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962
Stochastic Tracking of 3D Human Figures Using 2D Image Motion
 In European Conference on Computer Vision
, 2000
"... . A probabilistic method for tracking 3D articulated human gures in monocular image sequences is presented. Within a Bayesian framework, we de ne a generative model of image appearance, a robust likelihood function based on image graylevel dierences, and a prior probability distribution over pose an ..."
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Cited by 383 (33 self)
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. A probabilistic method for tracking 3D articulated human gures in monocular image sequences is presented. Within a Bayesian framework, we de ne a generative model of image appearance, a robust likelihood function based on image graylevel dierences, and a prior probability distribution over pose and joint angles that models how humans move. The posterior probability distribution over model parameters is represented using a discrete set of samples and is propagated over time using particle ltering. The approach extends previous work on parameterized optical ow estimation to exploit a complex 3D articulated motion model. It also extends previous work on human motion tracking by including a perspective camera model, by modeling limb self occlusion, and by recovering 3D motion from a monocular sequence. The explicit posterior probability distribution represents ambiguities due to image matching, model singularities, and perspective projection. The method relies only on a...
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2004
"... Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized ..."
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Cited by 261 (15 self)
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Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized data points sampled with noise from the manifold, we represent the local geometry of the manifold using tangent spaces learned by fitting an affine subspace in a neighborhood of each data point. Those tangent spaces are aligned to give the internal global coordinates of the data points with respect to the underlying manifold by way of a partial eigendecomposition of the neighborhood connection matrix. We present a careful error analysis of our algorithm and show that the reconstruction errors are of secondorder accuracy. We illustrate our algorithm using curves and surfaces both in 2D/3D and higher dimensional Euclidean spaces, and 64by64 pixel face images with various pose and lighting conditions. We also address several theoretical and algorithmic issues for further research and improvements.
Probabilistic Independent Component Analysis
, 2003
"... Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ..."
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Cited by 208 (13 self)
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Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ability to quantify statistical significance. We present an integrated approach to Probabilistic ICA for FMRI data that allows for nonsquare mixing in the presence of Gaussian noise. We employ an objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e. the number of activation and nonGaussian noise sources. Reduction of the data to this 'true' subspace before the ICA decomposition automatically results in an estimate of the noise, leading to the ability to assign significance to voxels in ICA spatial maps. Estimation of the number of intrinsic sources not only enables us to carry out probabilistic modelling, but also achieves an asymptotically unique decomposition of the data. This reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normafisation of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternativehypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and complex artificial FMRI data, and compared to the spatiotemporal accuracy of restfits obtaine...
HighDimensional Data Analysis: The Curses and Blessings of Dimensionality
, 2000
"... The coming century is surely the century of data. A combination of blind faith and serious purpose makes our society invest massively in the collection and processing of data of all kinds, on scales unimaginable until recently. Hyperspectral Imagery, Internet Portals, Financial tickbytick data, an ..."
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Cited by 169 (0 self)
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The coming century is surely the century of data. A combination of blind faith and serious purpose makes our society invest massively in the collection and processing of data of all kinds, on scales unimaginable until recently. Hyperspectral Imagery, Internet Portals, Financial tickbytick data, and DNA Microarrays are just a few of the betterknown sources, feeding data in torrential streams into scientific and business databases worldwide. In traditional statistical data analysis, we think of observations of instances of particular phenomena (e.g. instance ↔ human being), these observations being a vector of values we measured on several variables (e.g. blood pressure, weight, height,...). In traditional statistical methodology, we assumed many observations and a few, wellchosen variables. The trend today is towards more observations but even more so, to radically larger numbers of variables – voracious, automatic, systematic collection of hyperinformative detail about each observed instance. We are seeing examples where the observations gathered on individual instances are curves, or spectra, or images, or
Decomposing biological motion: A framework for analysis and synthesis of human gait patterns.
 Journal of Vision,
, 2002
"... Biological motion contains information about the identity of an agent as well as about his or her actions, intentions, and emotions. The human visual system is highly sensitive to biological motion and capable of extracting socially relevant information from it. Here we investigate the question of ..."
