real time visual tracking of complex structures presents a framework for three dimensional model based tracking graphical rendering technology is combined with constrained active contour tracking to create a robust wire frame tracking system it operates in real time at video frame rate 25 hz on standard hardware it is based on an internal cad model of the object to be tracked which is rendered using a binary space partition tree to perform hidden line removal a lie group formalism is used to cast the motion computation problem into simple geometric terms so that tracking becomes a simple optimization problem solved by means of iterative reweighted least squares a visual servoing system constructed using this framework is presented together with results showing the accuracy of the tracker the paper then describes how this tracking system has been extended to provide a general framework for tracking in complex configurations the adjoint representation of the group is used to transform measurements into common coordinate frames the constraints are then imposed by means of lagrange multipliers results from a number of experiments performed using this framework are presented and discussed

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

twist based acquisition and tracking of animal and human kinematics this paper demonstrates a new visual motion estimation technique that is able to recover high degree of freedom articulated human body configurations in complex video sequences we introduce the use and integration of a mathematical technique the product of exponential maps and twist motions into a differential motion estimation this results in solving simple linear systems and enables us to recover robustly the kinematic degrees of freedom in noise and complex self occluded configurations a new factorization technique lets us also recover the kinematic chain model itself we are able to track several human walk cycles several wallaby hop cycles and two walk cycels of the famous movements of eadweard muybridge s motion studies from the last century to the best of our knowledge this is the first computer vision based system that is able to process such challenging footage

unsupervised learning of human motion an unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts a moving human body in our examples automatically from unlabeled training data is presented the training data include both useful foreground features as well as features that arise from irrelevant background clutter the correspondence between parts and detected features is unknown the joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection to learn the model structure as well as model parameters an em like algorithm is developed where the labeling of the data part assignments is treated as hidden variables the unsupervised learning technique is not limited to decomposable triangulated graphs the efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences and testing the learned models on a variety of sequences

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

construction of a continuous stopping boundary from an alpha spending function lan and demets 1983 biometrika 70 659 663 proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall type i error alpha their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete time boundary values in this framework the cumulative distribution function of the continuous time stopping rule is used as an alpha spending function a key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic however clinical trials may be monitored more frequently when they are close to crossing the boundary in this situation the corresponding continuous time boundary should be used here we demonstrate how to construct a continuous stopping boundary from an alpha spending function this capability is useful in the design of clinical trials we use the beta blocker heart attack trial bhat and aids clinical trials group protocol 021 for illustration

shape from silhouette across time part i theory and algorithms shape from silhouette sfs is a shape reconstruction method which constructs a 3d shape estimate of an object using silhouette images of the object the output of a sfs algorithm is known as the visual hull vh traditionally sfs is either performed on static objects or separately at each time instant in the case of videos of moving objects in this paper we develop a theory of performing sfs across time estimating the shape of a dynamic object with unknown motion by combining all of the silhouette images of the object over time we first introduce a one dimensional element called a bounding edge to represent the visual hull we then show that aligning two visual hulls using just their silhouettes is in general ambiguous and derive the geometric constraints in terms of bounding edges that govern the alignment to break the alignment ambiguity we combine stereo information with silhouette information and derive a temporal sfs algorithm which consists of two steps 1 estimate the motion of the objects over time visual hull alignment and 2 combine the silhouette information using the estimated motion visual hull refinement the algorithm is first developed for rigid objects and then extended to articulated objects in the part ii of this paper we apply our temporal sfs algorithm to two human related applications 1 the acquisition of detailed human kinematic models and 2 marker less motion tracking

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

symplectic hamiltonian hdg methods for wave propagation phenomena abstract we devise the first symplectic hamiltonian hybridizable discontinuous galerkin hdg methods for the acoustic wave equation we discretize in space by using a hamiltonian hdg scheme that is an hdg method which preserves the hamiltonian structure of the wave equation and in time by using symplectic diagonally implicit and explicit partitioned runge kutta methods the fundamental feature of the resulting scheme is that the conservation of a discrete energy which is nothing but a discrete version of the original hamiltonian is guaranteed we present numerical experiments which indicate that the method achieves optimal approximations of order k 1 in the l 2 norm when polynomials of degree k 0 and runge kutta time marching methods of order k 1 are used in addition by means of post processing techniques and by increasing the order of the runge kutta method to k 2 we obtain superconvergent approximations of order k 2 in the l 2 norm for the displacement and the velocity we also present numerical examples that corroborate that the methods conserve energy and that they compare favorably with dissipative hdg schemes of similar accuracy properties for long time simulations

rigid and articulated point registration with expectation conditional maximization this paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration the problem is recast into a missing data framework where unknown correspondences are handled via mixture models adopting a maximum likelihood principle we introduce an innovative em like algorithm namely the expectation conditional maximization for point registration ecmpr algorithm the algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case we analyze in detail the associated consequences in terms of estimation of the registration parameters and propose an optimal method for estimating the rotational and translational parameters based on semidefinite positive relaxation we extend rigid registration to articulated registration robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the gaussian mixture model at hand we provide an in depth analysis of our method and compare it both theoretically and experimentally with other robust methods for point registration

