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81
A generic framework for tracking using particle filter with dynamic shape prior
 IEEE Trans. Image Processing
, 2007
"... Abstract—Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dyn ..."
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Cited by 13 (2 self)
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Abstract—Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter. The PF also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background. Index Terms—Dynamic shape prior, geometric active contours, particle filters (PFs), tracking, unscented Kalman filter. I.
Manifold Clustering of Shapes
 In Proc. of ICDM
, 2006
"... Shape clustering can significantly facilitate the automatic labeling of objects present in image collections. For example, it could outline the existing groups of pathological cells in a bank of cytoimages; the groups of species on photographs collected from certain aerials; or the groups of object ..."
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Cited by 11 (2 self)
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Shape clustering can significantly facilitate the automatic labeling of objects present in image collections. For example, it could outline the existing groups of pathological cells in a bank of cytoimages; the groups of species on photographs collected from certain aerials; or the groups of objects observed on surveillance scenes from an office building. Here we demonstrate that a nonlinear projection algorithm such as Isomap can attract together shapes of similar objects, suggesting the existence of isometry between the shape space and a low dimensional nonlinear embedding. Whenever there is a relatively small amount of noise in the data, the projection forms compact, convex clusters that can easily be learned by a subsequent partitioning scheme. We further propose a modification of the Isomap projection based on the concept of degreebounded minimum spanning trees. The proposed approach is demonstrated to move apart bridged clusters and to alleviate the effect of noise in the data. 1.
A computational model of multidimensional shape
 International Journal of Computer Vision, Online First
, 2010
"... We develop a computational model of shape that extends existing Riemannian models of shape of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. ..."
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Cited by 11 (0 self)
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We develop a computational model of shape that extends existing Riemannian models of shape of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. The model employs a representation of shape based on the discrete exterior derivative of parametrizations over a finite simplicial complex. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a localglobal formulation that accounts for regional shape differences and integrates them into a global measure of dissimilarity. The Riemannian shape spaces provide a common framework to treat numerous problems such as the statistical modeling of shapes, the comparison of shapes associated with different individuals and groups, and modeling and simulation of dynamical shapes. We give multiple examples of geodesic interpolations and illustrations of the use of the model in brain mapping, particularly, the analysis of anatomical variation based on neuroimaging data. 1
Statistical Shape Models Using ElasticString Representations
 Proceedings of Asian Conference on Computer Vision
, 2006
"... Abstract. To develop statistical models for shapes, we utilize an elastic string representation where curves (denoting shapes) can bend and locally stretch (or compress) to optimally match each other, resulting in geodesic paths on shape spaces. We develop statistical models for capturing variabil ..."
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Cited by 10 (3 self)
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Abstract. To develop statistical models for shapes, we utilize an elastic string representation where curves (denoting shapes) can bend and locally stretch (or compress) to optimally match each other, resulting in geodesic paths on shape spaces. We develop statistical models for capturing variability under the elasticstring representation. The basic idea is to project observed shapes onto the tangent spaces at sample means, and use finitedimensional approximations of these projections to impose probability models. We investigate the use of principal components for dimension reduction, termed tangent PCA or TPCA, and study (i) Gaussian, (ii) mixture of Gaussian, and (iii) nonparametric densities to model the observed shapes. We validate these models using hypothesis testing, statistics of likelihood functions, and random sampling. It is demonstrated that a mixture of Gaussian model on TPCA captures best the observed shapes. 1
Unsupervised Riemannian clustering of probability density functions
 In ECML PKKD
, 2008
"... Abstract. We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the squareroot reparametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this reparametrization is th ..."
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Cited by 9 (1 self)
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Abstract. We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the squareroot reparametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this reparametrization is that different families of pdfs form different submanifolds of the unit Hilbert sphere. Therefore, the problem of clustering pdfs reduces to the problem of clustering multiple submanifolds on the unit Hilbert sphere. We solve this problem by first learning a lowdimensional representation of the pdfs using generalizations of local nonlinear dimensionality reduction algorithms from Euclidean to Riemannian spaces. Then, by assuming that the pdfs from different groups are separated, we show that the null space of a matrix built from the local representation gives the segmentation of the pdfs. We also apply of our approach to the texture segmentation problem in computer vision.
A computational approach to fisher information geometry with applications to image analysis
 Proceedings of the EMMCVPR
, 2005
"... Abstract. We develop a computational approach to nonparametric Fisher information geometry and algorithms to calculate geodesic paths in this geometry. Geodesics are used to quantify divergence of probability density functions and to develop tools of data analysis in information manifolds. The met ..."
