knot concordance whitney towers and l 2 signatures we construct many examples of nonslice knots in 3 space that cannot be distinguished from slice knots by previously known invariants using whitney towers in place of embedded disks we define a geometric filtration of the 3 dimensional topological knot concordance group the bottom part of the filtration exhibits all classical concordance invariants including the cassongordon invariants as a first step we construct an infinite sequence of new obstructions that vanish on slice knots these take values in the l theory of skew fields associated to certain universal groups finally we use the dimension theory of von neumann algebras to define an l 2 signature and use this to detect the first unknown step in our obstruction theory

a superquadratic indefinite elliptic system and its morse conley floer homology we study critical points of the indefinite functional f h u v int nabla u cdot nabla v h x u v mathrm d x by applying floer s homology construction to the ordinary gradient flow of the functional f on a suitable sobolev space one of our main observations is that even though this flow is well posed in both time directions and lacks any kind of smoothing property one can still obtain compactness of connecting orbit spaces and thus define the floer homology for f h

periodic solutions for non autonomous hamiltonian systems possessing super quadratic potentials we consider the non autonomous hamiltonian system ju h t u 0 t u st r where h c1 r r2n r is t periodic in t variable and j 0 in in 0 denotes the standard symplectic matrix and denotes the gradient with respect to the u variable we are interested in the existence of t periodic solutions of 1 for the autonomous case i e h is independent of t in his pioneer work 8 rabinowitz rst proved the existence of at least one periodic solution for 1 many works have been done on this topics such as 2 13 we refer to 2 3 11 for further references at this paper we rst consider the case that h is symmetric in the u variable in 2 when h is super quadratic at in nitely and satis es h2 p there are constants c d 0 and p 1 2 such that h t u p 6 c h t u u d u r2n

on the quantum filtration of the khovanov rozansky cohomology abstract we prove the quantum filtration on the khovanov rozansky link cohomology h p with a general degree n 1 monic potential polynomial p x is invariant under reidemeister moves and construct a spectral sequence converging to h p that is invariant under reidemeister moves whose e 1 term is isomorphic to the khovanov rozansky sl n cohomology h n then we define a generalization of the rasmussen invariant and study some of its properties we also discuss relations between upper bounds of the self linking number of transversal links in standard contact s 3

partial linear gaussian models for tracking in image sequences using sequential monte carlo methods the recent development of sequential monte carlo methods also called particle filters has enabled the definition of efficient algorithms for tracking applications in image sequences the efficiency of these approaches depends on the quality of the state space exploration which may be inefficient due to a crude choice of the function used to sample in the associated probability space a careful study of this issue led us to consider the modeling of the tracked dynamic system with partial linear gaussian models such models are characterized by a non linear dynamic equation a linear measurement equation and additive gaussian noises they allow inferring an analytic expression of the optimal importance function used in the diffusion process of the particle filter and enable building a relevant approximation of a validation gate despite of these potential advantages partial linear gaussian models have not been investigated the aim of this paper is therefore to demonstrate that such models can be of real interest facing difficult usual issues such as occlusions ambiguities due to cluttered backgrounds and large state space three instances of these models are proposed after a theoretical analysis their significance is demonstrated by their performance for tracking points and planar objects in challenging real world image sequences

fitting parameterized three dimensional models to images model based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3 d model to matching 2 d image features the author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation variable dimensions or surface deformations numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters the levenberg marquardt method is used to always ensure convergence of the solution these techniques allow model based vision to be used for a much wider class of problems than was possible with previous methods their application is demonstrated for tracking the motion of curved parameterized objects

counterexamples to kauffman s conjectures on slice knots abstract in the late 1960s jerome levine classified the odd high dimensional knot concordance groups in terms of a linking matrix associated to an arbitrary bounding manifold for the knot his proof fails for classical knots in s 3 yet this philosophy has remained the only known strategy for understanding the classical knot concordance group we show that this strategy is fundamentally flawed specifically in 1982 in support of levine s philosophy louis kauffman conjectured that if a knot in s 3 is a slice knot then on any seifert surface for that knot there exists a homologically essential simple closed curve of self linking zero which is itself a slice knot or at least has arf invariant zero since that time considerable evidence has been amassed in support of this conjecture in particular many invariants that obstruct a knot from being a slice knot have been explicitly expressed in terms of invariants of such curves on its seifert surface we give counterexamples to kauffman s conjecture that is we exhibit smoothly slice knots that admit unique minimal genus seifert surfaces on which every homologically essential simple closed curve of self linking zero has non zero arf invariant and non zero signatures

