GAPS: Generator for Automatic Polynomial Solvers
About
Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or normal form based solution is very inefficient. Fortunately the Gr\"obner basis of a same polynomial system with different coefficients is found to share consistent inner structure. By precomputing such structures offline, Gr\"obner basis as well as the polynomial system solutions can be solved automatically and efficiently online. In the past decade, several tools have been released to generate automatic solvers for a general minimal problems. The most recent tool autogen from Larsson et al. is a representative of these tools with state-of-the-art performance in solver efficiency. GAPS wraps and improves autogen with more user-friendly interface, more functionality and better stability. We demonstrate in this report the main approach and enhancement features of GAPS. A short tutorial of the software is also included.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Perspective-n-Point (PnP) | Optimal PnP 5K random instances | Mean Log10 Residual Error-11.35 | 6 | |
| Absolute Pose Estimation | Abs. Pose P4Pfr elim. f 5K random instances | Mean Log10 Residual Error-11.67 | 3 | |
| Rolling Shutter Pose Estimation | Rolling shutter pose 8 sols | Latency (ms)0.32 | 3 | |
| Triangulation | Triangulation from satellite im. 5K random instances | Mean Log10 Residual-11.5 | 3 | |
| Absolute Pose Estimation | Abs. Pose P4Pfr (elim. f) (12 sols) | Time (ms)0.718 | 3 | |
| Absolute Pose Estimation | Abs. pose refractive P5P 16 sols | Time (ms)4.022 | 3 | |
| Absolute Pose Estimation | Abs. pose quivers 20 sols | Time (ms)2.996 | 3 | |
| Image Stitching | Stitching fλ+R+fλ 3pt (5K random instances) | Mean Log10 Residual Error-12.74 | 3 | |
| Optimal Perspective-n-Point | Optimal PnP Hesch 27 sols | Time (ms)1.454 | 3 | |
| Optimal Perspective-n-Point | Optimal PnP Cayley 40 sols | Execution Time (ms)3.005 | 3 |