Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
On an installation of Buchberger's algorithm
Journal of Symbolic Computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Maintaining Multiple Motion Model Hypotheses Over Many Views to Recover Matching and Structure
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
An Efficient Solution to the Five-Point Relative Pose Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
MonoSLAM: Real-Time Single Camera SLAM
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic Generator of Minimal Problem Solvers
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
The Five Points Pose Problem: A New and Accurate Solution Adapted to Any Geometric Configuration
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
Parallel Tracking and Mapping for Small AR Workspaces
ISMAR '07 Proceedings of the 2007 6th IEEE and ACM International Symposium on Mixed and Augmented Reality
Estimating Relative Camera Motion from the Antipodal-Epipolar Constraint
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper, we present a new epipolar constraint for computing the rotation between two images independently of the translation. Against the common belief in the field of geometric vision that it is not possible to find one independently of the other, we show how this can be achieved by relatively simple two-view constraints. We use the fact that translation and rotation cause fundamentally different flow fields on the unit sphere centered around the camera. This allows to establish independent constraints on translation and rotation, and the latter is solved using the Gröbner basis method. The rotation computation is completed by a solution to the cheiriality problem that depends neither on translation, nor on feature triangulations. Notably, we show for the first time how the constraint on the rotation has the advantage of remaining exact even in the case of translations converging to zero. We use this fact in order to remove the error caused by model selection via a non-linear optimization of rotation hypotheses. We show that our method operates in real-time and compare it to a standard existing approach in terms of both speed and accuracy.