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

a lattice based mrf model for dynamic near regular texture tracking a near regular texture nrt is a geometric and photometric deformation from its regular origin a congruent wallpaper pattern formed by 2d translations of a single tile a dynamic nrt is an nrt under motion although nrts are pervasive in man made and natural environments effective computational algorithms for nrts are few this paper addresses specific computational challenges in modeling and tracking dynamic nrts including ambiguous correspondences occlusions and drastic illumination and appearance variations we propose a lattice based markov random field mrf model for dynamic nrts in a 3d spatiotemporal space our model consists of a global lattice structure that characterizes the topological constraint among multiple textons and an image observation model that handles local geometry and appearance variations based on the proposed mrf model we develop a tracking algorithm that utilizes belief propagation and particle filtering to effectively handle the special challenges of the dynamic nrt tracking without any assumption on the motion types or lighting conditions we provide quantitative evaluations of the proposed method against existing tracking algorithms and demonstrate its applications in video editing

a slice genus lower bound from sl n khovanov rozansky homology we show that a generic perturbation of the doubly graded khovanov rozansky knot homology gives rise to a lower bound on the slice genus of a knot we prove a theorem about obtainable presentations of surfaces embedded in 4 space which we use to simplify significantly our algebraic computations

chern simons invariants of 3 manifolds decomposed along tori and the circle bundle over the representation space of t 2 we describe a cut and paste method for computing chern simons invariant of flatg connections on 3 manifolds decomposed along tori especially forg su 2 andsl 2 c we use this method to make computations ofsu 2 chern simons invariants of graph manifolds which generalize fintushel and stern s computations for seifert fibered spaces we also use this technique to give a simple derivation of a formula of yoshida relating the flatsl 2 c chern simons invariant of the holonomy representation to the volume and the metric chern simons invariant for cusped hyperbolic 3 manifolds

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

topologically slice knots with nontrivial alexander polynomial abstract let c t be the subgroup of the smooth knot concordance group generated by topologically slice knots and let c be the subgroup generated by knots with trivial alexander polynomial we prove that c t c is infinitely generated our methods reveal a similar structure in the 3 dimensional rational spin bordism group and lead to the construction of links that are topologically but not smoothly concordant to boundary links

periodic solutions of large norm of hamiltonian systems abstract hamiltonian systems of ordinary differential equations are studied the only assumption made on the hamiltonian is appropriately rapid growth at infinity it is proved that for any given period there is an unbounded sequence of periodic solutions of the system having the given period

an endomorphism of the khovanov invariant abstract we construct an endomorphism of the khovanov invariant to prove h thinness and pairing phenomena of the invariants for alternating links as a consequence it follows that the khovanov invariant of an oriented nonsplit alternating link is determined by its jones polynomial signature and the linking numbers of its components

approximate bayesian multibody tracking visual tracking of multiple targets is a challenging problem especially when efficiency is an issue occlusions if not properly handled are a major source of failure solutions supporting principled occlusion reasoning have been proposed but are yet unpractical for online applications this paper presents a new solution which effectively manages the trade off between reliable modeling and computational efficiency the hybrid joint separable hjs filter is derived from a joint bayesian formulation of the problem and shown to be efficient while optimal in terms of compact belief representation computational efficiency is achieved by employing a markov random field approximation to joint dynamics and an incremental algorithm for posterior update with an appearance likelihood that implements a physically based model of the occlusion process a particle filter implementation is proposed which achieves accurate tracking during partial occlusions while in cases of complete occlusion tracking hypotheses are bound to estimated occlusion volumes experiments show that the proposed algorithm is efficient robust and able to resolve long term occlusions between targets with identical appearance

periodic and subharmonic solutions for a class of superquadratic hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic hamiltonian systems by the minimax methods in critical point theory specially a local link theorem due to li and willem and the generalized mountain pass theorem respectively

