Interpolation in Riemannian manifolds

Shreya Bhattarai

    Research output: ThesisDoctoral Thesis

    362 Downloads (Pure)

    Abstract

    [Truncated abstract] It is a very natural task to connect the dots between patterns of data we see. This fundamental procedure of connecting the dots, or interpolation, arises in many contexts including graphics, robot path planning, and medical imagining. Although the subject of interpolation has been thoroughly studied for Euclidean spaces, the more general setting of interpolating in a Riemannian manifold has only relatively recently received attention. The central aim of this thesis is to present results concerning the interpolation of data points in Riemannian manifolds, and in particular Lie groups.

    Riemannian manifolds are smooth spaces where concepts such as distances and angles are defined using a metric.
    A dynamical system's state can often be represented as points in a Riemannian manifold and we can apply geometrical methods of inference to predict how the system would have behaved given a suitable model of the dynamics. This thesis in a broad sense looks at various ways to model a system's dynamical behaviour in order to interpolate effectively.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2013

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