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99
A Riemannian Framework for Tensor Computing
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2006
"... Positive definite symmetric matrices (socalled tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affineinvariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of ..."
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Cited by 286 (27 self)
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Positive definite symmetric matrices (socalled tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affineinvariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular manifold of constant curvature without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have
Human Detection via Classification on Riemannian Manifolds
 IN IEEE CONF. COMP. VISION AND PATTERN RECOGNITION (CVPR
, 2007
"... We present a new algorithm to detect humans in still images utilizing covariance matrices as object descriptors. Since these descriptors do not lie on a vector space, well known machine learning techniques are not adequate to learn the classifiers. The space of ddimensional nonsingular covariance ..."
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Cited by 170 (7 self)
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We present a new algorithm to detect humans in still images utilizing covariance matrices as object descriptors. Since these descriptors do not lie on a vector space, well known machine learning techniques are not adequate to learn the classifiers. The space of ddimensional nonsingular covariance matrices can be represented as a connected Riemannian manifold. We present a novel approach for classifying points lying on a Riemannian manifold by incorporating the a priori information about the geometry of the space. The algorithm is tested on INRIA human database where superior detection rates are observed over the previous approaches.
Pedestrian Detection Via Classification on Riemannian Manifolds
, 2008
"... Detecting different categories of objects in image and video content is one of the fundamental tasks in computer vision research. The success of many applications such as visual surveillance, image retrieval, robotics, autonomous vehicles, and smart cameras are conditioned on the accuracy of the det ..."
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Cited by 141 (3 self)
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Detecting different categories of objects in image and video content is one of the fundamental tasks in computer vision research. The success of many applications such as visual surveillance, image retrieval, robotics, autonomous vehicles, and smart cameras are conditioned on the accuracy of the detection process. Two main processing steps can be distinguished in a typical object detection algorithm. The first task is feature extraction, in which the most informative object descriptors regarding the detection process are obtained from the visual content. The second task is detection, in which the obtained object descriptors are utilized in a classification framework to detect the objects of interest. The feature extraction methods can be further categorized into two groups based on the representation. The first group of methods is the sparse representations, where a set of representative local regions is obtained as the result of an interest point detection algorithm. Reliable interest points should encapsulate valuable information about the local image content and remain stable under changes, such as in viewpoint and/or illumination. There exists an extensive literature on interest point detectors, and [14],[18],[21],[25], and [27] are only a few of the most commonly used methods that satisfy consistency over a large range of operating conditions.
Covariance tracking using model update based on lie algebra
 in IEEE Conference on Computer Vision and Pattern Recognition
, 2006
"... We propose a simple and elegant algorithm to track nonrigid objects using a covariance based object description and a Lie algebra based update mechanism. We represent an object window as the covariance matrix of features, therefore we manage to capture the spatial and statistical properties as well ..."
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Cited by 127 (8 self)
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We propose a simple and elegant algorithm to track nonrigid objects using a covariance based object description and a Lie algebra based update mechanism. We represent an object window as the covariance matrix of features, therefore we manage to capture the spatial and statistical properties as well as their correlation within the same representation. The covariance matrix enables efficient fusion of different types of features and modalities, and its dimensionality is small. We incorporated a model update algorithm using the Lie group structure of the positive definite matrices. The update mechanism effectively adapts to the undergoing object deformations and appearance changes. The covariance tracking method does not make any assumption on the measurement noise and the motion of the tracked objects, and provides the global optimal solution. We show that it is capable of accurately detecting the nonrigid, moving objects in nonstationary camera sequences while achieving a promising detection rate of 97.4 percent.
H.: Person reidentification by descriptive and discriminative classification
 In: Proc. SCIA. (2011
"... Abstract. Person reidentification, i.e., recognizing a single person across spatially disjoint cameras, is an important task in visual surveillance. Existing approaches either try to find a suitable description of the appearance or learn a discriminative model. Since these different representationa ..."