dependent multiple cue integration for robust tracking we propose a new technique for fusing multiple cues to robustly segment an object from its background in video sequences that suffer from abrupt changes of both illumination and position of the target robustness is achieved by the integration of appearance and geometric object features and by their estimation using bayesian filters such as kalman or particle filters in particular each filter estimates the state of a specific object feature conditionally dependent on another feature estimated by a distinct filter this dependence provides improved target representations permitting us to segment it out from the background even in nonstationary sequences considering that the procedure of the bayesian filters may be described by a hypotheses generation hypotheses correction strategy the major novelty of our methodology compared to previous approaches is that the mutual dependence between filters is considered during the feature observation that is into the hypotheses correction stage instead of considering it when generating the hypotheses this proves to be much more effective in terms of accuracy and reliability the proposed method is analytically justified and applied to develop a robust tracking system that adapts online and simultaneously the color space where the image points are represented the color distributions the contour of the object and its bounding box results with synthetic data and real video sequences demonstrate the robustness and versatility of our method

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

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

efficient visual tracking using particle filter with incremental likelihood calculation in this paper we propose a particle filter that determines the weight of each particle employing the incremental likelihood calculation since there is usually a large overlap region between the two particles that are sequentially generated determining the weight of the particle has only a small time cost therefore the real time performance of the proposed tracker can be dramatically improved extensive experimental results for single object and multiple object tracking scenarios are presented to demonstrate the efficiency of the proposed approach finally an interesting color based active vision system is developed for a free floating space robot testbed to facilitate teleoperation

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

incremental tensor subspace learning and its applications to foreground segmentation and tracking appearance modeling is very important for background modeling and object tracking subspace learning based algorithms have been used to model the appearances of objects or scenes current vector subspace based algorithms cannot effectively represent spatial correlations between pixel values current tensor subspace based algorithms construct an offline representation of image ensembles and current online tensor subspace learning algorithms cannot be applied to background modeling and object tracking in this paper we propose an online tensor subspace learning algorithm which models appearance changes by incrementally learning a tensor subspace representation through adaptively updating the sample mean and an eigenbasis for each unfolding matrix of the tensor the proposed incremental tensor subspace learning algorithm is applied to foreground segmentation and object tracking for grayscale and color image sequences the new background models capture the intrinsic spatiotemporal characteristics of scenes the new tracking algorithm captures the appearance characteristics of an object during tracking and uses a particle filter to estimate the optimal object state experimental evaluations against state of the art algorithms demonstrate the promise and effectiveness of the proposed incremental tensor subspace learning algorithm and its applications to foreground segmentation and object tracking

morse homology of super quadratic hamiltonian systems on r2n abstract we study periodic solutions of the hamiltonian system x t j h t x where j is the standard symplectic matrix h is 2 periodic in t and super quadratic in x in some sense using the morse homology theory developed in a abbondandolo p majer morse homology on hilbert spaces comm pure appl math 54 2001 689 758 we get some existence results of periodic solutions

an obstruction to sliceness via contact geometry and classical gauge theory in recent work beginning with 8 kronheimer and mrowka have developed the formidable machinery of gauge theory for embedded surfaces and deployed it against a host of problems of the general form what is the least genus of a smooth surface representing a specified homology class in a given 4 manifold one of their results the local thom conjecture can be used 19 to derive a lower bound the slice bennequin inequality hereinafter sbi for the murasuoi or slice genus of a knot k c s3 that is the smallest genus of a smooth oriented surface in d 4 with boundary k a knot is slice if it has murasugi genus 0 so in particular sbi provides an obstruction to sliceness though bennequin originally conjectured sbi in the context 1 of an investigation into 3 dimensional contact geometry to date sbi has not been proved using exclusively 3 dimensional methods such methods did success fully establish 1 the bennequin inequality pure and simple which sbi generalizes it appears they can also be used i 1 to answer the question of milnor on unknotting number achieved 4 dimensionally using the local thom conjecture in 8 the following corollary of sbi will be proved in w independently of sbi by combining ideas from dimensions 3 contact geometry and 4 classical gauge theory 4 earlier and comparatively simpler than 8 ifa knot k has non negative maximal thurston bennequin invariant tb k then k is not slice though tb k is defined analytically an alternative combinatorial definition recalled in w allows one to show tb k 0 and sometimes to calculate tb k for many interesting knots k in particular results of 19 on non sliceness of certain iterated doubled knots are recovered quickly and easily research partially supported by cnrs

