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Global nonrigid alignment of surface sequences
 Int. J. Comput. Vis
, 2012
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Cited by 21 (8 self)
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Your article is published under the Creative Commons Attribution license which allows users to read, copy, distribute and make derivative works, as long as the author of the original work is cited. You may selfarchive this article on your own website, an institutional repository or funder’s repository and make it publicly available immediately.
Global Motion Estimation from Point Matches
"... Abstract—Multiview structure recovery from a collection of images requires the recovery of the positions and orientations of the cameras relative to a global coordinate system. Our approach recovers camera motion as a sequence of two global optimizations. First, pairwise Essential Matrices are used ..."
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Cited by 15 (4 self)
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Abstract—Multiview structure recovery from a collection of images requires the recovery of the positions and orientations of the cameras relative to a global coordinate system. Our approach recovers camera motion as a sequence of two global optimizations. First, pairwise Essential Matrices are used to recover the global rotations by applying robust optimization using either spectral or semidefinite programming relaxations. Then, we directly employ feature correspondences across images to recover the global translation vectors using a linear algorithm based on a novel decomposition of the Essential Matrix. Our method is efficient and, as demonstrated in our experiments, achieves highly accurate results on collections of real images for which ground truth measurements are available. Keywordsstructure from motion; 3D reconstruction; camera motion estimation; convex relaxation; linear estimation I.
Network Principles for SfM: Disambiguating Repeated Structures with Local Context
"... Repeated features are common in urban scenes. Many objects, such as clock towers with nearly identical sides, or domes with strong radial symmetries, pose challenges for structure from motion. When similar but distinct features are mistakenly equated, the resulting 3D reconstructions can have errors ..."
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Cited by 8 (1 self)
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Repeated features are common in urban scenes. Many objects, such as clock towers with nearly identical sides, or domes with strong radial symmetries, pose challenges for structure from motion. When similar but distinct features are mistakenly equated, the resulting 3D reconstructions can have errors ranging from phantom walls and superimposed structures to a complete failure to reconstruct. We present a new approach to solving such problems by considering the local visibility structure of such repeated features. Drawing upon network theory, we present a new way of scoring features using a measure of local clustering. Our model leads to a simple, fast, and highly scalable technique for disambiguating repeated features based on an analysis of an underlying visibility graph, without relying on explicit geometric reasoning. We demonstrate our method on several very large datasets drawn from Internet photo collections, and compare it to a more traditional geometrybased disambiguation technique. 1.
Global Fusion of Relative Motions for Robust, Accurate and Scalable Structure from Motion
 ICCV, SYDNEY: AUSTRALIA
, 2013
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Simultaneous Multiple Rotation Averaging using Lagrangian Duality
, 2012
"... Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotation ..."
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Cited by 7 (0 self)
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Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations. In this paper we propose a simple procedure based on Lagrangian duality that can be used to verify global optimality of a local solution, by solving a linear system of equations. We show experimentally on real and synthetic data that unless the noise levels are extremely high this procedure always generates the globally optimal solution.
Robust Global Translations with 1DSfM
"... Abstract. We present a simple, effective method for solving structure from motion problems by averaging epipolar geometries. Based on recent successes in solving for global camera rotations using averaging schemes, we focus on the problem of solving for 3D camera translations given a network of noi ..."
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Cited by 5 (0 self)
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Abstract. We present a simple, effective method for solving structure from motion problems by averaging epipolar geometries. Based on recent successes in solving for global camera rotations using averaging schemes, we focus on the problem of solving for 3D camera translations given a network of noisy pairwise camera translation directions (or 3D point observations). To do this well, we have two main insights. First, we propose a method for removing outliers from problem instances by solving simpler lowdimensional subproblems, which we refer to as 1DSfM problems. Second, we present a simple, principled averaging scheme. We demonstrate this new method in the wild on Internet photo collections.
ShapeFit: Exact location recovery from corrupted pairwise directions
"... Abstract Let t 1 , . . . , t n ∈ R d and consider the location recovery problem: given a subset of pairwise direction observations {( , where a constant fraction of these observations are arbitrarily corrupted, find {t i } n i=1 up to a global translation and scale. We propose a novel algorithm for ..."
