Tom Botterill's Computer Vision Research

C++ Essential Matrix estimation

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..	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...