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Cited by 159 (20 self)
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Biological motion contains information about the identity of an agent as well as about his or her actions, intentions, and emotions. The human visual system is highly sensitive to biological motion and capable of extracting socially relevant information from it. Here we investigate the question of how such information is encoded in biological motion patterns and how such information can be retrieved. A framework is developed that transforms biological motion into a representation allowing for analysis using linear methods from statistics and pattern recognition. Using gender classification as an example, simple classifiers are constructed and compared to psychophysical data from human observers. The analysis reveals that the dynamic part of the motion contains more information about gender than motionmediated structural cues. The proposed framework can be used not only for analysis of biological motion but also to synthesize new motion patterns. A simple motion modeler is presented that can be used to visualize and exaggerate the differences in male and female walking patterns.
Functional data analysis for sparse longitudinal data.
 Journal of the American Statistical Association
, 2005
"... We propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data. The method aims at irregularly spaced longitudinal data, where the number of repeated measurements available per subject is small. In contrast, classical functional data a ..."
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Cited by 123 (24 self)
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We propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data. The method aims at irregularly spaced longitudinal data, where the number of repeated measurements available per subject is small. In contrast, classical functional data analysis requires a large number of regularly spaced measurements per subject. We assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random (subjectspecific) trajectory plus measurement errors. Basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories, and the estimation of the variance of the measurement errors. The eigenfunction basis is estimated from the data, and functional principal components score estimates are obtained by a conditioning step. This conditional estimation method is conceptually simple and straightforward to implement. A key step is the derivation of asymptotic consistency and distribution results under mild conditions, using tools from functional analysis. Functional data analysis for sparse longitudinal data enables prediction of individual smooth trajectories even if only one or few measurements are available for a subject. Asymptotic pointwise and simultaneous confidence bands are obtained for predicted individual trajectories, based on asymptotic distributions, for simultaneous bands under the assumption of a finite number of components. Model selection techniques, such as the Akaike information criterion, are used to choose the model dimension corresponding to the number of eigenfunctions in the model. The methods are illustrated with a simulation study, longitudinal CD4 data for a sample of AIDS patients, and timecourse gene expression data for the yeast cell cycle.
Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves
 Biometrics
, 1998
"... We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low rank, low frequency a ..."
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Cited by 114 (3 self)
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We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low rank, low frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as BLUP estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniquesAIC, BIC, and crossvalidation to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis. We illustrate it with two sets of data. 1 Introduction In recent years there ha...
Parameter estimation for differential equations: A generalized smoothing approach
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 2007
"... We propose a new method for estimating parameters in nonlinear differential equations. These models represent change in a system by linking the behavior of a derivative of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noi ..."
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Cited by 113 (12 self)
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We propose a new method for estimating parameters in nonlinear differential equations. These models represent change in a system by linking the behavior of a derivative of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to statistical techniques such as inference and interval estimation. This paper describes a new method that uses noisy data to estimate the parameters defining a system of nonlinear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive interval estimates and show that these have good coverage properties on data simulated from chemical engineering and neurobiology. The method is demonstrated using realworld data from chemistry and from the progress of the autoimmune disease lupus.
Spline Estimators for the Functional Linear Model: Consistency, Application and Splus Implementation
"... The functional linear model is a regression model in which the explanatory variable is a continuous time process observed in a closed interval of R: Hence, the "vector of parameters" to be estimated belongs to the infinite dimensional space of Rvalued operators defined on a space of fu ..."
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Cited by 104 (9 self)
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The functional linear model is a regression model in which the explanatory variable is a continuous time process observed in a closed interval of R: Hence, the "vector of parameters" to be estimated belongs to the infinite dimensional space of Rvalued operators defined on a space of functions. We propose here two estimators of the functional parameter of such a model by means of spline functions. These estimators take into account the dimensionality problem and we prove their consistency. The first one relies on a truncated functional principal components analysis and the second is based on penalized regression splines. These estimators are compared by means of simulations and applied to explain winter wheat yield with respect to climatic variations.