Various algorithms for estimating the Essential matrix, E, from five or seven points, are implemented. They can be used alone (see documentation in ransac/hypothesiser.h) or as the hypothesis generators in my RANSAC/BaySAC implementation (e.g. by setting parameter RANSAC.HypothesiseAlg=7PtEFast in your config file). The Levenberg-Marquardt-based fivepoint solvers will be described in "Fast RANSAC hypothesis generation for essential matrix estimation", DICTA 2011.
| Algorithm | Summary | Class name | Source code | RANSAC.HypothesisAlgorithm |
|---|---|---|---|---|
| 7-point with Gram-Schmid to compute basis | Very fast (~1 microsecond, compared with 10-20 microsecs for others), numerical errors not significant enough to influence RANSAC hypothesis generation (but degenerate for planar configurations). | C7ptEssentialMat_GS | essentialMat_Eigen.cpp | CRANSACParams::e7PtEFast |
| 5-point with Lev-Mar to compute E from basis vectors | Fast, only finds a subset of possible solutions. | CEssentialMatLMbasis | essentialMatLM2.cpp | CRANSACParams::e5Pt_GradientDesc |
| 5-point Polynomial | Algorithm by Nister (2004). Finds (almost) all solutions. | C5ptEssentialMat | essentialMat_Eigen.cpp | CRANSACParams::e5PtE |
| 5-point with Lev-Mar to compute E via a translation and quaternion | Not as fast as the basis-vectors method, only finds a subset of possible solutions. Either on manifold (eMinimalOnManifold) or with minimal 5D parameterisation (eMinimal). | CEssentialMatLM | essentialMatLM.cpp | - |
| 5-point with Grobner basis and eigendecomposition to compute E. | Algorithm by Stewenius (2006). Finds all solutions. Relatively slow. | C5ptEssentialMat | essentialMat_Eigen.cpp | - |
A MAPLE worksheet for expanding E as a function of a quaternion and a translation vector is available here.
Refinement
RANSAC/BaySAC only find approximately-correct essential matrices, which should be further refined to minimise some error function on the inlier set. Use the functions in refineEOnRTManifold.h to find the least-squares solution, or to minimise the Blake-Zisserman robust cost function of Sampson's error. Paper: "Refining essential matrix estimates from RANSAC". See example of use here...