Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Fundamental Matrix for Cameras with Radial Distortion
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Structure from Motion with Wide Circular Field of View Cameras
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)
Camera Models and Fundamental Concepts Used in Geometric Computer Vision
Foundations and Trends® in Computer Graphics and Vision
Unknown radial distortion centers in multiple view geometry problems
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
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A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Grobner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem.