Polynomial methods for structure from motion
Polynomial methods for structure from motion
Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C2 Maps [C5]
ACM Transactions on Mathematical Software (TOMS)
Linear Algorithm for Motion Estimation: How to Handle Degenerate Cases
Proceedings of the 4th International Conference on Pattern Recognition
Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion Parameter Estimation from Global Flow Field Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Symbolic Computation to Find Algebraic Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual motion and structure estimation using sliding mode observers
International Journal of Systems Science
| Hi-index | 0.14 |
The authors analyze the limitations of structure from motion (SFM) methods presented in the literature and propose the use of a polynomial system of equations, with the unit quaternions representing rotation, to recover SFM under perspective projection. The authors combine the equations by the method of resultants with the MAXIMA symbolic algebra system, reducing the system to a single polynomial. Its real roots are then found with Sturm sequences. Since this system has multiple solutions, a hypothesize-and-verify scheme is used to eliminate incorrect ones. The scheme diminishes the sensitivity of using polynomial equations. The authors examine the effect of different rotation axes and angles on SFM accuracy and compare the performance of the algorithm to a few earlier approaches. Generally, it is found that a large amount of motion is the most important factor in getting good SFM accuracy.