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Global Fusion of Relative Motions for Robust, Accurate and Scalable Structure from Motion
 ICCV, SYDNEY: AUSTRALIA
, 2013
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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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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.
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
A GLOBAL APPROACH FOR IMAGE ORIENTATION USING LIE ALGEBRAIC ROTATION AVERAGING AND CONVEX L ∞ MINIMISATION
"... In this paper we present a new global image orientation approach for a set of multiple overlapping images with given homologous point tuples which is based on a twostep procedure. The approach is independent on initial values, robust with respect to outliers and yields the global minimum solution u ..."
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In this paper we present a new global image orientation approach for a set of multiple overlapping images with given homologous point tuples which is based on a twostep procedure. The approach is independent on initial values, robust with respect to outliers and yields the global minimum solution under relatively mild constraints. The first step of the approach consists of the estimation of global rotation parameters by averaging relative rotation estimates for image pairs (these are determined from the homologous points via the essential matrix in a preprocessing step). For the averaging we make use of algebraic group theory in which rotations, as part of the special orthogonal group SO(3), form a Lie group with a Riemannian manifold structure. This allows for a mapping to the local Euclidean tangent space of SO(3), the Lie algebra. In this space the redundancy of relative orientations is used to compute an average of the absolute rotation for each image and furthermore to detect and eliminate outliers. In the second step translation parameters and the object coordinates of the homologous points are estimated within a convex L ∞ optimisation, in which the rotation parameters are kept fixed. As an optional third step the results can be used as initial values for a final bundle adjustment that does not suffer from bad initialisation and quickly converges to a globally optimal solution. We investigate our approach for global image orientation based on synthetic data. The results are compared to a robust least squares bundle adjustment. In this way we show that our approach is independent of initial values and more robust against outliers than a conventional bundle adjustment. 1.
Statistical Pose Averaging with Nonisotropic and Incomplete Relative Measurements
"... Abstract. In the last few years there has been a growing interest in optimization methods for averaging pose measurements between a set of cameras or objects (obtained, for instance, using epipolar geometry or pose estimation). Alas, existing approaches do not take into consideration that measureme ..."
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Abstract. In the last few years there has been a growing interest in optimization methods for averaging pose measurements between a set of cameras or objects (obtained, for instance, using epipolar geometry or pose estimation). Alas, existing approaches do not take into consideration that measurements might have different uncertainties (i.e., the noise might not be isotropically distributed), or that they might be incomplete (e.g., they might be known only up to a rotation around a fixed axis). We propose a Riemannian optimization framework which addresses these cases by using covariance matrices, and test it on synthetic and real data.