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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
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.
NONINCREMENTAL DERIVATION OF SCALE AND POSE FROM A NETWORK OF RELATIVE ORIENTATIONS
"... Commission III ..."
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Direct Structure Estimation for 3D Reconstruction
"... Most conventional structurefrommotion (SFM) techniques require camera pose estimation before computing any scene structure. In this work we show that when combined with single/multiple homography estimation, the general Euclidean rigidity constraint provides a simple formulation for scene stru ..."
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Most conventional structurefrommotion (SFM) techniques require camera pose estimation before computing any scene structure. In this work we show that when combined with single/multiple homography estimation, the general Euclidean rigidity constraint provides a simple formulation for scene structure recovery without explicit camera pose computation. This direct structure estimation (DSE) opens a new way to design a SFM system that reverses the order of structure and motion estimation. We show that this alternative approach works well for recovering scene structure and camera poses from sideway motion given planar or general manmade scenes. 1.
ROBUST GLOBAL MOTION ESTIMATIONWITH MATRIX COMPLETION
"... In this paper we address the problem of estimating the attitudes and positions of a set of cameras in an external coordinate system. Starting from a conventional global structurefrommotion pipeline, we present some substantial advances. In order to detect outlier relative rotations extracted from ..."
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In this paper we address the problem of estimating the attitudes and positions of a set of cameras in an external coordinate system. Starting from a conventional global structurefrommotion pipeline, we present some substantial advances. In order to detect outlier relative rotations extracted from pairs of views, we improve a stateoftheart algorithm based on cycle consistency, by introducing cycle bases. We estimate the angular attitudes of the cameras by proposing a novel gradient descent algorithm based on lowrank matrix completion, that naturally copes with the case of missing data. As for position recovery, we analyze an existing technique from a theoretical point of view, providing some insights on the conditions that guarantee solvability. We provide experimental results on both synthetic and real image sequences for which ground truth calibration is provided. 1
3D MODELING FROMMULTIVIEWS IMAGES FOR CULTURAL HERITAGE IN WATPHO, THAILAND
"... In Thailand, there are several types of (tangible) cultural heritages. This work focuses on 3D modeling of the heritage objects from multiviews images. The images are acquired by using a DSLR camera which costs around $1,500 (camera and lens). Comparing with a 3D laser scanner, the camera is cheape ..."
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In Thailand, there are several types of (tangible) cultural heritages. This work focuses on 3D modeling of the heritage objects from multiviews images. The images are acquired by using a DSLR camera which costs around $1,500 (camera and lens). Comparing with a 3D laser scanner, the camera is cheaper and lighter than the 3D scanner. Hence, the camera is available for public users and convenient for accessing narrow areas. The acquired images consist of various sculptures and architectures in WatPho which is a Buddhist temple located behind the Grand Palace (Bangkok, Thailand). WatPho is known as temple of the reclining Buddha and the birthplace of traditional Thai massage. To compute the 3D models, a diagram is separated into following steps; Data acquisition, Image matching, Image calibration and orientation, Dense matching and Point cloud processing. For the initial work, small heritages less than 3 meters height are considered for the experimental results. A set of multiviews images of an interested object is used as input data for 3D modeling. In our experiments, 3D models are obtained from MICMAC (open source) software developed by IGN, France. The output of 3D models will be represented by using standard formats of 3D point clouds and triangulated surfaces such as.ply,.off,.obj, etc. To compute for the efficient 3D models, postprocessing techniques are required for the final results e.g. noise reduction, surface simplification and reconstruction. The reconstructed 3D models can be provided for public access such as website, DVD, printed materials. The high accurate 3D models can also be used as reference data of the heritage objects that must be restored due to deterioration of a lifetime, natural disasters, etc. 1.