learning generative models for multi activity body pose estimation we present a method to simultaneously estimate 3d body pose and action categories from monocular video sequences our approach learns a generative model of the relationship of body pose and image appearance using a sparse kernel regressor body poses are modelled on a low dimensional manifold obtained by locally linear embedding dimensionality reduction in addition we learn a prior model of likely body poses and a dynamical model in this pose manifold sparse kernel regressors capture the nonlinearities of this mapping efficiently within a recursive bayesian sampling framework the potentially multimodal posterior probability distributions can then be inferred an activity switching mechanism based on learned transfer functions allows for inference of the performed activity class along with the estimation of body pose and 2d image location of the subject using a rough foreground segmentation we compare binary pca and distance transforms to encode the appearance as a postprocessing step the globally optimal trajectory through the entire sequence is estimated yielding a single pose estimate per frame that is consistent throughout the sequence we evaluate the algorithm on challenging sequences with subjects that are alternating between running and walking movements our experiments show how the dynamical model helps to track through poorly segmented low resolution image sequences where tracking otherwise fails while at the same time reliably classifying the activity type

tracking in low frame rate video a cascade particle filter with discriminative observers of different life spans tracking object in low frame rate video or with abrupt motion poses two main difficulties which most conventional tracking methods can hardly handle 1 poor motion continuity and increased search space 2 fast appearance variation of target and more background clutter due to increased search space in this paper we address the problem from a view which integrates conventional tracking and detection and present a temporal probabilistic combination of discriminative observers of different lifespans each observer is learned from different ranges of samples with different subsets of features to achieve varying level of discriminative power at varying cost an efficient fusion and temporal inference is then done by a cascade particle filter which consists of multiple stages of importance sampling experiments show significantly improved accuracy of the proposed approach in comparison with existing tracking methods under the condition of low frame rate data and abrupt motion of both target and camera

on the upsilon invariant and satellite knots we study the effect of satellite operations on the upsilon invariant of ozsvath stipsicz szabo we obtain results concerning when a knot and its satellites are independent for example we show that the set d 2 i 1 i 1 infty is a basis for an infinite rank summand of the group of smooth concordance classes of topologically slice knots for d the positive clasped untwisted whitehead double of any knot with positive tau invariant e g the right handed trefoil we also prove that the image of the mazur satellite operator on the smooth knot concordance group contains an infinite rank subgroup of topologically slice knots

chern simons functional and the homology cobordism group for each integral homology sphere y we construct a function y on the set of integers we establish that y depends only on the homology cobordism class of y and that it recovers the froyshov invariant we state a relation between y and fintushel and stern s r invariant we show that the value of y at each integer is related to the critical values of the chern simons functional and we give some topological applications of y in particular we show that if y is trivial then there is no simply connected homology cobordism from y to itself

approximate smoothing and parameter estimation in high dimensional state space models we present approximate algorithms for performing smoothing in a class of high dimensional state space models via sequential monte carlo methods particle filters in high dimensions a prohibitively large number of monte carlo samples particles growing exponentially in the dimension of the state space are usually required to obtain a useful smoother employing blocking approximations we exploit the spatial ergodicity properties of the model to circumvent this curse of dimensionality we thus obtain approximate smoothers that can be computed recursively in time and parallel in space first we show that the bias of our blocked smoother is bounded uniformly in the time horizon and in the model dimension we then approximate the blocked smoother with particles and derive the asymptotic variance of idealized versions of our blocked particle smoother to show that variance is no longer adversely effected by the dimension of the model finally we employ our method to successfully perform maximum likelihood estimation via stochastic gradient ascent and stochastic expectation maximization algorithms in a 100 dimensional state space model

instantons concordance and whitehead doubling we use moduli spaces of instantons and chern simons invariants of flat connections to prove that the whitehead doubles of 2 2 n 1 torus knots are independent in the smooth knot concordance group that is they freely generate a subgroup of infinite rank call two knots in the 3 sphere concordant if they arise as the boundary of a smooth and properly embedded cylinder in the 3 sphere times an interval concordance is clearly an equivalence relation modulo this relation the set of knots forms an abelian group c with the role of addition played by connected sum and inverse given by considering the mirror image with reversed orientation this concordance group is a much studied object well motivated by its role as a gateway into the mysterious world of 4 dimensional topology indeed even in this relative situation of studying 3 dimensional manifolds in relation to the 4 dimensional manifolds they bound one can observe the distinction between the smooth and topological categories in dimension four moreover the group structure afforded by passing to concordance paves a clearer path through the often intractable field of knot theory our results focus on a particular satellite operation positive untwisted whitehead doubling and its effect on the concordance group see figure 1 and section 3 1 for a definition our motivation comes from the following conjecture to state it recall that a knot is slice if it is concordant to the unknot or equivalently if it bounds a smooth and properly embedded disk in the 4 ball

