title: Nonlinear estimation of the fundamental matrix with minimal parameters.
abstract: The purpose of this paper is to give a very simple method for nonlinearly estimating the fundamental matrix using the minimum number of seven parameters. Instead of minimally parameterizing it, we rather update what we call its orthonormal representation, which is based on its singular value decomposition. We show how this method can be used for efficient bundle adjustment of point features seen in two views. Experiments on simulated and real data show that this implementation performs better than others in terms of computational cost, i.e., convergence is faster, although methods based on minimal parameters are more likely to fall into local minima than methods based on redundant parameters.
authors.affiliation: INRIA Rhone-Alpes, 655 avenue de l'Europe, 38334 Saint Ismier cedex, France. Adrien.Bartoli@inria.fr
authors.forename: Adrien
authors.initials: A
authors.lastname: Bartoli
authors.forename: Peter
authors.initials: P
authors.lastname: Sturm
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted