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Markerless kinematic model and motion capture from volume sequences
 In To appear in the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2003
, 2003
"... We present an approach for modelfree markerless motion capture of articulated kinematic structures. This approach is centered on our method for generating underlying nonlinear axes (or a skeleton curve) of a volume of genus zero (i.e., without holes). We describe the use of skeleton curves for deri ..."
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Cited by 37 (3 self)
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We present an approach for modelfree markerless motion capture of articulated kinematic structures. This approach is centered on our method for generating underlying nonlinear axes (or a skeleton curve) of a volume of genus zero (i.e., without holes). We describe the use of skeleton curves for deriving a kinematic model and motion (in the form of joint angles over time) from a captured volume sequence. Our motion capture method uses a skeleton curve, found in each frame of a volume sequence, to automatically determine kinematic postures. These postures are aligned to determine a common kinematic model for the volume sequence. The derived kinematic model is then reapplied to each frame in the volume sequence to find the motion sequence suited to this model. We demonstrate our method on several types of motion, from synthetically generated volume sequences with an arbitrary kinematic topology, to human volume sequences captured from a set of multiple calibrated cameras. 1.
Regularized Principal Manifolds
 In Computational Learning Theory: 4th European Conference
, 2001
"... Many settings of unsupervised learning can be viewed as quantization problems  the minimization ..."
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Cited by 32 (4 self)
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Many settings of unsupervised learning can be viewed as quantization problems  the minimization
Piecewise Linear Skeletonization Using Principal Curves
, 2002
"... We propose an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the "middle" of a cloud of points) and t ..."
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Cited by 32 (0 self)
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We propose an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the "middle" of a cloud of points) and the medial axis (smooth curves that go equidistantly from the contours of a character image). The central fittingandsmoothing step of the algorithm is an extension of the polygonal line algorithm [1, 2] which approximates principal curves of data sets by piecewise linear curves. The polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization: an initialization method to improve the structural quality of the skeleton produced by the initialization method.
Novel skeletal representation for articulated creatures
 In Proc. European Conf. on Computer Vision
, 2004
"... Abstract. Volumetric structures are frequently used as shape descriptors for 3D data. The capture of such data is being facilitated by developments in multiview video and range scanning, extending to subjects that are alive and moving. In this paper, we examine visionbased modeling and the related ..."
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Cited by 27 (1 self)
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Abstract. Volumetric structures are frequently used as shape descriptors for 3D data. The capture of such data is being facilitated by developments in multiview video and range scanning, extending to subjects that are alive and moving. In this paper, we examine visionbased modeling and the related representation of moving articulated creatures using spines. We define a spine as a branching axial structure representing the shape and topology of a 3D object’s limbs, and capturing the limbs’ correspondence and motion over time. Our spine concept builds on skeletal representations often used to describe the internal structure of an articulated object and the significant protrusions. The algorithms for determining both 2D and 3D skeletons generally use an objective function tuned to balance stability against the responsiveness to detail. Our representation of a spine provides for enhancements over a 3D skeleton, afforded by temporal robustness and correspondence. We also introduce a probabilistic framework that is needed to compute the spine from a sequence of surface data. We present a practical implementation that approximates the spine’s joint probability function to reconstruct spines for synthetic and real subjects that move.
Another Look at Principal Curves and Surfaces
, 2001
"... INTRODUCTION Consider a multivariate random variable X in R p with density function f and a random sample from X, namely X 1 , ..., X n . The first principal component can be viewed as the straight line which best fits the cloud of data (see, e.g., [17, pp. 386#387]). When the distribution of X is e ..."
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Cited by 20 (2 self)
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INTRODUCTION Consider a multivariate random variable X in R p with density function f and a random sample from X, namely X 1 , ..., X n . The first principal component can be viewed as the straight line which best fits the cloud of data (see, e.g., [17, pp. 386#387]). When the distribution of X is ellipsoidal the population first principal component is the main axis of the ellipsoids of equal concentration. In the past 40 years many works have appeared proposing extensions of principal components to distributions with nonlinear structure. We cite Shepard and Carroll [24], Gnanadesikan and Wilk [13], Srivastava [27], EtezadiAmoli and McDonald [10], Yohai, Ackermann and Haigh [33], Koyak [19] and Gifi [12], among others. Some of them look for nonlinear transformations of the observable variables into spaces admitting a doi:10
A KSegments Algorithm for Finding Principal Curves
 Pattern Recognition Letters
, 2000
"... We propose an incremental method to find principal curves. Line segments are fitted and connected to form polygonal lines. New segments are inserted until a performance criterion is met. Experimental results illustrate the performance of the method compared to other existing approaches. ..."
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Cited by 18 (2 self)
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We propose an incremental method to find principal curves. Line segments are fitted and connected to form polygonal lines. New segments are inserted until a performance criterion is met. Experimental results illustrate the performance of the method compared to other existing approaches.
Principal surfaces from unsupervised kernel regression
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the NadarayaWatson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides ..."
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Cited by 16 (9 self)
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Abstract—We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the NadarayaWatson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides a practical solution to the model selection problem because all parameters can be estimated by leaveoneout crossvalidation without additional computational cost. In addition, our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization, beyond classical initializations based on linear PCA. Furthermore, it shows a simple way to fit principal surfaces in general feature spaces, beyond the usual data space setup. The experimental results illustrate these convenient features on simulated and real data. Index Terms—Dimensionality reduction, principal curves, principal surfaces, density estimation, model selection, kernel methods. æ 1
Principal Curves: Learning, Design, And Applications
, 1999
"... The subjects of this thesis are unsupervised learning in general, and principal curves in particular. Principal curves were originally defined by Hastie \cite{Has84} and Hastie and Stuetzle \cite{HaSt89} (hereafter HS) to formally capture the notion of a smooth curve passing through the ``middle'' o ..."
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Cited by 14 (3 self)
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The subjects of this thesis are unsupervised learning in general, and principal curves in particular. Principal curves were originally defined by Hastie \cite{Has84} and Hastie and Stuetzle \cite{HaSt89} (hereafter HS) to formally capture the notion of a smooth curve passing through the ``middle'' of a $d$dimensional probability distribution or data cloud. Based on the definition, HS also developed an algorithm for constructing principal curves of distributions and data sets. The field has been very active since Hastie and Stuetzle's groundbreaking work. Numerous alternative definitions and methods for estimating principal curves have been proposed, and principal curves were further analyzed and compared with other unsupervised learning techniques. Several applications in various areas including image analysis, feature extraction, and speech processing demonstrated that principal curves are not only of theoretical interest, but they also have a legitimate place in the family of practical unsupervised learning techniques. Although the concept of principal curves as considered by HS has several appealing characteristics, complete theoretical analysis of the model seems to be rather hard. This motivated us to redefine principal curves in a manner that allowed us to carry out extensive theoretical analysis while preserving the informal notion of principal curves. Our first contribution to the area is, hence, a new {\em theoretical model} that is analyzed by using tools of statistical learning theory. Our main result here is the first known consistency proof of a principal curve estimation scheme. The theoretical model proved to be too restrictive to be practical. However, it inspired the design of a new {\em practical algorithm} to estimate principal curves based on data. The polygonal line algorithm, which compares favorably with previous methods both in terms of performance and computational complexity, is our second contribution to the area of principal curves. To complete the picture, in the last part of the thesis we consider an {\em application} of the polygonal line algorithm to handwritten character skeletonization.
Learning nonlinear image manifolds by global alignment of local linear models
 IEEE Trans. Pattern Analysis and Machine Intell
"... Abstract—Appearancebased methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than ..."
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Cited by 12 (0 self)
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Abstract—Appearancebased methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than the number of pixels in the image. If there is a smooth function that maps the DOF to the pixel values, then the images are confined to a lowdimensional manifold embedded in the image space. We propose a method based on probabilistic mixtures of factor analyzers to 1) model the density of images sampled from such manifolds and 2) recover global parameterizations of the manifold. A globally nonlinear probabilistic twoway mapping between coordinates on the manifold and images is obtained by combining several, locally valid, linear mappings. We propose a parameter estimation scheme that improves upon an existing scheme and experimentally compare the presented approach to selforganizing maps, generative topographic mapping, and mixtures of factor analyzers. In addition, we show that the approach also applies to finding mappings between different embeddings of the same manifold. Index Terms—Feature extraction or construction, machine learning, statistical image representation. 1