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Abstract Let t 1 , . . . , t n ∈ R d and consider the location recovery problem: given a subset of pairwise direction observations {( , where a constant fraction of these observations are arbitrarily corrupted, find {t i } n i=1 up to a global translation and scale. We propose a novel algorithm for the location recovery problem, which consists of a simple convex program over dn real variables. We prove that this program recovers a set of n i.i.d. Gaussian locations exactly and with high probability if the observations are given by an ErdősRényi graph, d is large enough, and provided that at most a constant fraction of observations involving any particular location are adversarially corrupted. We also prove that the program exactly recovers Gaussian locations for d = 3 if the fraction of corrupted observations at each location is, up to polylogarithmic factors, at most a constant. Both of these recovery theorems are based on a set of deterministic conditions that we prove are sufficient for exact recovery.
Point Track Creation in Unordered Image Collections Using GomoryHu Trees
"... Geometric reconstruction from image collections is a classical computer vision problem. The problem essentially consists of two steps; First, the identification of matches and assembling of point tracks, and second, multiple view geometry computations. In this paper we address the problem of constru ..."
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Geometric reconstruction from image collections is a classical computer vision problem. The problem essentially consists of two steps; First, the identification of matches and assembling of point tracks, and second, multiple view geometry computations. In this paper we address the problem of constructing point tracks using graph theoretical algorithms. From standard descriptor matches between all pairs of images we construct a graph representing all image points and all possible matches. Using GomoryHu trees we make cuts in the graph to construct the individual point tracks. We present both theoretical and experimental results (on real datasets) that clearly demonstrates the benefits of using our approach.
ShapeFit: Exact location recovery from corrupted pairwise directions
, 2015
"... Let t1,..., tn ∈ Rd and consider the location recovery problem: given a subset of pairwise direction observations {(ti − tj)/‖ti − tj‖2}i<j∈[n]×[n], where a constant fraction of these observations are arbitrarily corrupted, find {ti}ni=1 up to a global translation and scale. We propose a novel a ..."
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Let t1,..., tn ∈ Rd and consider the location recovery problem: given a subset of pairwise direction observations {(ti − tj)/‖ti − tj‖2}i<j∈[n]×[n], where a constant fraction of these observations are arbitrarily corrupted, find {ti}ni=1 up to a global translation and scale. We propose a novel algorithm for the location recovery problem, which consists of a simple convex program over dn real variables. We prove that this program recovers a set of n i.i.d. Gaussian locations exactly and with high probability if the observations are given by an ErdösRényi graph, d is large enough, and provided that at most a constant fraction of observations involving any particular location are adversarially corrupted. 1
Optimizing the Viewing Graph for StructurefromMotion
"... The viewing graph represents a set of views that are related by pairwise relative geometries. In the context of StructurefromMotion (SfM), the viewing graph is the input to the incremental or global estimation pipeline. Much effort has been put towards developing robust algorithms to overcome po ..."
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The viewing graph represents a set of views that are related by pairwise relative geometries. In the context of StructurefromMotion (SfM), the viewing graph is the input to the incremental or global estimation pipeline. Much effort has been put towards developing robust algorithms to overcome potentially inaccurate relative geometries in the viewing graph during SfM. In this paper, we take a fundamentally different approach to SfM and instead focus on improving the quality of the viewing graph before applying SfM. Our main contribution is a novel optimization that improves the quality of the relative geometries in the viewing graph by enforcing loop consistency constraints with the epipolar point transfer. We show that this optimization greatly improves the accuracy of relative poses in the viewing graph and removes the need for filtering steps or robust algorithms typically used in global SfM methods. In addition, the optimized viewing graph can be used to efficiently calibrate cameras at scale. We combine our viewing graph optimization and focal length calibration into a global SfM pipeline that is more efficient than existing approaches. To our knowledge, ours is the first global SfM pipeline capable of handling uncalibrated image sets. 1.