additive change detection in nonlinear systems with unknown change parameters we study the change detection problem in partially observed nonlinear systems which satisfy the hidden markov model hmm property the change parameters are assumed unknown and the changes can be slow or sudden a partially observed system needs to be tracked first before changes can be detected sudden changes result in significant loss of track these can be detected easily using the increase in tracking error te or observation likelihood ol or using a cusum type method applied to either of these however slow changes which result in small loss of track often get missed we propose here a statistic that uses the tracked component of the change to detect it and hence detects slow changes faster than te or ol we show both analytically and through simulations that this statistic complements ol and te for change detection

object trajectory based activity classification and recognition using hidden markov models motion trajectories provide rich spatiotemporal information about an object s activity this paper presents novel classification algorithms for recognizing object activity using object motion trajectory in the proposed classification system trajectories are segmented at points of change in curvature and the subtrajectories are represented by their principal component analysis pca coefficients we first present a framework to robustly estimate the multivariate probability density function based on pca coefficients of the subtrajectories using gaussian mixture models gmms we show that gmm based modeling alone cannot capture the temporal relations and ordering between underlying entities to address this issue we use hidden markov models hmms with a data driven design in terms of number of states and topology e g left right versus ergodic experiments using a database of over 5700 complex trajectories obtained from uci kdd data archives and columbia university multimedia group subdivided into 85 different classes demonstrate the superiority of our proposed hmm based scheme using pca coefficients of subtrajectories in comparison with other techniques in the literature

shape activity a continuous state hmm for moving deforming shapes with application to abnormal activity detection the aim is to model activity performed by a group of moving and interacting objects which can be people cars or different rigid components of the human body and use the models for abnormal activity detection previous approaches to modeling group activity include co occurrence statistics individual and joint histograms and dynamic bayesian networks neither of which is applicable when the number of interacting objects is large we treat the objects as point objects referred to as landmarks and propose to model their changing configuration as a moving and deforming shape using kendall s shape theory for discrete landmarks a continuous state hidden markov model is defined for landmark shape dynamics in an activity the configuration of landmarks at a given time forms the observation vector and the corresponding shape and the scaled euclidean motion parameters form the hidden state vector an abnormal activity is then defined as a change in the shape activity model which could be slow or drastic and whose parameters are unknown results are shown on a real abnormal activity detection problem involving multiple moving objects

on the use of a minimal path approach for target trajectory analysis vision based action recognition has multiple applications mainly focused in video surveillance systems the art of labeling each target behavior in crowded scenarios is a complicated field since usually we do not have visual confirmation of the parts of a target to infer its behavior thus trajectory analysis becomes a good choice to try to infer knowledge about target movements most of the contributions to this field involve a training period in which we obtain information a priori about the environment storing a dataset with all the possible usual routes based in the minimal path theory using geodesic active contours we present a novel architecture where no initial information about the scene is needed while it is possible to include it if necessary to specify constraints experimental results in two different application domains show the performance and flexibility of this method being able to be used in multiple trajectory analysis problems

distribution based dimensionality reduction applied to articulated motion recognition some articulated motion representations rely on frame wise abstractions of the statistical distribution of low level features such as orientation color or relational distributions as configuration among parts changes with articulated motion the distribution changes tracing a trajectory in the latent space of distributions which we call the configuration space these trajectories can then be used for recognition using standard techniques such as dynamic time warping the core theory in this paper concerns embedding the frame wise distributions which can be looked upon as probability functions into a low dimensional space so that we can estimate various meaningful probabilistic distances such as the chernoff bhattacharya matusita kullback leibler kl or symmetric kl distances based on dot products between points in this space apart from computational advantages this representation also affords speed normalized matching of motion signatures speed normalized representations can be formed by interpolating the configuration trajectories along their arc lengths without using any knowledge of the temporal scale variations between the sequences we experiment with five different probabilistic distance measures and show the usefulness of the representation in three different contexts sign recognition with large number of possible classes gesture recognition with person variations and classification of human human interaction sequences with segmentation problems we find the importance of using the right distance measure for each situation the low dimensional embedding makes matching two to three times faster while achieving recognition accuracies that are close to those obtained without using a low dimensional embedding we also empirically establish the robustness of the representation with respect to low level parameters embedding parameters and temporal scale parameters

the quadrilateral mindlin plate elements using the spline interpolation bases abstract by the mindlin reissner plate theory the displacement and rotations x y are interpolated by independent functions for which only c 0 continuity condition is required the difficulty for constructing interpolation bases on the quadrilateral element without isoparametric transformation can be overcome by using the spline method in this paper two sets of spline interpolation bases are adopted to construct two quadrilateral spline mindlin plate elements qsmp1 and qsmp2 with 12 degrees of freedom the spline elements can be applied for both thick and thin plates and can converge for the very thin case numerical examples are discussed to show that the mindlin plate element combined with the spline interpolation bases can possess good accuracy

