non rigid object contour tracking via a novel supervised level set model we present a novel approach to non rigid objects contour tracking in this paper based on a supervised level set model slsm in contrast to most existing trackers that use bounding box to specify the tracked target the proposed method extracts the accurate contours of the target as tracking output which achieves better description of the non rigid objects while reduces background pollution to the target model moreover conventional level set models only emphasize the regional intensity consistency and consider no priors differently the curve evolution of the proposed slsm is object oriented and supervised by the specific knowledge of the targets we want to track therefore the slsm can ensure a more accurate convergence to the exact targets in tracking applications in particular we firstly construct the appearance model for the target in an online boosting manner due to its strong discriminative power between the object and the background then the learnt target model is incorporated to model the probabilities of the level set contour by a bayesian manner leading the curve converge to the candidate region with maximum likelihood of being the target finally the accurate target region qualifies the samples fed to the boosting procedure as well as the target model prepared for the next time step we firstly describe the proposed mechanism of two phase slsm for single target tracking then give its generalized multi phase version for dealing with multi target tracking cases positive decrease rate is used to adjust the learning pace over time enabling tracking to continue under partial and total occlusion experimental results on a number of challenging sequences validate the effectiveness of the proposed method

diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

on the length and area regularization for multiphase level set segmentation in this paper we introduce novel regularization techniques for level set segmentation that target specifically the problem of multiphase segmentation when the multiphase model is used to obtain a partitioning of the image in more than two regions a new set of issues arise with respect to the single phase case in terms of regularization strategies for example if smoothing or shrinking each contour individually could be a good model in the single phase case this is not necessarily true in the multiphase scenario in this paper we address these issues designing enhanced length and area regularization terms whose minimization yields evolution equations in which each level set function involved in the multiphase segmentation can sense the presence of the other level set functions and evolve accordingly in other words the coupling of the level set function which before was limited to the data term i e the proper segmentation driving force is extended in a mathematically principled way to the regularization terms as well the resulting regularization technique is more suitable to eliminate spurious regions and other kind of artifacts an extensive experimental evaluation supports the model we introduce in this paper showing improved segmentation performance with respect to traditional regularization techniques

a multiphase dynamic labeling model for variational recognition driven image segmentation we propose a variational framework for the integration of multiple competing shape priors into level set based segmentation schemes by optimizing an appropriate cost functional with respect to both a level set function and a vector valued labeling function we jointly generate a segmentation by the level set function and a recognition driven partition of the image domain by the labeling function which indicates where to enforce certain shape priors our framework fundamentally extends previous work on shape priors in level set segmentation by directly addressing the central question of where to apply which prior it allows for the seamless integration of numerous shape priors such that while segmenting both multiple known and unknown objects the level set process may selectively use specific shape knowledge for simultaneously enhancing segmentation and recognizing shape

a shape representation with elastic quadratic polynomials preservation of high curvature points under noisy conditions we present a new shape representation technique for a planar shape using overlapping quadratic splines the technique refines the shape by iteratively updating each spline to reduce the cost associated with c 1 discontinuity it consists of a series of affine commutative linear operators producing a smooth bandpass frequency response the primary purpose of the technique is to remove minute high curvature points while preserving salient ones we compare the performance of the technique against those that are based on either linear splines cubic splines or wavelets we consider three criteria sensitivity of detecting salient high curvature points hausdorff distance between the representation and the original shape and computation time the results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small hausdorff distance and a computational cost

robust simultaneous registration and segmentation with sparse error reconstruction we introduce a fast and efficient variational framework for simultaneous registration and segmentation srs applicable to a wide variety of image sequences we demonstrate that a dense correspondence map between consecutive frames can be reconstructed correctly even in the presence of partial occlusion shading and reflections the errors are efficiently handled by exploiting their sparse nature in addition the segmentation functional is reformulated using a dual rudin osher fatemi rof model for fast implementation moreover nonparametric shape prior terms that are suited for this dual rof model are proposed the efficacy of the proposed method is validated with extensive experiments on both indoor outdoor natural and biological image sequences demonstrating the higher accuracy and efficiency compared to various state of the art methods

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 review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