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a probabilistic exclusion principle for tracking multiple objects tracking multiple targets is a challenging problem especially when the targets are identical in the sense that the same model is used to describe each target in this case simply instantiating several independent 1 body trackers is not an adequate solution because the independent trackers tend to coalesce onto the best fitting target this paper presents an observation density for tracking which solves this problem by exhibiting a probabilistic exclusion principle exclusion arises naturally from a systematic derivation of the observation density without relying on heuristics another important contribution of the paper is the presentation of partitioned sampling a new sampling method for multiple object tracking partitioned sampling avoids the high computational load associated with fully coupled trackers while retaining the desirable properties of coupling

impsac synthesis of importance sampling and random sample consensus this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation either due to large rotation or wide baseline of the cameras the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation the method operates on a pyramid from coarse to fine resolution thus raising the problem of how to propagate information from one level to another in a statistically consistent way the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles at the coarsest level a random sample consensus monte carlo markov chain ransac mcmc estimator is used to initialize this set of particles the posterior can then be approximated as a mixture of gaussians fitted to these particles the distribution at a coarser level influences the distribution at a finer level using the technique of sampling importance resampling sir and mcmc which allows for asymptotically correct approximations of the posterior distribution the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles which can be further improved by mcmc it is shown that the method is superior to previous single resolution ransac style feature matchers

tracking deforming objects using particle filtering for geometric active contours tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time tracking algorithms using kalman filters or particle filters have been proposed for finite dimensional representations of shape but these are dependent on the chosen parametrization and cannot handle changes in curve topology geometric active contours provide a framework which is parametrization independent and allow for changes in topology in the present work we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects to the best of our knowledge this is the first attempt to implement an approximate particle filtering algorithm for tracking on a theoretically infinite dimensional state space

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

structure regularized compressive tracking with online data driven sampling being a powerful appearance model compressive random projection derives effective haar like features from non rotated 4 d parameterized rectangles thus supporting fast and reliable object tracking in this paper we show that such successful fast compressive tracking scheme can be further significantly improved by structural regularization and online data driven sampling our major contribution is threefold first we find that superpixel guided compressive projection can generate more discriminative features by sufficiently capturing rich local structural information of images second we propose fast directional integration that enables low cost extraction of feasible haar like features from arbitrarily rotated 5 d parameterized rectangles to realize more accurate object localization third beyond naive dense uniform sampling we present two practical online data driven sampling strategies to produce less yet more effective candidate and training samples for object detection and classifier updating respectively extensive experiments on real world benchmark data sets validate the superior performance i e much better object localization ability and robustness of the proposed approach over state of the art trackers

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

multi target tracking by learning local to global trajectory models the multi target tracking problem is challenging when there exist occlusions tracking failures of the detector and severe interferences between detections in this paper we propose a novel detection based tracking method that links detections into tracklets and further forms long trajectories unlike many previous hierarchical frameworks which split the data association into two separate optimization problems linking detections locally and linking tracklets globally we introduce a unified algorithm that can automatically relearn the trajectory models from the local and global information for finding the joint optimal assignment in each temporal window the trajectory models are initialized by the local information to link those easy to connect detections into a set of tracklets then the trajectory models are updated by the reliable tracklets and reused to link separated tracklets into long trajectories we iteratively update the trajectory models by more information from more frames until the result converges the iterative process gradually improves the accuracy of the trajectory models which in turn improves the target id inferences for all detections by the mrf model experiment results revealed that our proposed method achieved state of the art multi target tracking performance highlightsa unified framework to online learn local to global trajectory models is proposed the iterative algorithm can alternately update the trajectory models we solve inferences of target ids for all the detections by using the mrf model our method has low complexity compared with most state of the art methods

