The algebraic eigenvalue problem
The algebraic eigenvalue problem
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion Field and Optical Flow: Qualitative Properties
IEEE Transactions on Pattern Analysis and Machine Intelligence
Subspace methods for recovering rigid motion I: algorithm and implementation
International Journal of Computer Vision
3-D interpretation of optical flow by renormalization
International Journal of Computer Vision
Passive navigation as a pattern recognition problem
International Journal of Computer Vision - Special issue on qualitative vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Linear Differential Algorithm for Motion Recovery: AGeometric Approach
International Journal of Computer Vision
Optimal Structure from Motion: Local Ambiguities and Global Estimates
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
The Role of Total Least Squares in Motion Analysis
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Motion analysis with a camera with unknown, and possibly varying intrinsic parameters
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Motion Estimation Using the Differential Epipolar Equation
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods
International Journal of Computer Vision
Particle Video: Long-Range Motion Estimation using Point Trajectories
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Over-Parameterized Variational Optical Flow
International Journal of Computer Vision
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We provide a theoretical proof showing that under a proportional noise model, the discrete eight point algorithm behaves similarly to the differential eight point algorithm when the motion is small. This implies that the discrete algorithm can handle arbitrarily small motion for a general scene, as long as the noise decreases proportionally with the amount of image motion and the proportionality constant is small enough. This stability result extends to all normalized variants of the eight point algorithm. Using simulations, we show that given arbitrarily small motions and proportional noise regime, the normalized eight point algorithms outperform their differential counterparts by a large margin. Using real data, we show that in practical small motion problems involving optical flow, these discrete structure from motion (SFM) algorithms also provide better estimates than their differential counterparts, even when the motion magnitudes reach sub-pixel level. The better performance of these normalized discrete variants means that there is much to recommend them as differential SFM algorithms that are linear and normalized.