Functions
int	arun (MatRefConst X, MatRefConst Y, SE3 &T)

int	gicp (MatRefConst X, MatRefConst Y, MatRefConst covX, MatRefConst covY, SE3 &T, double tol=1e-4)

int	weighted_point (MatRefConst X, MatRefConst Y, VectRefConst w, SE3 &T, double tol=1e-4)

Detailed Description

This header provides the available functions for Point Cloud Registration using the following methods. It assumes Data association and a correct index order for associated pairs.

These set of methods calculates the transformation T = [R t] between sets of points x in R^3 and y in R^3, such as: [0 1], where yh = T*xh and being xh and yh the homogeneous description of those points [x y z 1].

Function Documentation

◆ arun()

int mrob::PCRegistration::arun	(	MatRefConst	X,
		MatRefConst	Y,
		SE3 &	T
	)

This solution is based on the paper by Arun et al. "Least-squares fitting of two 3-D point sets", 1987 Given N points x = x_1,x_2,x_3 and their correspondences y_i, calculate the transformation T = [R t], such as: min sum (y_i - (R * x_i + t))^2

An improvement over it was proposed by Sinji Umeyama 1991, which uniqueness determine R

3 points in x and y are the minimum requirements, and provide the right solution IF there is no noise.

Returns 0 if failed and 1 if a correct solution was found

◆ gicp()

int mrob::PCRegistration::gicp	(	MatRefConst	X,
		MatRefConst	Y,
		MatRefConst	covX,
		MatRefConst	covY,
		SE3 &	T,
		double	tol = `1e-4`
	)

Custom implementation of the GICP using SE3 optimization (improvement over Euler rotations)

This method calculates the transformation T = [R t] between sets of points x in R^3 and y in R^3, such as: [0 1], where yh = R*xh + t

T = min sum || y - Tx ||_S^2

The covariances provided are of the form S = R diag(e,1,1) R', so they MUST have been already processed. The right way is a block matrix of covariances of the form Cov = [Cov_1, Cov_2,..., Cov_N], i.e, Cov R^{3x3N}

Returns the number of iterations until convergence

◆ weighted_point()

int mrob::PCRegistration::weighted_point	(	MatRefConst	X,
		MatRefConst	Y,
		VectRefConst	w,
		SE3 &	T,
		double	tol = `1e-4`
	)

Weighted point Cloud registration using SE3 optimization