Results 21  30
of
2,041
Robust Principal Component Analysis?
, 2009
"... This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the sparse co ..."
Abstract

Cited by 137 (6 self)
 Add to MetaCart
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the ℓ1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.
Wide Baseline Stereo Matching
 In Proc. ICCV
, 1998
"... The objective of this work is to enlarge the class of camera motions for which epipolar geometry and image correspondences can be computed automatically. This facilitates matching between quite disparate views  wide baseline stereo. Two extensions are made to the current small baseline algorithms ..."
Abstract

Cited by 134 (15 self)
 Add to MetaCart
The objective of this work is to enlarge the class of camera motions for which epipolar geometry and image correspondences can be computed automatically. This facilitates matching between quite disparate views  wide baseline stereo. Two extensions are made to the current small baseline algorithms: first, and most importantly, a viewpoint invariant measure is developed for assessing the affinity of corner neighbourhoods over image pairs; second, algorithms are given for generating putative corner matches between image pairs using local homographies. Two novel infrastructure developments are also described: the automatic generation of local homographies, and the combination of possibly conflicting sets of matches prior to RANSAC estimation. The wide baseline matching algorithm is demonstrated on a number of image pairs with varying relative motion, and for different scene types. All processing is automatic. 1 Introduction It is now possible to automatically compute the epipolar geom...
Robust parameter estimation in computer vision
 SIAM Reviews
, 1999
"... Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite smallscale noise in the data, occasional largescale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techni ..."
Abstract

Cited by 129 (10 self)
 Add to MetaCart
Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite smallscale noise in the data, occasional largescale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techniques, some borrowed from the statistics literature and others described in the computer vision literature, have been used in solving these parameter estimation problems. Ideally, these techniques should effectively ignore the outliers and measurements from other populations, treating them as outliers, when estimating the parameters of a single population. Two frequently used techniques are leastmedian of
Generalized principal component analysis (GPCA)
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... This paper presents an algebrogeometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a ..."
Abstract

Cited by 116 (29 self)
 Add to MetaCart
This paper presents an algebrogeometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a highdimensional space and with an unknown number of subspaces are also presented. Our experiments on lowdimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as Ksubspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.
Modeling the World from Internet Photo Collections
 INT J COMPUT VIS
, 2007
"... There are billions of photographs on the Internet, comprising the largest and most diverse photo collection ever assembled. How can computer vision researchers exploit this imagery? This paper explores this question from the standpoint of 3D scene modeling and visualization. We present structurefro ..."
Abstract

Cited by 115 (5 self)
 Add to MetaCart
There are billions of photographs on the Internet, comprising the largest and most diverse photo collection ever assembled. How can computer vision researchers exploit this imagery? This paper explores this question from the standpoint of 3D scene modeling and visualization. We present structurefrommotion and imagebased rendering algorithms that operate on hundreds of images downloaded as a result of keywordbased image search queries like “Notre Dame ” or “Trevi Fountain.” This approach, which we call Photo Tourism, has enabled reconstructions of numerous wellknown world sites. This paper presents these algorithms and results as a first step towards 3D modeling of the world’s wellphotographed sites, cities, and landscapes from Internet imagery, and discusses key open problems and challenges for the research community.
Superior Augmented Reality Registration by Integrating Landmark Tracking and Magnetic Tracking
, 1996
"... Accurate registration between real and virtual objects is crucial for augmented reality applications. Existing tracking methods are individually inadequate: magnetic trackers are inaccurate, mechanical trackers are cumbersome, and visionbased trackers are computationally problematic. We present a h ..."
Abstract

Cited by 113 (3 self)
 Add to MetaCart
Accurate registration between real and virtual objects is crucial for augmented reality applications. Existing tracking methods are individually inadequate: magnetic trackers are inaccurate, mechanical trackers are cumbersome, and visionbased trackers are computationally problematic. We present a hybrid tracking method that combines the accuracy of visionbased tracking with the robustness of magnetic tracking without compromising realtime performance or usability. We demonstrate excellent registration in three sample applications.
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 ..."
Abstract

Cited by 112 (17 self)
 Add to MetaCart
“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.
Fast and Globally Convergent Pose Estimation From Video Images
, 1998
"... Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effecti ..."
Abstract

Cited by 109 (4 self)
 Add to MetaCart
Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers. ChienPing Lu, Silicon Graphics Inc. cplu@engr.sgi.com y Greg Hager, Department of Computer...
Automatic Panoramic Image Stitching using Invariant Features
, 2007
"... This paper concerns the problem of fully automated panoramic image stitching. Though the 1D problem (single axis of rotation) is well studied, 2D or multirow stitching is more difficult. Previous approaches have used human input or restrictions on the image sequence in order to establish matching ..."
Abstract

Cited by 108 (2 self)
 Add to MetaCart
This paper concerns the problem of fully automated panoramic image stitching. Though the 1D problem (single axis of rotation) is well studied, 2D or multirow stitching is more difficult. Previous approaches have used human input or restrictions on the image sequence in order to establish matching images. In this work, we formulate stitching as a multiimage matching problem, and use invariant local features to find matches between all of the images. Because of this our method is insensitive to the ordering, orientation, scale and illumination of the input images. It is also insensitive to noise images that are not part of a panorama, and can recognise multiple panoramas in an unordered image dataset. In addition to providing more detail, this paper extends our previous work in the area (Brown and Lowe, 2003) by introducing gain compensation and automatic straightening steps.
Visual servo control Part I: basic approaches
 IEEE ROBOTICS AND AUTOMATION MAGAZINE
, 2006
"... This article is the first of a twopart series on the topic of visual servo control—using computer vision data in the servo loop to control the motion of a robot. In the present article, we describe the basic techniques that are by now well established in the field. We first give a general overview ..."
Abstract

Cited by 105 (28 self)
 Add to MetaCart
This article is the first of a twopart series on the topic of visual servo control—using computer vision data in the servo loop to control the motion of a robot. In the present article, we describe the basic techniques that are by now well established in the field. We first give a general overview of the formulation of the visual servo control problem. We then describe the two archetypal visual servo control schemes: imagebased and positionbased visual servo control. Finally, we discuss performance and stability issues that pertain to these two schemes, motivating the second article in the series, in which we consider advanced techniques.