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

active contour based visual tracking by integrating colors shapes and motions in this paper we present a framework for active contour based visual tracking using level sets the main components of our framework include contour based tracking initialization color based contour evolution adaptive shape based contour evolution for non periodic motions dynamic shape based contour evolution for periodic motions and the handling of abrupt motions for the initialization of contour based tracking we develop an optical flow based algorithm for automatically initializing contours at the first frame for the color based contour evolution markov random field theory is used to measure correlations between values of neighboring pixels for posterior probability estimation for adaptive shape based contour evolution the global shape information and the local color information are combined to hierarchically evolve the contour and a flexible shape updating model is constructed for the dynamic shape based contour evolution a shape mode transition matrix is learnt to characterize the temporal correlations of object shapes for the handling of abrupt motions particle swarm optimization is adopted to capture the global motion which is applied to the contour in the current frame to produce an initial contour in the next frame

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

dynamical statistical shape priors for level set based tracking in recent years researchers have proposed introducing statistical shape knowledge into level set based segmentation methods in order to cope with insufficient low level information while these priors were shown to drastically improve the segmentation of familiar objects so far the focus has been on statistical shape priors which are static in time yet in the context of tracking deformable objects it is clear that certain silhouettes such as those of a walking person may become more or less likely over time in this paper we tackle the challenge of learning dynamical statistical models for implicitly represented shapes we show how these can be integrated as dynamical shape priors in a bayesian framework for level set based image sequence segmentation we assess the effect of such shape priors with memory on the tracking of familiar deformable objects in the presence of noise and occlusion we show comparisons between dynamical and static shape priors between models of pure deformation and joint models of deformation and transformation and we quantitatively evaluate the segmentation accuracy as a function of the noise level and of the camera frame rate our experiments demonstrate that level set based segmentation and tracking can be strongly improved by exploiting the temporal correlations among consecutive silhouettes which characterize deforming shapes

black box multigrid one major problem with the multigrid method has been that each new grid configuration has required a major programming effort to develop a code that specifically handles that grid configuration such a penalty is not required for methods like sor iccg etc in these methods one need only specify the matrix problem no matter what the grid configuration in this paper we investigate such a situation for the multigrid method the end result is code boxmg in which one need only specify the logically rectangular positive definite matrix problem boxmg does everything else necessary to set up the auxilliary coarser problems to achieve a multigrid solution

a generic framework for tracking using particle filter with dynamic shape prior tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time tracking algorithms using kalman filters or particle filters pfs have been proposed for tracking such objects but these have limitations due to the lack of dynamic shape information in this paper we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter the pf also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background

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

behavior classification by eigendecomposition of periodic motions we show how periodic motions can be represented by a small number of eigenshapes that capture the whole dynamic mechanism of the motion spectral decomposition of a silhouette of a moving object serves as a basis for behavior classification by principle component analysis the boundary contour of the walking dog for example is first computed efficiently and accurately after normalization the implicit representation of a sequence of silhouette contours given by their corresponding binary images is used for generating eigenshapes for the given motion singular value decomposition produces these eigenshapes that are then used to analyze the sequence we show examples of object as well as behavior classification based on the eigendecomposition of the binary silhouette sequence

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

a combinatorial solution for model based image segmentation and real time tracking we propose a combinatorial solution to determine the optimal elastic matching of a deformable template to an image the central idea is to cast the optimal matching of each template point to a corresponding image pixel as a problem of finding a minimum cost cyclic path in the three dimensional product space spanned by the template and the input image we introduce a cost functional associated with each cycle which consists of three terms a data fidelity term favoring strong intensity gradients a shape consistency term favoring similarity of tangent angles of corresponding points and an elastic penalty for stretching or shrinking the functional is normalized with respect to the total length to avoid a bias toward shorter curves optimization is performed by lawler s minimum ratio cycle algorithm parallelized on state of the art graphics cards the algorithm provides the optimal segmentation and point correspondence between template and segmented curve in computation times that are essentially linear in the number of pixels to the best of our knowledge this is the only existing globally optimal algorithm for real time tracking of deformable shapes

linear dimensionality reduction by maximizing the chernoff distance in the transformed space linear dimensionality reduction ldr techniques are quite important in pattern recognition due to their linear time complexity and simplicity in this paper we present a novel ldr technique which though linear aims to maximize the chernoff distance in the transformed space thus augmenting the class separability in such a space we present the corresponding criterion which is maximized via a gradient based algorithm and provide convergence and initialization proofs we have performed a comprehensive performance analysis of our method combined with two well known classifiers linear and quadratic on synthetic and real life data and compared it with other ldr techniques the results on synthetic and standard real life data sets show that the proposed criterion outperforms the latter when combined with both linear and quadratic classifiers

