An iterative factorization method for projective structure and motion from image sequences

Heyden, Anders; Berthilsson, Rikard; Sparr, Gunnar

doi:10.1016/s0262-8856(99)00002-5

Cited by 101 publications

(83 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This approach, commonly called factorization, was initially proposed only for simplified camera models that are not able to fully capture the pinhole projection (Tomasi and Kanade 1992;Weinshall and Tomasi 1995). More recently, similar approaches have been presented also for perspective cameras (Sturm and Triggs 1996;Heyden et al 1999), however their need for having each point visible in each camera severely reduces their usability in practical scenarios where occlusion is usually abundant. For this reason incremental methods, which allow to add one or a few images at a time, are by far more popular in SfM applications.…”

Section: Structure From Motionmentioning

confidence: 99%

Imposing Semi-Local Geometric Constraints for Accurate Correspondences Selection in Structure from Motion: A Game-Theoretic Perspective

2011

View full text Add to dashboard Cite

Most Structure from Motion pipelines are based on the iterative refinement of an initial batch of feature correspondences. Typically this is performed by selecting a set of match candidates based on their photometric similarity; an initial estimate of camera intrinsic and extrinsic parameters is then computed by minimizing the reprojection error. Finally, outliers in the initial correspondences are filtered by enforcing some global geometric property such as the epipolar constraint. In the literature many different approaches have been proposed to deal with each of these three steps, but almost invariably they separate the first inlier selection step, which is based only on local image properties, from the enforcement of global geometric consistency. Unfortunately, these two steps are not independent since outliers can lead to inaccurate parameter estimation or even prevent convergence, leading to the well known sensitivity of all filtering approaches to the number of outliers, especially in the presence of structured noise, which can arise, for example, when the images present several repeated patterns. In this paper we introduce a novel stereo correspondence selection scheme that casts the problem into a Game-Theoretic framework in order to guide the inlier selection towards a consistent subset of correspondences. This is done by enforcing geometric constraints that do not depend on full knowledge of the motion parameters but rather on some semi-local property that can be estimated from the local appearance of A. Albarelli ( ) · E. Rodolà · A. Torsello Dipartimento di Scienze Ambientali, Informatica, Statistica, Università Ca' Foscari Venezia, Venice, Italy e-mail: albarelli@unive.it E. Rodolà e-mail: rodola@dsi.unive.it A. Torsello e-mail: torsello@unive.it the image features. The practical effectiveness of the proposed approach is confirmed by an extensive set of experiments and comparisons with state-of-the-art techniques.

show abstract

Section: Structure From Motionmentioning

confidence: 99%

Imposing Semi-Local Geometric Constraints for Accurate Correspondences Selection in Structure from Motion: A Game-Theoretic Perspective

2011

View full text Add to dashboard Cite

show abstract

“…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%

“…If both the variables λ ij and the camera matrices P are unknown, a projective reconstruction can be estimated by initializing the λ ij , for instance to 1, and iteratively solving Eqs. (11) and (12). To avoid a trivial solution we impose the constraint that the columns of W should have unit length.…”

Section: Projective Factorizationmentioning

confidence: 99%

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

Ackermann

Rosenhahn

2011

Computer Vision – ACCV 2010

View full text Add to dashboard Cite

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.

show abstract

“…Heyden et al firstly used the subspace constraint in pro− jective reconstruction and proposed an iterative factoriza− tion method based on 4D subspace constraint (IF4D), to recover the projective reconstruction from image sequence [9]. The key idea of the method is the fact that all the rows in the matrix which consists of all the image points and the depths span the same 4D linear subspace as the rows in the matrix consisting of projective structure.…”

Section: Introductionmentioning

confidence: 99%

“…The knowledge of the part coordinates enables us to solve the SFM problem by iterative factorization based on 1D subspace instead of 4D subspace as in Ref. 9. This simplifies the decomposition stage involved in the iterative factorization approach.…”

Section: Introductionmentioning

confidence: 99%

An iterative method based on 1D subspace for projective reconstruction

Liu¹,

Peng

Zeng

et al. 2011

Opto-Electronics Review

View full text Add to dashboard Cite

Heyden et al. introduced an iterative factorization method for projective reconstruction from image sequences. In their formulation, the projective structure and motion are computed by using an iterative factorization based on 4D subspace. In this paper, the problem is reformulated based on fact that the x, y, and z coordinates of each feature in projective space are known from their projection. The projective reconstruction, i.e., the relative depths w and the 3D motion, is obtained by a simple iterative factorization based on 1D subspace. This allows the use of very fast algorithms even when using a large number of features and large number of frames. The experiments with both simulate and real data show that the method presented in the paper is efficient and has good convergency.

show abstract

An iterative factorization method for projective structure and motion from image sequences

Cited by 101 publications

References 13 publications

Imposing Semi-Local Geometric Constraints for Accurate Correspondences Selection in Structure from Motion: A Game-Theoretic Perspective

Imposing Semi-Local Geometric Constraints for Accurate Correspondences Selection in Structure from Motion: A Game-Theoretic Perspective

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

An iterative method based on 1D subspace for projective reconstruction

Contact Info

Product

Resources

About