## S3 method for class 'SO3':
median(x, type = "projected",
epsilon = 1e-05, maxIter = 2000, ...)
## S3 method for class 'Q4':
median(x, type = "projected",
epsilon = 1e-05, maxIter = 2000, ...)
Arguments
x
$n\times p$ matrix where each row
corresponds to a random rotation in matrix form
($p=9$) or quaternion ($p=4$) form.
type
string indicating "projected" or "geometric"
type mean estimator.
epsilon
stopping rule.
maxIter
maximum number of iterations allowed
before returning most recent estimate.
...
additional arguments.
Value
An estimate of the projected or geometric mean.
Details
The median-type estimators are defined as
$$\widetilde{\bm{S}}=argmin_{\bm{S}\in
SO(3)}\sum_{i=1}^nd(\bm{R}_i,\bm{S}).$$ If the choice of distance metric $d$ is
Riemannian then the estimator is called the geometric
median, and if the distance metric in Euclidean then it
is called the projected median. The algorithm used in the
geometric case is discussed in Hartley et al.
(2011) and the projected case was written by the
authors.
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.