tracking with occlusions via graph cuts this work presents a new method for tracking and segmenting along time interacting objects within an image sequence one major contribution of the paper is the formalization of the notion of visible and occluded parts for each object we aim at tracking these two parts assuming that the velocity of each object is driven by a dynamical law predictions can be used to guide the successive estimations separating these predicted areas into good and bad parts with respect to the final segmentation and representing the objects with their visible and occluded parts permit handling partial and complete occlusions to achieve this tracking a label is assigned to each object and an energy function representing the multilabel problem is minimized via a graph cuts optimization this energy contains terms based on image intensities which enable segmenting and regularizing the visible parts of the objects it also includes terms dedicated to the management of the occluded and disappearing areas which are defined on the areas of prediction of the objects the results on several challenging sequences prove the strength of the proposed approach

a region merging prior for variational level set image segmentation in current level set image segmentation methods the number of regions is assumed to known beforehand as a result it remains constant during the optimization of the objective functional how to allow it to vary is an important question which has been generally avoided this study investigates a region merging prior related to regions area to allow the number of regions to vary automatically during curve evolution thereby optimizing the objective functional implicitly with respect to the number of regions we give a statistical interpretation to the coefficient of this prior to balance its effect systematically against the other functional terms we demonstrate the validity and efficiency of the method by testing on real images of intensity color and motion

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

automorphisms of certain groups and semigroups of matrices characterizations are given for automorphisms of semigroups of nonnegative matrices including doubly stochastic matrices row column stochastic matrices positive matrices and nonnegative monomial matrices the proofs utilize the structure of the automorphisms of the symmetric group realized as the group of permutation matrices and alternating group furthermore for each of the above semi groups of matrices a larger semi group of matrices is obtained by relaxing the nonnegativity assumption characterizations are also obtained for the automorphisms on the larger semi groups and their subgroups subsemigroups as well

matrix dependent prolongations and restrictions in a blackbox multigrid solver multigrid methods are studied for the solution of linear systems resulting from the 9 point discretization of a general linear second order elliptic partial differential equation in two dimensions the rate of convergence of standard multigrid methods often deteriorates when the coefficients in the differential equation are discontinuous or when dominating first order terms are present these difficulties may be overcome by choosing the prolongation and restriction operators in a special way a novel way to do this is proposed as a result a blackbox solver written in standard fortran 77 has been developed numerical experiments for several hard test problems are described and comparison is made with other algorithms the standard mg method and a method introduced by kettler a significant improvement of robustness and efficiency is found

similarity and affine invariant distances between 2d point sets we develop expressions for measuring the distance between 2d point sets which are invariant to either 2d affine transformations or 2d similarity transformations of the sets and assuming a known correspondence between the point sets we discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images we then give a general metric definition of the distance between images which leads to the same expressions for the similarity and affine cases this definition avoids ad hoc decisions about normalization moreover it makes it possible to compute the distance between images under different conditions including cases where the images are treated asymmetrically we demonstrate these results with real and simulated images

learning the dynamics and time recursive boundary detection of deformable objects we propose a principled framework for recursively segmenting deformable objects across a sequence of frames we demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle the approach involves a technique for learning the system dynamics together with methods of particle based smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart the dynamic system state is a low dimensional representation of the boundary and the boundary estimation involves incorporating curve evolution into recursive state estimation by formulating the problem as one of state estimation the segmentation at each particular time is based not only on the data observed at that instant but also on predictions based on past and future boundary estimates although this paper focuses on left ventricle segmentation the method generalizes to temporally segmenting any deformable object

linear maps preserving permutation and stochastic matrices abstract let s be the set of n n sub permutation matrices doubly sub stochastic matrices or the set of m n column or row sub stochastic matrices we characterize those linear maps t on the linear span of s that satisfy t s s partial results concerning those linear maps t satisfying t s s are also presented

the denominator rule for share weighting aggregation abstract in this paper we prove that the denominator rule namely that weighting shares should be defined in term of the denominator variable of the relevant index is a necessary and sufficient condition for consistent arithmetic aggregation of any ratio type performance measures including efficiency indices we then illustrate the applicability of the denominator rule in the aggregation of scale efficiency measures of the effect of input congestion and of capacity utilization indices