conditional mean estimation via jump diffusion processes in multiple target tracking recognition a new algorithm is presented for generating the conditional mean estimates of functions of target positions orientations and type in recognition and tracking of an unknown number of targets and target types taking a bayesian approach a posterior measure is defined on the tracking target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model and a prior based on airplane dynamics the newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion the conditional mean estimates are generated using a random sampling algorithm based on jump diffusion processes for empirically generating mmse estimates of functions of these random target positions orientations and type under the posterior measure results are presented on target tracking and identification from an implementation of the algorithm on a networked silicon graphics workstation and decmpp maspar parallel machine

braids transversal links and the khovanov rozansky theory we establish some inequalities for the khovanov rozansky cohomologies of braids these give new upper bounds of the self linking numbers of transversal links in standard contact s 3 which are sharper than the well known bound given by the homfly polynomial we also introduce a sequence of transversal link invariants and discuss some of their properties

bayesian neighborhood component analysis learning a distance metric in feature space potentially improves the performance of the k nearest neighbor classifier and is useful in many real world applications many metric learning ml algorithms are however based on the point estimation of a quadratic optimization problem which is time consuming susceptible to overfitting and lacks a natural mechanism to reason with parameter uncertainty a property useful especially when the training set is small and or noisy to deal with these issues we present a novel bayesian ml bml method called bayesian neighborhood component analysis nca based on the well known nca method in which the metric posterior is characterized by the local label consistency constraints of observations encoded with a similarity graph instead of independent pairwise constraints for efficient bayesian inference we explore the variational lower bound over the log likelihood of the original nca objective experiments on several publicly available data sets demonstrate that the proposed method is able to learn robust metric measures from small size data set and or from challenging training set with labels contaminated by errors the proposed method is also shown to outperform a previous pairwise constrained bml method

instanton homology of seifert fibred homology three spheres for an oriented integral homology 3 sphere 2 a casson has introduced an integer invariant a 2 that is defined by using the space 2 of conjugacy classes of irreducible representations of 2 into su 2 see 1 this invariant a 2 can be computed from a surgery or heegard description of 2 and satisfies a 2 ju 2 mod 2 where i 2 is the kervaire milnor rochlin invariant of 2 this powerful new invariant was used to settle an outstanding problem in 3 manifold topology namely showing that if 2 is a homotopy 3 sphere then ju 2 o c taubes 17 utilizing gauge theoretic considerations has reinterpreted casson s invariant in terms of flat connections refining this approach a floer 13 has recently defined another invariant of 2 its instanton homology which takes the form of an abelian group 2 with a natural z8 grading that is an enhancement of a 2 in that

tracking by affine kernel transformations using color and boundary cues kernel based trackers aggregate image features within the support of a kernel a mask regardless of their spatial structure these trackers spatially fit the kernel usually in location and in scale such that a function of the aggregate is optimized we propose a kernel based visual tracker that exploits the constancy of color and the presence of color edges along the target boundary the tracker estimates the best affinity of a spatially aligned pair of kernels one of which is color related and the other of which is object boundary related in a sense this work extends previous kernel based trackers by incorporating the object boundary cue into the tracking process and by allowing the kernels to be affinely transformed instead of only translated and isotropically scaled these two extensions make for more precise target localization a more accurately localized target also facilitates safer updating of its reference color model further enhancing the tracker s robustness the improved tracking is demonstrated for several challenging image sequences

periodic solutions of second order superquadratic hamiltonian systems with potential changing sign ii abstract we consider the periodic solutions of the second order hamiltonian system x x h t v x with v being positive and superquadratic at infinity h being c 1 2 periodic sign changing and all zeros being simple some existence and multiplicity results of periodic solutions are given

