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39
Partial and approximate symmetry detection for 3D geometry
 ACM TRANSACTIONS ON GRAPHICS
, 2006
"... “Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a com ..."
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Cited by 176 (26 self)
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“Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important highlevel information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.
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.
Nonlinear Mean Shift over Riemannian Manifolds
, 2009
"... The original mean shift algorithm is widely applied for nonparametric clustering in vector spaces. In this paper we generalize it to data points lying on Riemannian manifolds. This allows us to extend mean shift based clustering and filtering techniques to a large class of frequently occurring non ..."
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Cited by 37 (1 self)
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The original mean shift algorithm is widely applied for nonparametric clustering in vector spaces. In this paper we generalize it to data points lying on Riemannian manifolds. This allows us to extend mean shift based clustering and filtering techniques to a large class of frequently occurring nonvector spaces in vision. We present an exact algorithm and prove its convergence properties as opposed to previous work which approximates the mean shift vector. The computational details of our algorithm are presented for frequently occurring classes of manifolds such as matrix Lie groups, Grassmann manifolds, essential matrices and symmetric positive definite matrices. Applications of the mean shift over these manifolds are shown.
Intrinsic Mean Shift for Clustering on Stiefel and Grassmann Manifolds
"... The mean shift algorithm, which is a nonparametric density estimator for detecting the modes of a distribution on a Euclidean space, was recently extended to operate on analytic manifolds. The extension is extrinsic in the sense that the inherent optimization is performed on the tangent spaces of th ..."
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Cited by 25 (0 self)
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The mean shift algorithm, which is a nonparametric density estimator for detecting the modes of a distribution on a Euclidean space, was recently extended to operate on analytic manifolds. The extension is extrinsic in the sense that the inherent optimization is performed on the tangent spaces of these manifolds. This approach specifically requires the use of the exponential map at each iteration. This paper presents an alternative mean shift formulation, which performs the iterative optimization “on ” the manifold of interest and intrinsically locates the modes via consecutive evaluations of a mapping. In particular, these evaluations constitute a modified gradient ascent scheme that avoids the computation of the exponential maps for Stiefel and Grassmann manifolds. The performance of our algorithm is evaluated by conducting extensive comparative studies on synthetic data as well as experiments on object categorization and segmentation of multiple motions. 1.
Group Motion Segmentation Using a SpatioTemporal Driving Force Model
"... We consider the ‘group motion segmentation ’ problem and provide a solution for it. The group motion segmentation problem aims at analyzing motion trajectories of multiple objects in video and finding among them the ones involved in a ‘group motion pattern’. This problem is motivated by and serves a ..."
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Cited by 13 (1 self)
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We consider the ‘group motion segmentation ’ problem and provide a solution for it. The group motion segmentation problem aims at analyzing motion trajectories of multiple objects in video and finding among them the ones involved in a ‘group motion pattern’. This problem is motivated by and serves as the basis for the ‘multiobject activity recognition ’ problem, which is currently an active research topic in event analysis and activity recognition. Specifically, we learn a SpatioTemporal Driving Force Model to characterize a group motion pattern and design an approach for segmenting the group motion. We illustrate the approach using videos of American football plays, where we identify the offensive players, who follow an offensive motion pattern, from motions of all players in the field. Experiments using GaTech Football Play Dataset validate the effectiveness of the segmentation algorithm. 1.
Estimation of the Epipole using Optical Flow at Antipodal Points
"... This paper develops an algorithm for estimating the epipole or direction of translation of a moving monocular observer. To this end, we use constraints arising from two points that are antipodal on the image sphere. The antipodal point condition is necessary for decoupling rotation from translation. ..."
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Cited by 9 (2 self)
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This paper develops an algorithm for estimating the epipole or direction of translation of a moving monocular observer. To this end, we use constraints arising from two points that are antipodal on the image sphere. The antipodal point condition is necessary for decoupling rotation from translation. One such pair of points constrains the epipole to lie on a plane, and using two pairs of points, we have two such planes. The intersection of these two planes gives an estimate of the epipole. This means we require image motion measurements at two pairs of antipodal points to obtain an estimate. Repeating this will yield a set of possible solutions and a variety of methods could be applied to obtain a robust and refined estimate from this set. One robust and simple method is chosen for illustrative purposes and results on real images are shown. With real sequences, results of below 2 ◦ error in the estimate of the epipole can be obtained. Since antipodal points on an image sphere are required, this algorithm must use some kind of omnidirectional or large fieldofview (FOV) sensor. 1.
