School of Mathematics and Statistics

Postgraduate research

Research being undertaken by our current postgraduates:

Contact

Shreya Bhattarai


Supervisors

Start date

Jun 2008

Submission date

Shreya Bhattarai

Thesis

Interpolation in Riemannian manifolds

Summary

Suppose we have a set of time values t_0 < ... < t_n and some points {x_0, ..., x_n} in a manifold. Interpolation, loosely speaking, is

finding a suitable curve x : [t_0, t_n] -> M such that x(t_i) = x_i.

Just what is meant by the word suitable depends on the application.

Numerous algorithms exist for different methods of interpolation in Euclidean space but there is not much done in the more general setting of a manifold. My thesis is focused on the theory and production of working tools for interpolating on a manifold using a special class of interpolant known as natural Riemannian cubic splines (and closely related classes of interpolants such as piecewise Riemannian cubics in tension). Natural Riemannian cubic splines are variational generalisations of the popular natural cubic splines in Euclidean space. In particular, I am studying the asymptotics of such curves on various Lie groups as well as designing algorithms for their use in applications.

Why my research is important

There are many issues in fields such as engineering, computer vision and mechanics that come to a problem of interpolation. One example is rotating a camera in a smooth manner so that it passes through various orientations at prescribed times. The orientation of a camera can be considered an element of the Lie group SO(3) and algorithms for interpolating in a non-Euclidean space are needed to determine the motion the camera should take. A set of tools to perform such a rudimentary task should exist and my research will make this possible.



Statistics clinic

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.

 

School of Mathematics and Statistics

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Last updated:
Monday, 16 June, 2014 2:41 PM

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