karcher.mean.sphere: Karcher mean on the sphere

In retistruct: Retinal Reconstruction Program

Karcher mean on the sphere

Description

The Karcher mean of a set of points on a manifold is defined as the point whose sum of squared Riemann distances to the points is minimal. On a sphere using spherical coordinates this distance can be computed using the formula for central angle.

Usage

karcher.mean.sphere(x, na.rm = FALSE, var = FALSE)

Arguments

x	Matrix of points on sphere as N-by-2 matrix with labelled columns phi (latitude) and lambda (longitude)
na.rm	logical value indicating whether NA values should be stripped before the computation proceeds.
var	logical value indicating whether variance should be returned too.

Value

Vector of means with components named phi and lambda. If var is TRUE, a list containing mean and variance in elements mean and var.

Author(s)

David Sterratt

References

Heo, G. and Small, C. G. (2006). Form representations and means for landmarks: A survey and comparative study. Computer Vision and Image Understanding, 102:188-203.

See Also

central.angle

retistruct documentation built on April 3, 2025, 5:58 p.m.