Multi-view structure computation without explicitly estimating motion

Li, Hongdong

doi:10.1109/cvpr.2010.5540005

Cited by 21 publications

(45 citation statements)

References 30 publications

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“…The problem can be modeled by a graph, where the points are associated to the nodes, and the direction constraints to the edges. As such, this problem has appeared under similar forms in different settings, such as (to cite a few) sensor network localization [2], [6], [17] and formation control [4], [7], [16], [20] in controls and robotics, Structure from Motion [5], [12] in computer vision, and graph drawings [14] in discrete mathematics. See Figure 1 for a schematic example.…”

Section: Introductionmentioning

confidence: 97%

Rigid components identification and rigidity control in bearing-only localization using the graph cycle basis

Tron

Carlone

Dellaert

et al. 2015

2015 American Control Conference (ACC)

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Bearing-only localization can be formulated in terms of optimal graph embedding: for each node in the graph, find the coordinates that satisfy as close as possible all the bearing-only constraints on the edges. If the graph is parallel rigid, this can be done via spectral methods. When the graph is not rigid the solution is ambiguous, as different subsets of vertices can be scaled differently. It is then important to first partition the problem into maximal rigid components. In this paper we show that the cycle basis matrix of the graph can be used for this task, and that it can also be used to provide a more intuitive look at graph rigidity. We can explain, for instance, why triangulated graphs are rigid and why graphs with longer cycles may loose this property. Furthermore, we can obtain tools for enforcing rigidity by controlling the addition of new measurements.

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Section: Introductionmentioning

confidence: 97%

Rigid components identification and rigidity control in bearing-only localization using the graph cycle basis

Tron

Carlone

Dellaert

et al. 2015

2015 American Control Conference (ACC)

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“…Also, an SDP approach is introduced in [40] in order to jointly estimate motion and structure from noisy feature correspondences. We note that our work is significantly different from [40]: While we use parallel rigidity, [40] employs classical rigidity, leading to completely different SDP formulations. [3,9], for the Notre-Dame data set from [52].…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…In contrast to the sensitivity of the quasi-convex method of [50] to outliers, the method in [57] is based on optimizing a functional of the ℓ 2 norm, and hence produces more accurate location estimates. Additionally, [40] introduces a framework based on classical rigidity theory (involving pairwise distance information), which aims to identify rigid instances of the joint motion and structure estimation problem. Also, an SDP approach is introduced in [40] in order to jointly estimate motion and structure from noisy feature correspondences.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…Additionally, [40] introduces a framework based on classical rigidity theory (involving pairwise distance information), which aims to identify rigid instances of the joint motion and structure estimation problem. Also, an SDP approach is introduced in [40] in order to jointly estimate motion and structure from noisy feature correspondences. We note that our work is significantly different from [40]: While we use parallel rigidity, [40] employs classical rigidity, leading to completely different SDP formulations.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

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Stable Camera Motion Estimation Using Convex Programming

Özyeşil¹,

Singer²,

Basri³

2015

SIAM J. Imaging Sci.

113

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Abstract. We study the inverse problem of estimating n locations t 1 , t 2 , . . . , tn (up to global scale, translation and negation) in R d from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy measurements of ± t i −t j t i −t j 2 for some pairs (i, j) (where the signs are unknown). This problem is at the core of the structure from motion (SfM) problem in computer vision, where the t i 's represent camera locations in R 3 . The noiseless version of the problem, with exact line measurements, has been considered previously under the general title of parallel rigidity theory, mainly in order to characterize the conditions for unique realization of locations. For noisy pairwise line measurements, current methods tend to produce spurious solutions that are clustered around a few locations. This sensitivity of the location estimates is a well-known problem in SfM, especially for large, irregular collections of images.In this paper we introduce a semidefinite programming (SDP) formulation, specially tailored to overcome the clustering phenomenon. We further identify the implications of parallel rigidity theory for the location estimation problem to be well-posed, and prove exact (in the noiseless case) and stable location recovery results. We also formulate an alternating direction method to solve the resulting semidefinite program, and provide a distributed version of our formulation for large numbers of locations. Specifically for the camera location estimation problem, we formulate a pairwise line estimation method based on robust camera orientation and subspace estimation. Lastly, we demonstrate the utility of our algorithm through experiments on real images.Key words. Structure from motion, parallel rigidity, semidefinite programming, convex relaxation, alternating direction method of multipliers AMS subject classifications. 68T45, 52C25, 90C22, 90C251. Introduction. Global positioning of n objects from partial information about their relative locations is prevalent in many applications spanning fields such as sensor network localization [8,58,16,18], structural biology [31], and computer vision [27,9]. A well-known instance that attracted much attention from both the theoretical and algorithmic perspectives is that of estimating the locations t 1 , t 2 , . . . , t n ∈ R d from their pairwise Euclidean distances t i − t j 2 . In this case, the large body of literature in rigidity theory (cf. [4, 54]) provides conditions under which the localization is unique given a set of noiseless distance measurements. Also, much progress has been made with algorithms that estimate positions from noisy distances, starting with classical multidimensional scaling [48] to the more recent semidefinite programming (SDP) approaches (see, e.g., [8,7]).Here we consider a different global positioning problem, in which the locations t 1 , . . . , t n need to be estimated from a subset of (potentially noisy) measurements of the pairwise lines that connect them (see Figure 1.1 for a ...

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“…We take a similar strategy to [13] to "convexify" the constraints, proposing to minimize the trace norm of Y rather than enforcing the rank-constraint implicitly. Finally we reach a trace norm minimization problem as:…”

Section: Single View 3d Reconstructionmentioning

confidence: 99%

Single-shot extrinsic calibration of a generically configured RGB-D camera rig from scene constraints

Yang

Dai

et al. 2013

2013 IEEE International Symposium on Mixed and Augmented Reality (ISMAR)

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With the increasing use of commodity RGB-D cameras for computer vision, robotics, mixed and augmented reality and other areas, it is of significant practical interest to calibrate the relative pose between a depth (D) camera and an RGB camera in these types of setups. In this paper, we propose a new single-shot, correspondence-free method to extrinsically calibrate a generically configured RGB-D camera rig. We formulate the extrinsic calibration problem as one of geometric 2D-3D registration which exploits scene constraints to achieve single-shot extrinsic calibration. Our method first reconstructs sparse point clouds from a singleview 2D image. These sparse point clouds are then registered with dense point clouds from the depth camera. Finally, we directly optimize the warping quality by evaluating scene constraints in 3D point clouds. Our single-shot extrinsic calibration method does not require correspondences across multiple color images or across different modalities and it is more flexible than existing methods. The scene constraints can be very simple and we demonstrate that a scene containing three sheets of paper is sufficient to obtain reliable calibration and with a lower geometric error than existing methods.

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Multi-view structure computation without explicitly estimating motion

Abstract: Abstract

Cited by 21 publications

References 30 publications

Rigid components identification and rigidity control in bearing-only localization using the graph cycle basis

Rigid components identification and rigidity control in bearing-only localization using the graph cycle basis

Stable Camera Motion Estimation Using Convex Programming

Single-shot extrinsic calibration of a generically configured RGB-D camera rig from scene constraints

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