Iterative projective reconstruction from multiple views

Mahamud, S.; Hebert, Martial

doi:10.1109/cvpr.2000.854872

Cited by 79 publications

(47 citation statements)

References 12 publications

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“…(6) and their method relies on fundamental matrices to solve for the projective depths. Subsequently, Heyden et al [16], Ueshiba & Tomita [17], and Mahamud & Hebert [18] proposed iterative methods to solve the Sturm/Triggs projective factorization problem.…”

Section: Previous Workmentioning

confidence: 99%

Multiple Camera Calibration Using Robust Perspective Factorization

Zaharescu

Horaud

Ronfard

et al. 2006

Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)

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In this paper we address the problem of recovering structure and motion from a large number of intrinsically calibrated perspective cameras. We describe a method that combines (1) weak-perspective reconstruction in the presence of noisy and missing data and (2) an algorithm that updates weakperspective reconstruction to perspective reconstruction by incrementally estimating the projective depths. The method also solves for the reversal ambiguity associated with affine factorization techniques. The method has been successfully applied to the problem of calibrating the external parameters (position and orientation) of several multiple-camera setups. Results obtained with synthetic and experimental data compare favourably with results obtained with nonlinear minimization such as bundle adjustment.

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Section: Previous Workmentioning

confidence: 99%

Multiple Camera Calibration Using Robust Perspective Factorization

Zaharescu

Horaud

Ronfard

et al. 2006

Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)

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“…It is known that 3D-reconstruction from point correspondences can be achieved by means of an iterative version of the so-called factorization algorithm [15,12]. It involves fitting a 4-dimensional subspace to data.…”

Section: Real-image Applicationmentioning

confidence: 99%

A Linear Solution to 1-Dimensional Subspace Fitting under Incomplete Data

Ackermann

Rosenhahn

2011

Computer Vision – ACCV 2010

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Abstract. Computing a 1-dimensional linear subspace is an important problem in many computer vision algorithms. Its importance stems from the fact that maximizing a linear homogeneous equation system can be interpreted as subspace fitting problem. It is trivial to compute the solution if all coefficients of the equation system are known, yet for the case of incomplete data, only approximation methods based on variations of gradient descent have been developed. In this work, an algorithm is presented in which the data is embedded in projective spaces. We prove that the intersection of these projective spaces is identical to the desired subspace. Whereas other algorithms approximate this subspace iteratively, computing the intersection of projective spaces defines a linear problem. This solution is therefore not an approximation but exact in the absence of noise. We derive an upper boundary on the number of missing entries the algorithm can handle. Experiments with synthetic data confirm that the proposed algorithm successfully fits subspaces to data even if more than 90% of the data is missing. We demonstrate an example application with real image sequences.

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“…Their methods were later extended in [2] to the recursive case in which more images can be incorporated when new tracked feature points become available. Another iterative approach that is similar to [2] but that leads to a different optimization problem is recently reported in [14].…”

Section: Introductionmentioning

confidence: 99%