Angle Independent Bundle Adjustment Refinement

Zhang, Jeffrey; Aliaga, Daniel G.; Boutin, Mireille; Insley, Robert G.

doi:10.1109/3dpvt.2006.30

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…The proposed method works in 2D and is only theorized to extend to 3D; further, it is very dependent on accurate intrinsic camera calibration. Zhang et al [20] have also eliminated camera orientation from the traditional bundle adjustment formulation. Our approach is similar to theirs in the sense of omitting camera orientation parameters by using an invariant-based formulation.…”

Section: Previous Workmentioning

confidence: 99%

“…Thus, we seek a formulation that encapsulates equations ( 4) and ( 5) but with less camera parameters and that can be evaluated using either world-space coordinates or canonical space coordinates. As described in Zhang et al [20], this can be found by using Fels-Olver moving frame method [1] to find a functionally independent generating set of invariants. Functionally independent means they are not redundant and being a generating set implies that any other reconstruction equation set which is independent of camera orientation can be derived from these equations.…”

Section: Reformulating 3d Reconstructionmentioning

confidence: 99%

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Simplifying the Reconstruction of 3D Models using Parameter Elimination

Aliaga

Zhang

Boutin³

2007

2007 IEEE 11th International Conference on Computer Vision

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Reconstructing large models from images is a significant challenge for computer vision, computer graphics, and related fields. In this paper, we present an approach for simplifying the reconstruction process by mathematically eliminating external camera parameters. This results in less parameters to estimate and in an overall significantly more robust and accurate reconstruction. We reformulate the problem in such a manner as to be able to identify invariants, eliminate superfluous parameters, and measure the performance of our formulation under various conditions. We compare a two-step camera orientation-free method, where the majority of the points are reconstructed using a linear equation set, and a camera position-andorientation free method, using a degree-two equation set. Both approaches use a full perspective camera and are applied to synthetic and real-world datasets.

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Section: Previous Workmentioning

confidence: 99%

Section: Reformulating 3d Reconstructionmentioning

confidence: 99%

Simplifying the Reconstruction of 3D Models using Parameter Elimination

Aliaga

Zhang

Boutin³

2007

2007 IEEE 11th International Conference on Computer Vision

Self Cite

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A Fast Adjustment Algorithm Based on the Theory of One by One Parameter Estimation

Yuan

Liu

et al. 2010

2010 International Conference on E-Product E-Service and E-Entertainment

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Pose-Free Structure From Motion Using Depth From Motion Constraints

Zhang

Boutin

Aliaga

2011

IEEE Trans. on Image Process.

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Abstract-Structure from motion (SFM) is the problem of recovering the geometry of a scene from a stream of images taken from unknown viewpoints. One popular approach to estimate the geometry of a scene is to track scene features on several images and reconstruct their position in 3D. During this process, the unknown camera pose must also be recovered. Unfortunately recovering the pose can be an ill-conditioned problem which, in turn, can make the SFM problem difficult to solve accurately. We propose an alternative formulation of the SFM problem with fixed internal camera parameters known a priori. In this formulation, obtained by algebraic variable elimination, the external camera pose parameters do not appear. As a result, the problem is better conditioned in addition to involving much fewer variables. Variable elimination is done in three steps. First, we take the standard SFM equations in projective coordinates and eliminate the camera orientations from the equations. We then further eliminate the camera center positions. Finally, we also eliminate all 3D point positions coordinates, except for their depths with respect to the camera center, thus obtaining a set of simple polynomial equations of degree two and three. We show that, when there are merely a few points and pictures, these "depthonly equations" can be solved in a global fashion using homotopy methods. We also show that, in general, these same equations can be used to formulate a pose-free cost function to refine SFM solutions in a way that is more accurate than by minimizing the total reprojection error, as done when using the bundle adjustment method. The generalization of our approach to the case of varying internal camera parameters is briefly discussed.

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Angle Independent Bundle Adjustment Refinement

Abstract: Abstract

Cited by 4 publications

References 12 publications

Simplifying the Reconstruction of 3D Models using Parameter Elimination

Simplifying the Reconstruction of 3D Models using Parameter Elimination

A Fast Adjustment Algorithm Based on the Theory of One by One Parameter Estimation

Pose-Free Structure From Motion Using Depth From Motion Constraints

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