representations of knot groups in su 2 this paper is a study of the structure of the space r k of representations of classical knot groups into su 2 let r k equal the set of conjugacy classes of irreducible representations in gi we interpret the relations in a presentation of the knot group in terms of the geometry of su 2 using this technique we calculate r k for k equal to the torus knots twist knots and the whitehead link we also determine a formula for the number of binary dihedral representations of an arbitrary knot group we prove using techniques introduced by culler and shalen that if the dimension of r k is greater than 1 then the complement in sj of a tubular neighborhood of k contains closed nonboundary parallel incompressible surfaces we also show how for certain nonprime and doubled knots r k has dimension greater than one in gii we calculate the zariski tangent space tp r k for an arbitrary knot k at a reducible representation p using a technique due to weil we prove that for all but a finite number of the reducible representations dimtp r k 3 these nonexceptional representations possess neighborhoods in r k containing only reducible representations at the exceptional representations which correspond to real roots of the alexander polynomial dim tp r k 3 2k for a positive integer k in those examples analyzed in this paper these exceptional representations can be expressed as limits of arcs of irreducible representations we also give an interpretation of these extra tangent vectors as representations in the group of euclidean isometries of the plane 0 introduction this paper is a study of the space r k of representations of the fundamental group of the complement of a knot k into the lie group su 2 the major results are as follows 1 a calculation of the topological type of r k for k a torus knot a twist knot or the whitehead link 2 a determination of the zariski tangent space to r k at a reducible representation for an arbitrary knot k and 3 a proposition and some examples relating the dimension of r k to incompressible surfaces in the complement of k while the idea of representing 3 manifold groups in su 2 is a fairly recent one the representation of these groups in other groups has a substantial history we will not attempt to chronicle this history in detail but will comment here on received by the editors january 18 1989 and in revised form july 25 1989 1980 mathematics subject classification 1985 revision primary 57m05 57m25

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

a categorification of the jones polynomial author s khovanov mikhail abstract we construct a bigraded cohomology theory of links whose euler characteristic is the jones polynomial

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

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

particle filter with a mode tracker for visual tracking across illumination changes in this correspondence our goal is to develop a visual tracking algorithm that is able to track moving objects in the presence of illumination variations in the scene and that is robust to occlusions we treat the illumination and motion x y translation and scale parameters as the unknown state sequence the observation is the entire image and the observation model allows for occasional occlusions modeled as outliers the nonlinearity and multimodality of the observation model necessitate the use of a particle filter pf due to the inclusion of illumination parameters the state dimension increases thus making regular pfs impractically expensive we show that the recently proposed approach using a pf with a mode tracker can be used here since even in most occlusion cases the posterior of illumination conditioned on motion and the previous state is unimodal and quite narrow the key idea is to importance sample on the motion states while approximating importance sampling by posterior mode tracking for estimating illumination experiments demonstrate the advantage of the proposed algorithm over existing pf based approaches for various face and vehicle tracking we are also able to detect illumination model changes e g those due to transition from shadow to sunlight or vice versa by using the generalized expected log likelihood statistics and successfully compensate for it without ever loosing track

explaining activities as consistent groups of events we propose a method for disambiguating uncertain detections of events by seeking global explanations for activities given a noisy visual input and exploiting our knowledge of the activity and its constraints one can provide a consistent set of events explaining all the detections the paper presents a complete framework that starts with a general way to formalise the set of global explanations for a given activity using attribute multiset grammars amg an amg combines the event hierarchy with the necessary features for recognition and algebraic constraints defining allowable combinations of events and features parsing a set of detections by such a grammar finds a consistent set of events that satisfies the activity s constraints each parse tree has a posterior probability in a bayesian sense to find the best parse tree the grammar and a finite set of detections are mapped into a bayesian network the set of possible labellings of the bayesian network corresponds to the set of all parse trees for a given set of detections we compare greedy multiple hypotheses trees reversible jump mcmc and integer programming for finding the maximum a posteriori map solution over the space of explanations the framework is tested for two applications the activity in a bicycle rack and around a building entrance

intrackability characterizing video statistics and pursuing video representations videos of natural environments contain a wide variety of motion patterns of varying complexities which are represented by many different models in the vision literature in many situations a tracking algorithm is formulated as maximizing a posterior probability in this paper we propose to measure the video complexity by the entropy of the posterior probability called the intrackability to characterize the video statistics and pursue optimal video representations based on the definition of intrackability our study is aimed at three objectives firstly we characterize video clips of natural scenes by intrackability we calculate the intrackabilities of image points to measure the local inferential uncertainty and collect the histogram of the intrackabilities over the video in space and time as the global video statistics we find that a pca scatter plot based on the first two principle components of intrackability histograms can reflect the major variations i e image scaling and object density in natural video clips secondly we show that different video representations including deformable contours tracking kernels with various appearance features dense motion fields and dynamic texture models are connected by the change of intrackability and thus develop a simple criterion for model transition and for pursuing the optimal video representation thirdly we derive the connections between the intrackability measure and other criteria in the literature such as the shi tomasi texturedness measure conditional number and harris stephens r score and compare with the shi tomasi measure in tracking experiments