principal components null space analysis for image and video classification we present a new classification algorithm principal component null space analysis pcnsa which is designed for classification problems like object recognition where different classes have unequal and nonwhite noise covariance matrices pcnsa first obtains a principal components subspace pca space for the entire data in this pca space it finds for each class i an m sub i dimensional subspace along which the class intraclass variance is the smallest we call this subspace an approximate null space ans since the lowest variance is usually much smaller than the highest a query is classified into class i if its distance from the class mean in the class ans is a minimum we derive upper bounds on classification error probability of pcnsa and use these expressions to compare classification performance of pcnsa with that of subspace linear discriminant analysis slda we propose a practical modification of pcnsa called progressive pcnsa that also detects new untrained classes finally we provide an experimental comparison of pcnsa and progressive pcnsa with slda and pca and also with other classification algorithms linear svms kernel pca kernel discriminant analysis and kernel slda for object recognition and face recognition under large pose expression variation we also show applications of pcnsa to two classification problems in video an action retrieval problem and abnormal activity detection

the simulation tabulation method for classical diffusion monte carlo abstract many important classes of problems in materials science and biotechnology require the solution of the laplace or poisson equation in disordered two phase domains in which the phase interface is extensive and convoluted green s function first passage gffp methods solve such problems efficiently by generalizing the walk on spheres wos method to allow first passage fp domains to be not just spheres but a wide variety of geometrical shapes in particular this solves the difficulty of slow convergence with wos by allowing fp domains that contain patches of the phase interface previous studies accomplished this by using geometries for which the green s function was available in quasi analytic form here we extend these studies by using the simulation tabulation st method we simulate and then tabulate surface green s functions that cannot be obtained analytically the st method is applied to the solc stockmayer model with zero potential to the mean trapping rate of a diffusing particle in a domain of nonoverlapping spherical traps and to the effective conductivity for perfectly insulating nonoverlapping spherical inclusions in a matrix of finite conductivity in all cases this class of algorithms provides the most efficient methods known to solve these problems to high accuracy

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

simulating diffusions with piecewise constant coefficients using a kinetic approximation using a kinetic approximation of a linear diffusion operator we propose an algorithm that allows one to deal with the simulation of a multi dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities numerical examples are given in dimensions one to three on pdes or stochastic pdes with or without source terms

new monte carlo schemes for simulating diffusions in discontinuous media we introduce new monte carlo simulation schemes for diffusions in a discontinuous media divided in subdomains with piecewise constant diffusivity these schemes are higher order extensions of the usual schemes and take into account the two dimensional aspects of the diffusion at the interface between subdomains this is achieved using either stochastic process techniques or an approach based on finite differences numerical tests on elliptic parabolic and eigenvalue problems involving an operator in divergence form show the efficiency of these new schemes

monte carlo methods for calculating some physical properties of large molecules in this paper we describe monte carlo methods for solving some boundary value problems for elliptic partial differential equations arising in the computation of physical properties of large molecules the constructed algorithms are based on walk on spheres green s function first passage walk in subdomains techniques and finite difference approximations of the boundary condition the methods are applied to calculating the diffusion limited reaction rate the electrostatic energy of a molecule and point values of an electrostatic field

transmission subspace tracking for mimo systems with low rate feedback this paper describes a feedback algorithm for tracking the dominant subspaces of continuously time varying channels in multiantenna communication systems the nature of the problem is quantization of subspaces it is well known that subspaces can be mathematically modeled as points in a grassmann manifold we model the variations between the dominant subspaces of channels at adjacent time instants to be along geodesics in the grassmann manifold instead of quantizing the subspaces themselves we propose to quantize the geodesic trajectory connecting two subspaces more specifically we quantize a key entity that characterizes a geodesic arc the velocity matrix which resembles angular speed in a one dimensional complex space two techniques are proposed for quantizing the velocity matrix of the geodesic in the first a 1 bit feedback is utilized to indicate the preferred sign of a random velocity matrix of the geodesic in the other the velocity matrix is quantized using a gaussian vector quantization codebook numerical results show that the performance of the proposed 1 bit feedback algorithm is better than a previously proposed grassmannian subspace packing scheme at low to medium doppler frequencies and better than a gradient sign feedback scheme at all doppler frequencies in our simulations the gaussian vector quantization algorithm is always better than the 1 bit feedback algorithm

deformotion deforming motion shape average and the joint registration and approximation of structures in images what does it mean for a deforming object to be moving how can we separate the overall motion a finite dimensional group action from the more general deformation a diffeomorphism in this paper we propose a definition of motion for a deforming object and introduce a notion of shape average as the entity that separates the motion from the deformation our definition allows us to derive novel and efficient algorithms to register non identical shapes using region based methods and to simultaneously approximate and align structures in greyscale images we also extend the notion of shape average to that of a moving average in order to track moving and deforming objects through time the algorithms we propose extend prior work on landmark based matching to smooth curves and involve the numerical integration of partial differential equations which we address within the framework of level set methods

