Projective Bundle Adjustment from Arbitrary Initialization Using the Variable Projection Method

Hong, Je Hyeong; Zach, Christopher; Fitzgibbon, Andrew; Cipolla, Roberto

doi:10.1007/978-3-319-46448-0_29

Cited by 18 publications

(19 citation statements)

References 23 publications

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“…As has been noted previously [9,36,37], the affine case is a very stable and useful approximation to perspective projection. The reader is referred to the supplementary material for a detailed review of this camera model.…”

Section: Point Correspondence Loss L Corrmentioning

confidence: 62%

3D Surface Reconstruction by Pointillism

Wiles

Zisserman

2019

Lecture Notes in Computer Science

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The objective of this work is to infer the 3D shape of an object from a single image. We use sculptures as our training and test bed, as these have great variety in shape and appearance. To achieve this we build on the success of multiple view geometry (MVG) which is able to accurately provide correspondences between images of 3D objects under varying viewpoint and illumination conditions, and make the following contributions: first, we introduce a new loss function that can harness image-to-image correspondences to provide a supervisory signal to train a deep network to infer a depth map. The network is trained end-to-end by differentiating through the camera. Second, we develop a processing pipeline to automatically generate a large scale multi-view set of correspondences for training the network. Finally, we demonstrate that we can indeed obtain a depth map of a novel object from a single image for a variety of sculptures with varying shape/texture, and that the network generalises at test time to new domains (e.g. synthetic images).

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Section: Point Correspondence Loss L Corrmentioning

confidence: 62%

3D Surface Reconstruction by Pointillism

Wiles

Zisserman

2019

Lecture Notes in Computer Science

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“…For [22] we counted only its running time (excluding the running time of the initialization method). For [10] we set a time limit of 12 hours. We ran all the methods on the same computer under the same conditions.…”

Section: Resultsmentioning

confidence: 99%

“…The paper demonstrated both superior re-projection accuracy and running time, compared to existing methods. VarPro [10]. This method first applies affine bundle adjustment followed by projective BA.…”

Section: Resultsmentioning

confidence: 99%

“…Update F (t) using ( 7) For k = 1, ..., m, update B (t) k using (9) For k = 1, ..., m, update Γ (t) k using (10) end For k = 1, ..., m, retrieve camera matrices for triplet τ (k) (Corollary 1) P ← Bring cameras to a global projective frame of reference (Sec. 3.2) X ← Triangulate points from points tracks P, X ← Refine solution using Bundle Adjustment Return P, X…”

Section: Methodsmentioning

confidence: 99%

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GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

Kasten

Geifman

Galun

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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This paper addresses the problem of recovering projective camera matrices from collections of fundamental matrices in multiview settings. We make two main contributions. First, given n 2 fundamental matrices computed for n images, we provide a complete algebraic characterization in the form of conditions that are both necessary and sufficient to enabling the recovery of camera matrices. These conditions are based on arranging the fundamental matrices as blocks in a single matrix, called the n-view fundamental matrix, and characterizing this matrix in terms of the signs of its eigenvalues and rank structures. Secondly, we propose a concrete algorithm for projective structure-frommotion that utilizes this characterization. Given a complete or partial collection of measured fundamental matrices, our method seeks camera matrices that minimize a global algebraic error for the measured fundamental matrices. In contrast to existing methods, our optimization, without any initialization, produces a consistent set of fundamental matrices that corresponds to a unique set of cameras (up to a choice of projective frame). Our experiments indicate that our method achieves state of the art performance in both accuracy and running time.

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“…In structure from motion problems, where the main interest is the extraction of camera matrices from B and 3D points from C, this is typically the preferred option [5]. In a series of recent papers Hong et al showed that optimization with the VarPro algorithm is remarkably robust to local minima converging to accurate solutions [17,18,19]. In [21] they further showed how uncalibrated rigid structure from motion with a proper perspective projection can be solved within a factorization framework.…”

Section: Introductionmentioning

confidence: 99%

Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion

Iglesias¹,

Olsson²,

Örnhag³

2020

Preprint

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Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weighted nuclear norm priors, direct optimization over the elements of the matrix is typically used. Due to non-differentiability of the resulting objective function, first order sub-gradient or splitting methods are predominantly used. While these offer rapid iterations it is well known that they become inefficent near the minimum due to zig-zagging and in practice one is therefore often forced to settle for an approximate solution.In this paper we show that more accurate results can in many cases be achieved with 2nd order methods. Our main result shows how to construct bilinear formulations, for a general class of regularizers including weighted nuclear norm penalties, that are provably equivalent to the original problems. With these formulations the regularizing function becomes twice differentiable and 2nd order methods can be applied. We show experimentally, on a number of structure from motion problems, that our approach outperforms state-of-the-art methods.

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Projective Bundle Adjustment from Arbitrary Initialization Using the Variable Projection Method

Cited by 18 publications

References 23 publications

3D Surface Reconstruction by Pointillism

3D Surface Reconstruction by Pointillism

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion

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