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

synergy between object recognition and image segmentation using the expectation maximization algorithm in this work we formulate the interaction between image segmentation and object recognition in the framework of the expectation maximization em algorithm we consider segmentation as the assignment of image observations to object hypotheses and phrase it as the e step while the m step amounts to fitting the object models to the observations these two tasks are performed iteratively thereby simultaneously segmenting an image and reconstructing it in terms of objects we model objects using active appearance models aams as they capture both shape and appearance variation during the e step the fidelity of the aam predictions to the image is used to decide about assigning observations to the object for this we propose two top down segmentation algorithms the first starts with an oversegmentation of the image and then softly assigns image segments to objects as in the common setting of em the second uses curve evolution to minimize a criterion derived from the variational interpretation of em and introduces aams as shape priors for the m step we derive aam fitting equations that accommodate segmentation information thereby allowing for the automated treatment of occlusions apart from top down segmentation results we provide systematic experiments on object detection that validate the merits of our joint segmentation and recognition approach

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

tracking using motion estimation with physically motivated inter region constraints we propose a method for tracking structures e g ventricles and myocardium in cardiac images e g magnetic resonance by propagating forward in time a previous estimate of the structures using a new physically motivated motion estimation scheme our method estimates motion by regularizing only within structures so that differing motions among different structures are not mixed it simultaneously satisfies the physical constraints at the interface between a fluid and a medium that the normal component of the fluid s motion must match the normal component of the medium s motion and the no slip condition which states that the tangential velocity approaches zero near the interface we show that these conditions lead to partial differential equations with robin boundary conditions at the interface which couple the motion between structures we show that propagating a segmentation across frames using our motion estimation scheme leads to more accurate segmentation than traditional motion estimation that does not use physical constraints our method is suited to interactive segmentation prominently used in commercial applications for cardiac analysis where segmentation propagation is used to predict a segmentation in the next frame we show that our method leads to more accurate predictions than a popular and recent interactive method used in cardiac segmentation

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

statistical deformable model based segmentation of image motion we present a statistical method for the motion based segmentation of deformable structures undergoing nonrigid movements the proposed approach relies on two models describing the shape of interest its variability and its movement the first model corresponds to a statistical deformable template that constrains the shape and its deformations the second model is introduced to represent the optical flow field inside the deformable template these two models are combined within a single probability distribution which enables to derive shape and motion estimates using a maximum likelihood approach the method requires no manual initialization and is demonstrated on synthetic data and on a medical x ray image sequence

a variational framework for multiregion pairwise similarity based image segmentation variational cost functions that are based on pairwise similarity between pixels can be minimized within level set framework resulting in a binary image segmentation in this paper we extend such cost functions and address multi region image segmentation problem by employing a multi phase level set framework for multi modal images cost functions become more complicated and relatively difficult to minimize we extend our previous work proposed for background foreground separation to the segmentation of images in more than two regions we also demonstrate an efficient implementation of the curve evolution which reduces the computational time significantly finally we validate the proposed method on the berkeley segmentation data set by comparing its performance with other segmentation techniques

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

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

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

optimal multiple surface segmentation with shape and context priors segmentation of multiple surfaces in medical images is a challenging problem further complicated by the frequent presence of weak boundary evidence large object deformations and mutual influence between adjacent objects this paper reports a novel approach to multi object segmentation that incorporates both shape and context prior knowledge in a 3 d graph theoretic framework to help overcome the stated challenges we employ an arc based graph representation to incorporate a wide spectrum of prior information through pair wise energy terms in particular a shape prior term is used to penalize local shape changes and a context prior term is used to penalize local surface distance changes from a model of the expected shape and surface distances respectively the globally optimal solution for multiple surfaces is obtained by computing a maximum flow in a low order polynomial time the proposed method was validated on intraretinal layer segmentation of optical coherence tomography images and demonstrated statistically significant improvement of segmentation accuracy compared to our earlier graph search method that was not utilizing shape and context priors the mean unsigned surface positioning errors obtained by the conventional graph search approach 6 30 1 58 m was improved to 5 14 0 99 m when employing our new method with shape and context priors