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Cited by 44 (5 self)
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Abstract. Person reidentification, i.e., recognizing a single person across spatially disjoint cameras, is an important task in visual surveillance. Existing approaches either try to find a suitable description of the appearance or learn a discriminative model. Since these different representational strategies capture a large extent of complementary information we propose to combine both approaches. First, given a specific query, we rank all samples according to a featurebased similarity, where appearance is modeled by a set of region covariance descriptors. Next, a discriminative model is learned using boosting for feature selection, which provides a more specific classifier. The proposed approach is demonstrated on two datasets, where we show that the combination of a generic descriptive statistical model and a discriminatively learned featurebased model attains considerably better results than the individual models alone. In addition, we give a comparison to the stateoftheart on a publicly available benchmark dataset. 1
Simultaneous multiple 3D motion estimation via mode finding on Lie groups
 In Proc. 10th intl. conf. on computer vision
, 2005
"... We propose a new method to estimate multiple rigid motions from noisy 3D point correspondences in the presence of outliers. The method does not require prior specification of number of motion groups and estimates all the motion parameters simultaneously. We start with generating samples from the rig ..."
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Cited by 39 (11 self)
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We propose a new method to estimate multiple rigid motions from noisy 3D point correspondences in the presence of outliers. The method does not require prior specification of number of motion groups and estimates all the motion parameters simultaneously. We start with generating samples from the rigid motion distribution. The motion parameters are then estimated via mode finding operations on the sampled distribution. Since rigid motions do not lie on a vector space, classical statistical methods can not be used for mode finding. We develop a mean shift algorithm which estimates modes of the sampled distribution using the Lie group structure of the rigid motions. We also show that proposed mean shift algorithm is general and can be applied to any distribution having a matrix Lie group structure. Experimental results on synthetic and real image data demonstrate the superior performance of the algorithm. 1.
A Riemannian approach to diffusion tensor images segmentation
 IN PROC. IPMI, 591–602
, 2005
"... We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images. Our approach is grounded on the theoretically wellfounded differential geometrical properties of the space of multivariate normal distributions. We introduce a variational formulation, in ..."
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Cited by 24 (4 self)
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We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images. Our approach is grounded on the theoretically wellfounded differential geometrical properties of the space of multivariate normal distributions. We introduce a variational formulation, in the level set framework, to estimate the optimal segmentation according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. Moreover, we must respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the diffusion tensor image. We validate our algorithm on synthetic data and report interesting results on real datasets. We focus on two structures of the white matter with different properties and respectively known as the corpus callosum and the corticospinal tract.
Saliency Driven Total Variation Segmentation
"... This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of ..."
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Cited by 24 (1 self)
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This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of the image by applying affinity propagation clustering to efficiently calculated local color and texture models. Each salient region then serves as an independent initialization for a figure/ground segmentation. Segmentation is done by minimizing a convex energy functional based on weighted total variation leading to a global optimal solution. Each salient region provides an accurate figure/ground segmentation highlighting different parts of the image. These highly redundant results are combined into one composite segmentation by analyzing local segmentation certainty. Our formulation is quite general, and other salient region detection algorithms in combination with any semisupervised figure/ground segmentation approach can be used. We demonstrate the high quality of our method on the wellknown Berkeley segmentation database. Furthermore we show that our method can be used to provide good spatial support for recognition frameworks. 1.
Covariance Tracking using Model Update Based on Means on . . .
 PROC. IEEE CONF. ON COMPUTER VISION AND PATTERN RECOGNITION
, 2005
"... We propose a simple and elegant algorithm to track nonrigid objects using a covariance based object description and a Lie algebra based update mechanism. We represent an object window as the covariance matrix of features, therefore we manage to capture the spatial and statistical properties as well ..."
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Cited by 21 (1 self)
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We propose a simple and elegant algorithm to track nonrigid objects using a covariance based object description and a Lie algebra based update mechanism. We represent an object window as the covariance matrix of features, therefore we manage to capture the spatial and statistical properties as well as their correlation within the same representation. The covariance matrix enables efficient fusion of different types of features and modalities, and its dimensionality is small. We incorporated a model update algorithm using the Lie group structure of the positive definite matrices. The update mechanism effectively adapts to the undergoing object deformations and appearance changes. The covariance tracking method does not make any assumption on the measurement noise and the motion of the tracked objects, and provides the global optimal solution. We show that it is capable of accurately detecting the nonrigid, moving objects in nonstationary camera sequences while achieving a promising detection rate of 97.4 percent.