Spectral Solution of Large-Scale Extrinsic Camera Calibration as a Graph Embedding Problem

Brand, Matthew; Antone, Matthew; Teller, Seth

doi:10.1007/978-3-540-24671-8_21

Cited by 48 publications

(99 citation statements)

References 9 publications

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“…[42,3,26,24,57]. On the other hand, global estimation of camera locations, specifically for large, unordered sets of images, usually suffers from instability to errors in feature correspondences (resulting in solutions clustered around a few locations, as for [3,9,51]), sensitivity to outliers in pairwise line measurements (e.g., the ℓ ∞ approach of [50,34]) and susceptibility to local solutions in non-convex formulations (e.g., [24]). Hence, a well-formulated, robust, efficient method for global location estimation (scalable to large sets of images) with provable convergence and stability guarantees is of high value.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…Early works of [23,9] on location estimation reduce the problem to that of solving a set of linear equations that originate from the pairwise line measurements. Finding solutions to these linear systems can be done in a computationally efficient manner.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…However, this non-convex method is susceptible to convergence to local optima. The spectral formulation of [3], which is based on a novel decomposition of the essential matrix and is similar to [23,9] in its formulation of the problem, yields an efficient linear solution for the locations, though, it also suffers from spurious clustered solutions. Yet another formulation related to our work is the quasi-convex formulation of [50], which relies on (iteratively) optimizing a functional of the ℓ ∞ norm and requires the estimation of the signed directions of the pairwise lines, i.e.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…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]. The solution of [52] is taken as the ground truth.…”

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

“…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 , .…”

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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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Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

Section: Camera Location Estimation In Sfmmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Stable Camera Motion Estimation Using Convex Programming

Özyeşil¹,

Singer²,

Basri³

2015

SIAM J. Imaging Sci.

113

View full text Add to dashboard Cite

show abstract

ShapeFit: Exact Location Recovery from Corrupted Pairwise Directions

Hand

Lee

Voroninski

2017

Comm Pure Appl Math

101

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A Survey of Distributed Computer Vision Algorithms

Radke

2010

Handbook of Ambient Intelligence and Smart Environments

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Recent years have seen great advances in computer vision research dealing with large numbers of cameras. However, many multi-camera computer vision algorithms assume that the information from all cameras is losslessly communicated to a central processor that solves the problem. This assumption is unrealistic for emerging wireless camera networks, which may contain processors with limited capability, antennas with limited power, and batteries with limited life. In this chapter, we will overview algorithms that solve computer vision problems in a distributed manner, making them well-suited for implementation on a visual sensor network.

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Spectral Solution of Large-Scale Extrinsic Camera Calibration as a Graph Embedding Problem

Cited by 48 publications

References 9 publications

Stable Camera Motion Estimation Using Convex Programming

Stable Camera Motion Estimation Using Convex Programming

ShapeFit: Exact Location Recovery from Corrupted Pairwise Directions

A Survey of Distributed Computer Vision Algorithms

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