We investigate higher-order geometric k-splines for template matching on Lie groups. This is
motivated by the need to apply diffeomorphic template matching to a series of images, eg, in …

In a connected Riemannian manifold, generalised Bézier curves are C∞ curves defined by
a generalisation, in which line segments are replaced by minimal geodesics, of the classical …

Motivated by applications in computational anatomy, we consider a second-order problem in
the calculus of variations on object manifolds that are acted upon by Lie groups of smooth …

Finding a geodesic joining two given points in a complete path-connected Riemannian
manifold requires much more effort than determining a geodesic from initial data. This is …

The quadrotor unmanned aerial vehicles (UAVs) have already gained an enormous
popularity, due to their versatility, ease of use and relatively low cost. However, the high …

Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with
countless applications in science and technology. In several emerging fields, for example …

For all n> 2, we study n th order generalisations of Riemannian cubics, which are second-
order variational curves used for interpolation in semi-Riemannian manifolds M. After finding …

The classical de Casteljau algorithm for constructing Bézier curves can be generalised to a
sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The …

Quadratures and cubics in SO(3) and SO(1,2) Page 1 IMA Journal of Mathematical Control
and Information (2006) 23, 463−473 doi:10.1093/imamci/dni069 Advance Access …

Let H be a closed subgroup of a connected finite-dimensional Lie group G, where the
canonical projection π: G→ G/H is a Riemannian submersion with respect to a bi-invariant …