median: Median Rotation

In heike/rotations: Tools for working with rotational data

Description

Compute the projected or geometric median of a sample of rotations

Usage

  median(x, ...)

  ## S3 method for class 'SO3'
 median(Rs, type = "projected",
    epsilon = 1e-05, maxIter = 2000)

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

Arguments

x	A n-by-p matrix where each row corresponds to a random rotation in matrix form (p=9) or quaternion form (p=4)
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
...	additional arguments

Details

The median-type estimators are defined as

argmin∑ d(Ri,S)

. If the choice of distance metrid, d, is Riemannian then the estimator is called the geometric, and if the distance metric in Euclidean then it projected. The algorithm used in the geometric case is discussed in Hartley et al. (2011) and the projected case was written by the authors.

Value

an estimate of the projected or geometric mean

References

Hartley R, Aftab K and Trumpf J (2011). "L1 rotation averaging using the Weiszfeld algorithm." In _2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_, pp. 3041-3048. IEEE.

See Also

mean.SO3

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