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Cited by 8 (0 self)
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Abstract. We develop a computational approach to nonparametric Fisher information geometry and algorithms to calculate geodesic paths in this geometry. Geodesics are used to quantify divergence of probability density functions and to develop tools of data analysis in information manifolds. The methodology developed is applied to several image analysis problems using a representation of textures based on the statistics of multiple spectral components. Histograms of filter responses are viewed as elements of a nonparametric statistical manifold, and local texture patterns are compared using information geometry. Appearancebased object recognition experiments, as well as regionbased image segmentation experiments are carried out to test both the representation and metric. The proposed representation of textures is also applied to the development of a spectral cartoon model of images. 1
Statistical analysis on manifolds and its applications to video analysis
, 2010
"... The analysis and interpretation of video data is an important component of modern vision applications such as biometrics, surveillance, motionsynthesis and webbased user interfaces. A common requirement among these very different applications is the ability to learn statistical models of appearance ..."
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Cited by 7 (3 self)
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The analysis and interpretation of video data is an important component of modern vision applications such as biometrics, surveillance, motionsynthesis and webbased user interfaces. A common requirement among these very different applications is the ability to learn statistical models of appearance and motion from a collection of videos, and then use them for recognizing actions or persons in a new video. These applications in video analysis require statistical inference methods to be devised on nonEuclidean spaces or more formally on manifolds. This chapter outlines a broad survey of applications in video analysis that involve manifolds. We develop the required mathematical tools needed to perform statistical inference on manifolds and show their effectiveness in real videounderstanding applications.
Nearestneighbor search algorithms on noneuclidean manifolds for computer vision applications
 in ICVGIP
, 2010
"... ABSTRACT Nearestneighbor searching is a crucial component in many computer vision applications such as face recognition, object recognition, texture classification, and activity recognition. When large databases are involved in these applications, it is also important to perform these searches in ..."
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ABSTRACT Nearestneighbor searching is a crucial component in many computer vision applications such as face recognition, object recognition, texture classification, and activity recognition. When large databases are involved in these applications, it is also important to perform these searches in a fast manner. Depending on the problem at hand, nearest neighbor strategies need to be devised over feature and model spaces which in many cases are not Euclidean in nature. Thus, metrics that are tuned to the geometry of this space are required which are also known as geodesics. In this paper, we address the problem of fast nearest neighbor searching in nonEuclidean spaces, where in addition to dealing with the large size of the dataset, the significant computational load involves geodesic computations. We study the applicability of the various classes of nearest neighbor algorithms toward this end. Exact nearest neighbor methods that rely solely on the existence of a metric can be extended, albeit with a huge computational cost. We derive an approximate method of searching via approximate embeddings using the logarithmic map. We study the error incurred in such an embedding and show that it performs well in real experiments.
A Phase Field Model Incorporating Generic and Specific Prior Knowledge Applied to Road Network Extraction from
 VHR Satellite Images, in "Proc. British Machine Vision Conference (BMVC
, 2007
"... We address the problem of updating road maps in dense urban areas by extracting the main road network from a very high resolution (VHR) satellite image. Our model of the region occupied by the road network in the image is innovative. It incorporates three different types of prior geometric knowledge ..."
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Cited by 7 (3 self)
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We address the problem of updating road maps in dense urban areas by extracting the main road network from a very high resolution (VHR) satellite image. Our model of the region occupied by the road network in the image is innovative. It incorporates three different types of prior geometric knowledge: generic boundary smoothness constraints, equivalent to a standard active contour prior; knowledge of the geometric properties of road networks (i.e. that they occupy regions composed of long, lowcurvature segments joined at junctions), equivalent to a higherorder active contour prior; and knowledge of the road network at an earlier date derived from GIS data, similar to other ‘shape priors ’ in the literature. In addition, we represent the road network region as a ‘phase field’, which offers a number of important advantages over other region modelling frameworks. All three types of prior knowledge prove important for overcoming the complexity of geometric ‘noise ’ in VHR images. Promising results and a comparison with several other techniques demonstrate the effectiveness of our approach. 1
Banachlike metrics and metrics of compact sets.
, 2007
"... We present and study a family of metrics on the space of compact subsets of � N (that we call “shapes”). These metrics are “geometric”, that is, they are independent of rotation and translation; and these metrics enjoy many interesting properties, as, for example, the existence of minimal geodesics. ..."
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Cited by 6 (3 self)
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We present and study a family of metrics on the space of compact subsets of � N (that we call “shapes”). These metrics are “geometric”, that is, they are independent of rotation and translation; and these metrics enjoy many interesting properties, as, for example, the existence of minimal geodesics. We view our space of shapes as a subset of Banach (or Hilbert) manifolds: so we can define a “tangent manifold ” to shapes, and (in a very weak form) talk of a “Riemannian Geometry” of shapes. Some of the metrics that we propose are topologically equivalent to the Hausdorff metric; but at the same time, they are more “regular”, since we can hope for a local uniqueness of minimal geodesics. We also study general properties of the metrics obtained by isometrically identifying a generic metric space with a subset of a Banach space and we obtain a rigidity result.