epimorphisms of infinite triangular and unitriangular matrices we discuss the form of all epimorphisms of t f the group of all infinite upper triangular matrices over a field into itself we show that every such epimorphism is a composition of some standard maps moreover we present an analogous result for ut f we use the obtained results to describe the groups of automorphisms of these groups

on the denominator rule and a theorem by janos aczel abstract in this note we compare and contrast arithmetic and geometric share weighting aggregations of ratio expressions i e relative scores and we provide conditions under which they result in approximately the same value of the aggregate measure we also provide some comparative empirical results about the differences among the suggested alternative aggregate measures

fast pixelwise adaptive visual tracking of non rigid objects in this paper we present a new algorithm for real time single object tracking in videos in unconstrained environments the algorithm comprises two different components that are trained in one shot at the first video frame a detector that makes use of the generalized hough transform with color and gradient descriptors and a probabilistic segmentation method based on global models for foreground and background color distributions both components work at pixel level and are used for tracking in a combined way adapting each other in a co training manner moreover we propose an adaptive shape model as well as a new probabilistic method for updating the scale of the tracker through effective model adaptation and segmentation the algorithm is able to track objects that undergo rigid and non rigid deformations and considerable shape and appearance variations the proposed tracking method has been thoroughly evaluated on challenging benchmarks and outperforms the state of the art tracking methods designed for the same task finally a very efficient implementation of the proposed models allows for extremely fast tracking

a variational model for object segmentation using boundary information and shape prior driven by the mumford shah functional in this paper we propose a new variational model to segment an object belonging to a given shape space using the active contour method a geometric shape prior and the mumford shah functional the core of our model is an energy functional composed by three complementary terms the first one is based on a shape model which constrains the active contour to get a shape of interest the second term detects object boundaries from image gradients and the third term drives globally the shape prior and the active contour towards a homogeneous intensity region the segmentation of the object of interest is given by the minimum of our energy functional this minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well known level set method we also prove the existence of this minimum in the space of functions with bounded variation applications of the proposed model are presented on synthetic and medical images

multi class pairwise linear dimensionality reduction using heteroscedastic schemes linear dimensionality reduction ldr techniques have been increasingly important in pattern recognition pr due to the fact that they permit a relatively simple mapping of the problem onto a lower dimensional subspace leading to simple and computationally efficient classification strategies although the field has been well developed for the two class problem the corresponding issues encountered when dealing with multiple classes are far from trivial in this paper we argue that as opposed to the traditional ldr multi class schemes if we are dealing with multiple classes it is not expedient to treat it as a multi class problem per se rather we shall show that it is better to treat it as an ensemble of chernoff based two class reductions onto different subspaces whence the overall solution is achieved by resorting to either voting weighting or to a decision tree strategy the experimental results obtained on benchmark datasets demonstrate that the proposed methods are not only efficient but that they also yield accuracies comparable to that obtained by the optimal bayes classifier

multiplicative preservers on semigroups of matrices we characterize multiplicative maps on semigroups of square matrices satisfying p p for matrix sets p such as rank k idempotent matrices totally nonnegative matrices p0 matrices m0 matrices positive semidefinite matrices hermitian matrices normal matrices and contractions we also characterize multiplicative maps satisfying g x x for various functions g on square matrices such as the spectrum spectral radius numerical range numerical radius and matrix norms

on symmetry perspectivity and level set based segmentation we introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion information on the symmetry axis of the object and the distorting transformation is obtained as a by product of the segmentation process the key idea is the use of a flip or a rotation of the image to segment as if it were another view of the object we call this generated image the symmetrical counterpart image we show that the symmetrical counterpart image and the source image are related by planar projective homography this homography is determined by the unknown planar projective transformation that distorts the object symmetry the proposed segmentation method uses a level set based curve evolution technique the extraction of the object boundaries is based on the symmetry constraint and the image data the symmetrical counterpart of the evolving level set function provides a dynamic shape prior it supports the segmentation by resolving possible ambiguities due to noise clutter occlusions and assimilation with the background the homography that aligns the symmetrical counterpart to the source level set is recovered via a registration process carried out concurrently with the segmentation promising segmentation results of various images of approximately symmetrical objects are shown