human motion tracking with a kinematic parameterization of extremal contours this paper addresses the problem of human motion tracking from multiple image sequences the human body is described by five articulated mechanical chains and human body parts are described by volumetric primitives with curved surfaces if such a surface is observed with a camera an extremal contour appears in the image whenever the surface turns smoothly away from the viewer we describe a method that recovers human motion through a kinematic parameterization of these extremal contours the method exploits the fact that the observed image motion of these contours is a function of both the rigid displacement of the surface and of the relative position and orientation between the viewer and the curved surface first we describe a parameterization of an extremal contour point velocity for the case of developable surfaces second we use the zero reference kinematic representation and we derive an explicit formula that links extremal contour velocities to the angular velocities associated with the kinematic model third we show how the chamfer distance may be used to measure the discrepancy between predicted extremal contours and observed image contours moreover we show how the chamfer distance can be used as a differentiable multi valued function and how the tracker based on this distance can be cast into a continuous non linear optimization framework fourth we describe implementation issues associated with a practical human body tracker that may use an arbitrary number of cameras one great methodological and practical advantage of our method is that it relies neither on model to image nor on image to image point matches in practice we model people with 5 kinematic chains 19 volumetric primitives and 54 degrees of freedom we observe silhouettes in images gathered with several synchronized and calibrated cameras the tracker has been successfully applied to several complex motions gathered at 30 frames second

explicit finite element methods for symmetric hyperbolic equations a family of explicit space time finite element methods for the initial boundary value problem for linear symmetric hyperbolic systems of equations is described and analyzed the method generalizes the discontinuous galerkin method and as is typical for this method obtains error estimates of order o h n 1 2 for approximations by polynomials of degree le n

robust temporally coherent laplacian protrusion segmentation of 3d articulated bodies in motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data in order to describe motion patterns in a compact way and to discriminate between them in an unsupervised context i e no prior model of the moving object s is available such a structure has to be learned from the data in a bottom up fashion in recent times volumetric approaches in which the motion is captured from a number of cameras and a voxel set representation of the body is built from the camera views have gained ground due to attractive features such as inherent view invariance and robustness to occlusions automatic unsupervised segmentation of moving bodies along entire sequences in a temporally coherent and robust way has the potential to provide a means of constructing a bottom up model of the moving body and track motion cues that may be later exploited for motion classification spectral methods such as locally linear embedding can be useful in this context as they preserve protrusions i e high curvature regions of the 3d volume of articulated shapes while improving their separation in a lower dimensional space making them in this way easier to cluster in this paper we therefore propose a spectral approach to unsupervised and temporally coherent body protrusion segmentation along time sequences volumetric shapes are clustered in an embedding space clusters are propagated in time to ensure coherence and merged or split to accommodate changes in the body s topology experiments on both synthetic and real sequences of dense voxel set data are shown this supports the ability of the proposed method to cluster body parts consistently over time in a totally unsupervised fashion its robustness to sampling density and shape quality and its potential for bottom up model construction

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

probabilistic tracking with exemplars in a metric space a new exemplar based probabilistic paradigm for visual tracking is presented probabilistic mechanisms are attractive because they handle fusion of information especially temporal fusion in a principled manner exemplars are selected representatives of raw training data used here to represent probabilistic mixture distributions of object configurations their use avoids tedious hand construction of object models and problems with changes of topology using exemplars in place of a parameterized model poses several challenges addressed here with what we call the metric mixture m2 approach which has a number of attractions principally it provides alternatives to standard learning algorithms by allowing the use of metrics that are not embedded in a vector space secondly it uses a noise model that is learned from training data lastly it eliminates any need for an assumption of probabilistic pixelwise independence experiments demonstrate the effectiveness of the m2 model in two domains tracking walking people using chamfer distances on binary edge images and tracking mouth movements by means of a shuffle distance

symplectic mixed finite element approximation of linear acoustic wave equations we apply mixed finite element approximations to the first order form of the acoustic wave equation the semidiscrete method exactly conserves the system energy a fully discrete method employing the symplectic euler time method in time exactly conserves a positive definite pertubed energy functional that is equivalent to the actual energy under a cfl condition in addition to proving optimal order l infty l 2 l l2 estimates we also develop a bootstrap technique that allows us to derive stability and error bounds for the time derivatives and divergence of the vector variable beyond the standard under some additional regularity assumptions

miscellanea properties of spending function boundaries clinical trials are monitored periodically for safety and efficacy resulting in several looks at interim data if no account is taken of this the type i error rate may be substantially higher than planned one of the most popular methods of generating interim boundaries that result in an overall type i error rate of is the spending function approach this paper proves several properties of these boundaries including a continuity like property for looks occurring close to each other and a monotonicity property when additional looks are taken how past monitoring affects future boundaries is also studied