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

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

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

robust tracking with discriminative ranking lists in this paper we propose a novel tracking algorithm i e the discriminative ranking list based tracker drltracker the drltracker models the target object and its local background by using ranking lists of patches of different scales within object bounding boxes the ranking list of each of such patches is its k nearest neighbors patches of the same scale with ranking lists of high purity values meaning high probabilities to be on the target object and some confusable background patches constitute the object model under that scale a pair of object models of two different scales collaborate to determine which patches may belong to the target object in the next frame the drltracker can effectively alleviate the distraction problem and its superior ability over several representative and state of the art trackers is demonstrated through extensive experiments

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

a bayesian approach to tracking multiple targets using sensor arrays and particle filters we present a bayesian approach to tracking the direction of arrival doa of multiple moving targets using a passive sensor array the prior is a description of the dynamic behavior we expect for the targets which is modeled as constant velocity motion with a gaussian disturbance acting on the target s heading direction the likelihood function is arrived at by defining an uninformative prior for both the signals and noise variance and removing these parameters from the problem by marginalization advances in sequential monte carlo smc techniques specifically the particle filter algorithm allow us to model and track the posterior distribution defined by the bayesian model using a collection of target states that can be viewed as samples from the posterior of interest we describe two versions of this algorithm and finally present results obtained using synthetic data

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

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

robust visual tracking by integrating multiple cues based on co inference learning visual tracking can be treated as a parameter estimation problem that infers target states based on image observations from video sequences a richer target representation may incur better chances of successful tracking in cluttered and dynamic environments and thus enhance the robustness richer representations can be constructed by either specifying a detailed model of a single cue or combining a set of rough models of multiple cues both approaches increase the dimensionality of the state space which results in a dramatic increase of computation to investigate the integration of rough models from multiple cues and to explore computationally efficient algorithms this paper formulates the problem of multiple cue integration and tracking in a probabilistic framework based on a factorized graphical model structured variational analysis of such a graphical model factorizes different modalities and suggests a co inference process among these modalities based on the importance sampling technique a sequential monte carlo algorithm is proposed to provide an efficient simulation and approximation of the co inferencing of multiple cues this algorithm runs in real time at around 30 hz our extensive experiments show that the proposed algorithm performs robustly in a large variety of tracking scenarios the approach presented in this paper has the potential to solve other problems including sensor fusion problems

quasipositivity as an obstruction to sliceness for an oriented link l s 3 d 4 let s l be the greatest euler characteristic f of an oriented 2 manifold f without closed components smoothly embedded in d 4 with boundary l a knot k is slice if s k 1 realize d 4 in c 2 as z w z 2 w 2 1 it has been conjectured that if v is a nonsingular complex plane curve transverse to s 3 then s v s 3 v d 4 kronheimer and mrowka have proved this conjecture in the case that v d 4 is the milnor fiber of a singularity i explain how this seemingly special case implies both the general case and the slice bennequin inequality for braids as applications i show that various knots are not slice e g pretzel knots like p 3 5 7 all knots obtained from a positive trefoil o 2 3 by iterated untwisted positive doubling

differential earth mover s distance with its applications to visual tracking the earth mover s distance emd is a similarity measure that captures perceptual difference between two distributions its computational complexity however prevents a direct use in many applications this paper proposes a novel differential emd demd algorithm based on the sensitivity analysis of the simplex method and offers a speedup at orders of magnitude compared with its brute force counterparts the demd algorithm is discussed and empirically verified in the visual tracking context the deformations of the distributions for objects at different time instances are accommodated well by the emd and the differential algorithm makes the use of emd in real time tracking possible to further reduce the computation signatures i e variable size descriptions of distributions are employed as an object representation the new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard mean shift tracker is demonstrated

khovanov homology and the slice genus we use lee s work on the khovanov homology to define a knot invariant s we show that s k is a concordance invariant and that it provides a lower bound for the smooth slice genus of k as a corollary we give a purely combinatorial proof of the milnor conjecture

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4