weighted.mean.Q4: Weighted Rotation Median

In heike/rotations: Tools for working with rotational data

Description

Compute the weighted projected or geometric mean of a sample of rotations

Usage

  ## S3 method for class 'Q4'
 weighted.mean(Qs, w, type = "projected",
    epsilon = 1e-05, maxIter = 2000)

Arguments

Qs	A n\times 4 matrix where each row corresponds to a random rotation in unit quaternion
w	a numerical vector of weights the same length as Rs giving the weights to use for elements of Rs
type	String indicating 'projeted' or 'geometric' type mean estimator
epsilon	Stopping rule for the geometric method
maxIter	The maximum number of iterations allowed before returning most recent estimate

Details

This function takes a sample of n unit quaternions and approximates the mean rotation. If the projected mean is called for then the quaternions are turned reparameterized to matrices and mean.SO3 is called. If the geometric mean is called then according to Gramkow (2001) a better approximation is achieved by taking average quaternion and normalizing. Our simulations don't match this claim.

Value

weighted projected or geometric mean of the sample

References

Gramkow C (2001). "On averaging rotations." _Journal of Mathematical Imaging and Vision_, *15*(1), pp. 7-16.

Manton J (2004). "A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups." In _8th Conference on Control, Automation, Robotics and Vision, (ICARCV) _, volume 3, pp. 2211-2216. IEEE.

Moakher M (2002). "Means and averaging in the group of rotations." _SIAM Journal on Matrix Analysis and Applications_, *24*(1), pp. 1-16.

See Also

mean.SO3

Examples

r<-rvmises(20,0.01)
wt<-abs(1/r)
Qs<-genR(r,space="Q4")
weighted.mean(Qs,wt)

heike/rotations documentation built on May 17, 2019, 3:24 p.m.