tracking monotonically advancing boundaries in image sequences using graph cuts and recursive kernel shape priors we introduce a probabilistic computer vision technique to track monotonically advancing boundaries of objects within image sequences our method incorporates a novel technique for including statistical prior shape information into graph cut based segmentation with the aid of a majorization minimization algorithm extension of segmentation from single images to image sequences then follows naturally using sequential bayesian estimation our methodology is applied to two unrelated sets of real biomedical imaging data and a set of synthetic images our results are shown to be superior to manual segmentation

determining merged relative scores the starting point in this paper is the following type of situation performances of people or technologies are measured by their scores with respect to different benchmarks relative to those of some base performance in order to arrive at a decision one wants to merge average aggregate the scores of each individual or technology into a single number which can then be compared with that of another individual or technology the situation is similar at least technically to price indices where present prices of different products are considered relative to prices of these products in a base year and we again want to merge these into one number in this paper one solves most of these problems one also states a few problems which are still open

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

deform pf mt particle filter with mode tracker for tracking nonaffine contour deformations we propose algorithms for tracking the boundary contour of a deforming object from an image sequence when the nonaffine local deformation over consecutive frames is large and there is overlapping clutter occlusions low contrast or outlier imagery when the object is arbitrarily deforming each or at least most contour points can move independently contour deformation then forms an infinite in practice very large dimensional space direct application of particle filters pf for large dimensional problems is impractically expensive however in most real problems at any given time most of the contour deformation occurs in a small number of dimensions effective basis space while the residual deformation in the rest of the state space residual space is small this property enables us to apply the particle filtering with mode tracking pf mt idea that was proposed for such large dimensional problems in recent work since most contour deformation is low spatial frequency we propose to use the space of deformation at a subsampled set of locations as the effective basis space the resulting algorithm is called deform pf mt it requires significant modifications compared to the original pf mt because the space of contours is a non euclidean infinite dimensional space

discriminative metric preservation for tracking low resolution targets tracking low resolution lr targets is a practical yet quite challenging problem in real video analysis applications lack of discriminative details in the visual appearance of the lr target leads to the matching ambiguity which confronts most existing tracking methods although artificially enhancing the video resolution by superresolution sr techniques before analyzing might be an option the high demand of computational cost can hardly meet the requirements of the tracking scenario this paper presents a novel solution to track lr targets without explicitly performing sr this new approach is based on discriminative metric preservation that preserves the data affinity structure in the high resolution hr feature space for effective and efficient matching of lr images in addition we substantialize this new approach in a solid case study of differential tracking under metric preservation and derive a closed form solution to motion estimation for lr video in addition this paper extends the basic linear metric preservation method to a more powerful nonlinear kernel metric preservation method such a solution to lr target tracking is discriminative robust and efficient extensive experiments validate the entrustments and effectiveness of the proposed approach and demonstrate the improved performance of the proposed method in tracking lr targets

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

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

geometric observers for dynamically evolving curves this paper proposes a deterministic observer design for visual tracking based on nonparametric implicit level set curve descriptions the observer is continuous discrete with continuous time system dynamics and discrete time measurements its state space consists of an estimated curve position augmented by additional states e g velocities associated with every point on the estimated curve multiple simulation models are proposed for state prediction measurements are performed through standard static segmentation algorithms and optical flow computations special emphasis is given to the geometric formulation of the overall dynamical system the discrete time measurements lead to the problem of geometric curve interpolation and the discrete time filtering of quantities propagated along with the estimated curve interpolation and filtering are intimately linked to the correspondence problem between curves correspondences are established by a laplace equation approach the proposed scheme is implemented completely implicitly by eulerian numerical solutions of transport equations and thus naturally allows for topological changes and subpixel accuracy on the computational grid

merging relative scores abstract this paper considers the problem of scoring alternative technologies based on their performance on different benchmarks normalizing the scores relative to those of a base technology and then finding a merged or combined score based on the normalized or relative scores similar problems occur if we score alternative job candidates or students on the basis of different tests or criteria and seek to merge relative scores after normalization they also occur when we obtain index numbers such as price indices here we measure different items at different times normalize relative to some base time and merge the relative measures of the different items obtained at a fixed time we attempt to identify merging methods which will guarantee that certain types of conclusions based on them will be invariant if the base technology job candidate student or time is changed

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

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes

linear maps leaving the alternating group invariant abstract let an be the group of n n even permutation matrices and let vn be the real linear space spanned by an the purpose of this note is to characterize those linear operators on vn satisfying an an this answers a question raised by c k li b s tam n k tsing linear algebra appl to appear