a finite set of dynamical models subject to uncertainty candidate edge points obtained along each radius include the measurement of the object position and some false returns the modeling approach enables us to use the interacting multiple model estimator along with a probabilistic data association filter for contour extraction the convergence rate of the method is very fast because it does not employ any numerical optimization the robustness and accuracy of the method are demonstrated by segmenting contours from a series of ultrasound images the results are validated through comparison with manual segmentations performed by an expert an application of the method in segmenting bone contours from computed tomography images is also presented

the contracting curve density algorithm fitting parametric curve models to images using local self adapting separation criteria the task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications such as image segmentation pose estimation object tracking and 3 d reconstruction in this article we propose the contracting curve density ccd algorithm as a solution to the curve fitting problem the ccd algorithm extends the state of the art in two important ways first it applies a novel likelihood function for the assessment of a fit between the curve model and the image data this likelihood function can cope with highly inhomogeneous image regions because it is formulated in terms of local image statistics the local image statistics are learned on the fly from the vicinity of the expected curve they provide therefore locally adapted criteria for separating the adjacent image regions these local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties the second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters these blurred curve models enable the algorithm to trade off two conflicting objectives namely heaving a large area of convergence and achieving high accuracy we apply the ccd algorithm to several challenging image segmentation and 3 d pose estimation problems our experiments with rgb images show that the ccd algorithm achieves a high level of robustness and sub pixel accuracy even in the presence of severe texture shading clutter partial occlusion and strong changes of illumination

adjoints of rationally induced composition operators abstract we give an elementary proof of a formula recently obtained by hammond moorhouse and robbins for the adjoint of a rationally induced composition operator on the hardy space h 2 christopher hammond jennifer moorhouse marian e robbins adjoints of composition operators with rational symbol j math anal appl 341 2008 626 639 we discuss some variants and implications of this formula and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator

shapes from pixels continuous domain visual signals are usually captured as discrete digital images this operation is not invertible in general in the sense that the continuous domain signal cannot be exactly reconstructed based on the discrete image unless it satisfies certain constraints e g bandlimitedness in this paper we study the problem of recovering shape images with smooth boundaries from a set of samples thus the reconstructed image is constrained to regenerate the same samples consistency as well as forming a shape bilevel image we initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes next we relax the non convex shape constraint to transform the problem into minimizing the total variation over consistent non negative valued images we also introduce a requirement called reducibility that guarantees equivalence between the two problems we illustrate that the reducibility property effectively sets a requirement on the minimum sampling density we also evaluate the performance of the relaxed alternative in various numerical experiments

elastic model based segmentation of 3 d neuroradiological data sets this paper presents a new technique for the automatic model based segmentation of three dimensional 3 d objects from volumetric image data the development closely follows the seminal work of taylor and cootes on active shape models but is based on a hierarchical parametric object description rather than a point distribution model the segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models geometric models are derived from a sample set of image data which have been segmented by experts the surfaces of these binary objects are converted into parametric surface representations which are normalized to get an invariant object centered coordinate system surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes it is shown that invariant object surface parametrization provides a good approximation to automatically determine object homology in terms of sets of corresponding sets of surface points gray level information near object boundaries is represented by 1 d intensity profiles normal to the surface considering automatic segmentation of brain structures as their driving application the authors choice of coordinates for object alignment was the well accepted stereotactic coordinate system major variation of object shapes around the mean shape also referred to as shape eigenmodes are calculated in shape parameter space rather than the feature space of point coordinates segmentation makes use of the object shape statistics by restricting possible elastic deformations into the range of the training shapes the mean shapes are initialized in a new data set by specifying the landmarks of the stereotactic coordinate system the model elastically deforms driven by the displacement forces across the object s surface which are generated by matching local intensity profiles elastical deformations are limited by setting bounds for the maximum variations in eigenmode space the technique has been applied to automatically segment left and right hippocampus thalamus putamen and globus pallidus from volumetric magnetic resonance scans taken from schizophrenia studies the results have been validated by comparison of automatic segmentation with the results obtained by interactive expert segmentation

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

shape tracking with occlusions via coarse to fine region based sobolev descent we present a method to track the shape of an object from video the method uses a joint shape and appearance model of the object which is propagated to match shape and radiance in subsequent frames determining object shape self occlusions and dis occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking they are unable to adapt to new shape and appearance information leading to inaccurate shape detection in this work we model self occlusions and dis occlusions in a joint shape and appearance tracking framework self occlusions and the warp to propagate the model are coupled thus we formulate a joint optimization problem we derive a coarse to fine optimization method advantageous in tracking that initially perturbs the model by coarse perturbations before transitioning to finer scale perturbations seamlessly this coarse to fine behavior is automatically induced by gradient descent on a novel infinite dimensional riemannian manifold that we introduce the manifold consists of planar parameterized regions and the metric that we introduce is a novel sobolev metric experiments on video exhibiting occlusions dis occlusions complex radiance and background show that occlusion dis occlusion modeling leads to superior shape accuracy

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

hierarchical active shape models using the wavelet transform active shape models asms are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability this paper presents a method that overcomes this limitation by using a hierarchical formulation of active shape models using the wavelet transform the statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis and used as priors in the contour s deformation some of these priors reflect relatively global shape characteristics of the object boundaries whereas some of them capture local and high frequency shape characteristics and thus serve as local smoothness constraints this formulation achieves two objectives first it is robust when only a limited number of training samples is available second by using local statistics as smoothness constraints it eliminates the need for adopting ad hoc physical models such as elasticity or other smoothness models which do not necessarily reflect true biological variability examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved even with as few as five training samples

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners