Results 1  10
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42
Visual tracking via incremental logeuclidean riemannian subspace learning
 In Proceedings IEEE Conference Computer Vision and Pattern Recognition
, 2008
"... Recently, a novel LogEuclidean Riemannian metric [28] is proposed for statistics on symmetric positive definite (SPD) matrices. Under this metric, distances and Riemannian means take a much simpler form than the widely used affineinvariant Riemannian metric. Based on the LogEuclidean Riemannian m ..."
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Cited by 33 (3 self)
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Recently, a novel LogEuclidean Riemannian metric [28] is proposed for statistics on symmetric positive definite (SPD) matrices. Under this metric, distances and Riemannian means take a much simpler form than the widely used affineinvariant Riemannian metric. Based on the LogEuclidean Riemannian metric, we develop a tracking framework in this paper. In the framework, the covariance matrices of image features in the five modes are used to represent object appearance. Since a nonsingular covariance matrix is a SPD matrix lying on a connected Riemannian manifold, the LogEuclidean Riemannian metric is used for statistics on the covariance matrices of image features. Further, we present an effective online LogEuclidean Riemannian subspace learning algorithm which models the appearance changes of an object by incrementally learning a loworder LogEuclidean eigenspace representation through adaptively updating the sample mean and eigenbasis. Tracking is then led by the Bayesian state inference framework in which a particle filter is used for propagating sample distributions over the time. Theoretic analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed framework. 1.
Spatiotemporal covariance descriptors for action and gesture recognition
 In IEEE Workshop on Applications of Computer Vision (WACV
, 2013
"... We propose a new action and gesture recognition method based on spatiotemporal covariance descriptors and a weighted Riemannian locality preserving projection approach that takes into account the curved space formed by the descriptors. The weighted projection is then exploited during boosting to cr ..."
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Cited by 13 (3 self)
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We propose a new action and gesture recognition method based on spatiotemporal covariance descriptors and a weighted Riemannian locality preserving projection approach that takes into account the curved space formed by the descriptors. The weighted projection is then exploited during boosting to create a final multiclass classification algorithm that employs the most useful spatiotemporal regions. We also show how the descriptors can be computed quickly through the use of integral video representations. Experiments on the UCF sport, CK+ facial expression and Cambridge hand gesture datasets indicate superior performance of the proposed method compared to several recent stateoftheart techniques. The proposed method is robust and does not require additional processing of the videos, such as foreground detection, interestpoint detection or tracking. 1.
On landmark selection and sampling in highdimensional data analysis. arXiv:0906.4582v1[stat.ML
, 2009
"... In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the lowdimensional structure often prevalent in highdimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasi ..."
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Cited by 10 (3 self)
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In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the lowdimensional structure often prevalent in highdimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nyström extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of realworld examples drawn from the field of computer vision, whereby lowdimensional manifold structure is shown to emerge from highdimensional video data streams.
Curvature Analysis of Frequency Modulated Manifolds in Dimensionality Reduction
"... Recent advances in the analysis of highdimensional signal data have triggered an increasing interest in geometrybased methods for nonlinear dimensionality reduction (NDR). In many applications, highdimensional datasets typically contain redundant information, and NDR methods are important for an ..."
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Cited by 5 (5 self)
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Recent advances in the analysis of highdimensional signal data have triggered an increasing interest in geometrybased methods for nonlinear dimensionality reduction (NDR). In many applications, highdimensional datasets typically contain redundant information, and NDR methods are important for an efficient analysis of their properties. During the last few years, concepts from differential geometry were used to create a whole new range of NDR methods. In the construction of such geometrybased strategies, a natural question is to understand their interaction with classical and modern signal processing tools (convolution transforms, Fourier analysis, wavelet functions). In particular, an important task is the analysis of the incurred geometrical deformation when applying signal transforms to the elements of a dataset. In this paper, we propose the concepts of frequency modulation maps and modulation manifolds for the construction of particular datasets relevant in signal processing and NDR. Moreover, we design a numerical algorithm for analyzing geometrical properties of the modulation manifolds, with a particular focus on their scalar curvature. Finally, in our numerical examples, we apply the resulting geometrybased analysis algorithm to two model problems, where we present geometrical and topological effects of relevance in manifold learning.
Maximal linear embedding for dimensionality reduction
, 2011
"... Over the past few decades, dimensionality reduction has been widely exploited in computer vision and pattern analysis. This paper proposes a simple but effective nonlinear dimensionality reduction algorithm, named Maximal Linear Embedding (MLE). MLE learns a parametric mapping to recover a single g ..."
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Cited by 5 (2 self)
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Over the past few decades, dimensionality reduction has been widely exploited in computer vision and pattern analysis. This paper proposes a simple but effective nonlinear dimensionality reduction algorithm, named Maximal Linear Embedding (MLE). MLE learns a parametric mapping to recover a single global lowdimensional coordinate space and yields an isometric embedding for the manifold. Inspired by geometric intuition, we introduce a reasonable definition of locally linear patch, Maximal Linear Patch (MLP), which seeks to maximize the local neighborhood in which linearity holds. The input data are first decomposed into a collection of local linear models, each depicting an MLP. These local models are then aligned into a global coordinate space, which is achieved by applying MDS to some randomly selected landmarks. The proposed alignment method, called Landmarksbased Global Alignment (LGA), can efficiently produce a closedform solution with no risk of local optima. It just involves some smallscale eigenvalue problems, while most previous aligning techniques employ timeconsuming iterative optimization. Compared with traditional methods such as ISOMAP and LLE, our MLE yields an explicit modeling of the intrinsic variation modes of the observation data. Extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm.