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

a survey of convergence results on particle filtering methods for practitioners optimal filtering problems are ubiquitous in signal processing and related fields except for a restricted class of models the optimal filter does not admit a closed form expression particle filtering methods are a set of flexible and powerful sequential monte carlo methods designed to solve the optimal filtering problem numerically the posterior distribution of the state is approximated by a large set of dirac delta masses samples particles that evolve randomly in time according to the dynamics of the model and the observations the particles are interacting thus classical limit theorems relying on statistically independent samples do not apply in this paper our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners

recognizing interactive group activities using temporal interaction matrices and their riemannian statistics while video based activity analysis and recognition has received much attention a large body of existing work deals with activities of a single subject modeling and recognition of coordinated multi subject activities or group activities present in a variety of applications such as surveillance sports and biological monitoring records etc is the main objective of this paper unlike earlier attempts which model the complex spatial temporal constraints among multiple subjects with a parametric bayesian network we propose a compact and discriminative descriptor referred to as the temporal interaction matrix for representing a coordinated group motion pattern moreover we characterize the space of the temporal interaction matrices using the discriminative temporal interaction manifold dtim and use it as a framework within which we develop a data driven strategy to characterize the group motion pattern without employing specific domain knowledge in particular we establish probability densities on the dtim for compactly describing the statistical properties of the coordinations and interactions among multiple subjects in a group activity for each class of group activity we learn a multi modal density function on the dtim a maximum a posteriori map classifier on the manifold is then designed for recognizing new activities in addition we have extended this model to one with which we can explicitly distinguish the participants from non participants we demonstrate how the framework can be applied to motions represented by point trajectories as well as articulated human actions represented by images experiments on both cases show the effectiveness of the proposed approach

shape distributions of nonlinear dynamical systems for video based inference this paper presents a shape theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video based inference tasks traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks a novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics the proposed framework has two main advantages over traditional approaches a representation of the dynamical system is derived directly from the observational data without any inherent assumptions and b the proposed features show stability under different time series lengths where traditional dynamical invariants fail we illustrate our idea using nonlinear dynamical models such as lorenz and rossler systems where our feature representations shape distribution support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature our experimental analyses on these models also indicate that the proposed framework show stability for different time series lengths which is useful when the available number of samples are small variable the specific applications of interest in this paper are 1 activity recognition using motion capture and rgbd sensors 2 activity quality assessment for applications in stroke rehabilitation and 3 dynamical scene classification we provide experimental validation through action and gesture recognition experiments on motion capture and kinect datasets in all these scenarios we show experimental evidence of the favorable properties of the proposed representation

simulating diffusion processes in discontinuous media in this article we propose new monte carlo techniques for moving a diffusive particle in a discontinuous media in this framework we characterize the stochastic process that governs the positions of the particle the key tool is the reduction of the process to a skew brownian motion sbm in a zone where the coefficients are locally constant on each side of the discontinuity the new position of the particle after a constant time step is sampled from the exact distribution of the sbm process at the considered time to do so we propose two different but equivalent algorithms a two steps simulation with a stop at the discontinuity and a one step direct simulation of the sbm dynamic some benchmark tests illustrate their effectiveness

the complex bingham distribution and shape analysis summary a complex version of the bingham distribution is defined on the unit complex sphere in ck various statistical properties including asymptotic normality under high concentration are derived symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions strengths and weaknesses of this approach are investigated links and contrasts with bookstein co ordinates are discussed a hybrid approach to principal component analysis based on complex and real co ordinates is suggested

canonical correlation analysis of video volume tensors for action categorization and detection this paper addresses a spatiotemporal pattern recognition problem the main purpose of this study is to find a right representation and matching of action video volumes for categorization a novel method is proposed to measure video to video volume similarity by extending canonical correlation analysis cca a principled tool to inspect linear relations between two sets of vectors to that of two multiway data arrays or tensors the proposed method analyzes video volumes as inputs avoiding the difficult problem of explicit motion estimation required in traditional methods and provides a way of spatiotemporal pattern matching that is robust to intraclass variations of actions the proposed matching is demonstrated for action classification by a simple nearest neighbor classifier we moreover propose an automatic action detection method which performs 3d window search over an input video with action exemplars the search is speeded up by dynamic learning of subspaces in the proposed cca experiments on a public action data set kth and a self recorded hand gesture data showed that the proposed method is significantly better than various state of the art methods with respect to accuracy our method has low time complexity and does not require any major tuning parameters

simulating diffusion processes in discontinuous media benchmark tests abstract we present several benchmark tests for monte carlo methods simulating diffusion in one dimensional discontinuous media these benchmark tests aim at studying the potential bias of the schemes and their impact on the estimation of micro or macroscopic quantities repartition of masses fluxes mean residence time these benchmark tests are backed by a statistical analysis to filter out the bias from the unavoidable monte carlo error we apply them on four different algorithms the results of the numerical tests give a valuable insight into the fine behavior of these schemes as well as rules to choose between them