building roadmaps of minima and transitions in visual models becoming trapped in suboptimal local minima is a perennial problem when optimizing visual models particularly in applications like monocular human body tracking where complicated parametric models are repeatedly fitted to ambiguous image measurements we show that trapping can be significantly reduced by building roadmaps of nearby minima linked by transition pathways paths leading over low mountain passes in the cost surface found by locating the transition state codimension 1 saddle point at the top of the pass and then sliding downhill to the next minimum we present two families of transition state finding algorithms based on local optimization in eigenvector tracking unconstrained newton minimization is modified to climb uphill towards a transition state while in hypersurface sweeping a moving hypersurface is swept through the space and moving local minima within it are tracked using a constrained newton method these widely applicable numerical methods which appear not to be known in vision and optimization generalize methods from computational chemistry where finding transition states is critical for predicting reaction parameters experiments on the challenging problem of estimating 3d human pose from monocular images show that our algorithms find nearby transition states and minima very efficiently but also underline the disturbingly large numbers of minima that can exist in this and similar model based vision problems

spending functions and continuous monitoring boundaries clinical trials are monitored periodically for safety efficacy and futility the spending function is a popular tool for efficacy monitoring because it does not require pre specification of the number or timing of interim analyses but there are infinitely many spending functions so some guidance on how to choose one is helpful we consider spending functions that are generated from different continuous monitoring boundaries for brownian motion we use properties of the continuous monitoring boundaries to derive properties of the associated spending function copyright 2012 john wiley sons ltd

recovering 3d human pose from monocular images we describe a learning based method for recovering 3d human body pose from single images and monocular image sequences our approach requires neither an explicit body model nor prior labeling of body parts in the image instead it recovers pose by direct nonlinear regression against shape descriptor vectors extracted automatically from image silhouettes for robustness against local silhouette segmentation errors silhouette shape is encoded by histogram of shape contexts descriptors we evaluate several different regression methods ridge regression relevance vector machine rvm regression and support vector machine svm regression over both linear and kernel bases the rvms provide much sparser regressors without compromising performance and kernel bases give a small but worthwhile improvement in performance the loss of depth and limb labeling information often makes the recovery of 3d pose from single silhouettes ambiguous to handle this the method is embedded in a novel regressive tracking framework using dynamics from the previous state estimate together with a learned regression value to disambiguate the pose we show that the resulting system tracks long sequences stably for realism and good generalization over a wide range of viewpoints we train the regressors on images resynthesized from real human motion capture data the method is demonstrated for several representations of full body pose both quantitatively on independent but similar test data and qualitatively on real image sequences mean angular errors of 4 6 spl deg are obtained for a variety of walking motions

first exit densities of brownian motion through one sided moving boundaries let a a e be a sequence of curved boundaries which tend to infinity as a increases let t a inf t 0 w t geqq psi a t where w t denotes the standard brownian motion under regularity conditions on the boundaries uniform approximations for the first exit densities of ta are derived the consequences for upper and lower class functions are discussed the approximations for the first exit densities of brownian motion with drift which are also derived lead to uniform approximations for the power functions of sequential tests the quality of the approximations is demonstrated by some figures

human motion tracking by registering an articulated surface to 3d points and normals we address the problem of human motion tracking by registering a surface to 3 d data we propose a method that iteratively computes two things maximum likelihood estimates for both the kinematic and free motion parameters of an articulated object as well as probabilities that the data are assigned either to an object part or to an outlier cluster we introduce a new metric between observed points and normals on one side and a parameterized surface on the other side the latter being defined as a blending over a set of ellipsoids we claim that this metric is well suited when one deals with either visual hull or visual shape observations we illustrate the method by tracking human motions using sparse visual shape data 3 d surface points and normals gathered from imperfect silhouettes

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

optimal discontinuous galerkin methods for the acoustic wave equation in higher dimensions in this paper we develop and analyze a new class of discontinuous galerkin dg methods for the acoustic wave equation in mixed form traditional mixed finite element fe methods produce energy conserving schemes but these schemes are implicit making the time stepping inefficient standard dg methods give explicit schemes but these approaches are typically dissipative or suboptimally convergent depending on the choice of numerical fluxes our new method can be seen as a compromise between these two kinds of techniques in the way that it is both explicit and energy conserving locally and globally moreover it can be seen as a generalized version of the raviart thomas fe method and the finite volume method stability and convergence of the new method are rigorously analyzed and we have shown that the method is optimally convergent furthermore in order to apply the new method for unbounded domains we apply our new method with the first order absorbing boundary condition the stability of the resulting numerical scheme is analyzed

sequential monitoring of clinical trials the role of information and brownian motion sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades this paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings the central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form through a stochastic process that can be shown to approximate classical brownian motion the ideas are developed in a simple step by step fashion and illustrated by several practical examples