Manifoldbased learning and synthesis
 IEEE Trans. Syst., Man, Cybern. B, Cybern
, 2009
"... Abstract—This paper proposes a new approach to analyze highdimensional data set using lowdimensional manifold. This manifoldbased approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in man ..."
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Cited by 4 (0 self)
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Abstract—This paper proposes a new approach to analyze highdimensional data set using lowdimensional manifold. This manifoldbased approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in many existing algorithms. The first problem is the local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. For the outofsample data points, the proposed approach gives simple solutions to transverse between the input space and the feature space. In addition, this method can be used to estimate the underlying dimension and is robust to the number of neighbors. Experiments on both lowdimensional data and real image data are performed to illustrate the theory. Index Terms—Dimensionality reduction, learning and synthesis, manifold learning, outofsample extension. I.
Manifold Précis: An Annealing Technique for Diverse Sampling of Manifolds
"... In this paper, we consider the Précis problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and prefiltering. We formulate a general theory which encompas ..."
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Cited by 4 (2 self)
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In this paper, we consider the Précis problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and prefiltering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also nonEuclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealingbased iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach. 1
A Review of Subspace Segmentation: Problem, Nonlinear Approximations, and Applications to Motion Segmentation
, 2013
"... The subspace segmentation problem is fundamental in many applications. The goal is to cluster data drawn from an unknown union of subspaces. In this paper we state the problem and describe its connection to other areas of mathematics and engineering. We then review the mathematical and algorithmic m ..."
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Cited by 4 (1 self)
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The subspace segmentation problem is fundamental in many applications. The goal is to cluster data drawn from an unknown union of subspaces. In this paper we state the problem and describe its connection to other areas of mathematics and engineering. We then review the mathematical and algorithmic methods created to solve this problem and some of its particular cases. We also describe the problem of motion tracking in videos and its connection to the subspace segmentation problem and compare the various techniques for solving it.
Endoscopic Video Manifolds for Targeted Optical Biopsy
 IEEE Trans. on Medical Imaging
, 2012
"... Abstract—Gastrointestinal (GI) endoscopy is a widely used clinical procedure for screening and surveillance of digestive tract diseases ranging from Barrett’s Oesophagus to oesophageal cancer. Current surveillance protocol consists of periodic endoscopic examinations performed in 3–4 month interva ..."
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Cited by 2 (0 self)
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Abstract—Gastrointestinal (GI) endoscopy is a widely used clinical procedure for screening and surveillance of digestive tract diseases ranging from Barrett’s Oesophagus to oesophageal cancer. Current surveillance protocol consists of periodic endoscopic examinations performed in 3–4 month intervals including expert’s visual assessment and biopsies taken from suspicious tissue regions. Recent development of a new imaging technology, called probebased confocal laser endomicroscopy (pCLE), enabled the acquisition of in vivo optical biopsies without removing any tissue sample. Besides its several advantages, i.e., noninvasiveness, realtime and in vivo feedback, optical biopsies involve a new challenge for the endoscopic expert. Due to their noninvasive nature, optical biopsies do not leave any scar on the tissue and therefore recognition of the previous optical biopsy sites in surveillance endoscopy becomes very challenging. In this work, we introduce a clustering and classification framework to facilitate retargeting previous optical biopsy sites in surveillance upper GIendoscopies. A new representation of endoscopic videos based on manifold learning, “endoscopic video manifolds ” (EVMs), is proposed. The low dimensional EVM representation is adapted to facilitate two different clustering tasks; i.e., clustering of informative frames and patient specific endoscopic segments, only by changing the similarity measure. Each step of the proposed framework is validated on three in vivo patient datasets containing 1834, 3445, and 1546 frames, corresponding to endoscopic videos of 73.36, 137.80, and 61.84 s, respectively. Improvements achieved by the introduced EVM representation are demonstrated by quantitative analysis in comparison to the original image representation and principal component analysis. Final experiments evaluating the complete framework demonstrate the feasibility of the proposed method as a promising step for assisting the endoscopic expert in retargeting the optical biopsy sites. Index Terms—Classification, clustering, gastrointestinal (GI)endoscopy, manifold learning, optical biopsy.
Parallel vector field embedding
 Journal of Machine Learning Research
"... We propose a novel local isometry based dimensionality reduction method from the perspective of vector fields, which is called parallel vector field embedding (PFE). We first give a discussion on local isometry and global isometry to show the intrinsic connection between parallel vector fields and i ..."
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Cited by 2 (2 self)
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We propose a novel local isometry based dimensionality reduction method from the perspective of vector fields, which is called parallel vector field embedding (PFE). We first give a discussion on local isometry and global isometry to show the intrinsic connection between parallel vector fields and isometry. The problem of finding an isometry turns out to be equivalent to finding orthonormal parallel vector fields on the data manifold. Therefore, we first find orthonormal parallel vector fields by solving a variational problem on the manifold. Then each embedding function can be obtained by requiring its gradient field to be as close to the corresponding parallel vector field as possible. Theoretical results show that our method can precisely recover the manifold if it is isometric to a connected open subset of Euclidean space. Both synthetic and real data examples demonstrate the effectiveness of our method even if there is heavy noise and high curvature.