Votingbased pose estimation for robotic assembly using a 3D sensor
 in Proc. IEEE Int. Conf. Robotics and Automation
"... Abstract: We propose a votingbased pose estimation algorithm applicable to 3D sensors, which are fast replacing their 2D counterparts in many robotics, computer vision, and gaming applications. It was recently shown that a pair of oriented 3D points, which are points on the object surface with norm ..."
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Cited by 9 (3 self)
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Abstract: We propose a votingbased pose estimation algorithm applicable to 3D sensors, which are fast replacing their 2D counterparts in many robotics, computer vision, and gaming applications. It was recently shown that a pair of oriented 3D points, which are points on the object surface with normals, in a voting framework enables fast and robust pose estimation. Although oriented surface points are discriminative for objects with sufficient curvature changes, they are not compact and discriminative enough for many industrial and realworld objects that are mostly planar. As edges play the key role in 2D registration, depth discontinuities are crucial in 3D. In this paper, we investigate and develop a family of pose estimation algorithms that better exploit this boundary information. In addition to oriented surface points, we use two other primitives: boundary points with directions and boundary line segments. Our experiments show that these carefully chosen primitives encode more information compactly and thereby provide higher accuracy for a wide class of industrial parts and enable faster computation. We demonstrate a practical robotic binpicking system using the proposed algorithm and a 3D sensor.
GPCA with denoising: A momentsbased convex approach
 In IEEE Conference on Computer Vision and Pattern Recognition (CVPR
, 2010
"... This paper addresses the problem of segmenting a combination of linear subspaces and quadratic surfaces from sample data points corrupted by (not necessarily small) noise. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimi ..."
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Cited by 8 (0 self)
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This paper addresses the problem of segmenting a combination of linear subspaces and quadratic surfaces from sample data points corrupted by (not necessarily small) noise. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Exploiting the linear matrix inequality based characterization of the moments problem and appealing to well known convex relaxations of rank leads to an overall semidefinite optimization problem. We apply our method to problems such as simultaneous 2D motion segmentation and motion segmentation from two perspective views and illustrate that our formulation substantially reduces the noise sensitivity of existing approaches. 1.
Semiintrinsic mean shift on riemannian manifolds
 Proc. European Conference on Computer Vision (ECCV), Lecture Notes in Computer Science
, 2012
"... Abstract. The original mean shift algorithm [1] on Euclidean spaces (MS) was extended in [2] to operate on general Riemannian manifolds. This extension is extrinsic (ExtMS) since the mode seeking is performed on the tangent spaces [3], where the underlying curvature is not fully considered (tangen ..."
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Cited by 7 (2 self)
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Abstract. The original mean shift algorithm [1] on Euclidean spaces (MS) was extended in [2] to operate on general Riemannian manifolds. This extension is extrinsic (ExtMS) since the mode seeking is performed on the tangent spaces [3], where the underlying curvature is not fully considered (tangent spaces are only valid in a small neighborhood). In [3] was proposed an intrinsic mean shift designed to operate on two particular Riemannian manifolds (IntGSMS), i.e. Grassmann and Stiefel manifolds (using manifolddedicated density kernels). It is then natural to ask whether mean shift could be intrinsically extended to work on a large class of manifolds. We propose a novel paradigm to intrinsically reformulate the mean shift on general Riemannian manifolds. This is accomplished by embedding the Riemannian manifold into a Reproducing Kernel Hilbert Space (RKHS) by using a general and mathematically wellfounded Riemannian kernel function, i.e. heat kernel [4]. The key issue is that when the data is implicitly mapped to the Hilbert space, the curvature of the manifold is taken into account (i.e. exploits the underlying information of the data). The inherent optimization is then performed on the embedded space. Theoretic analysis and experimental results demonstrate the promise and effectiveness of this novel paradigm. 1