Bibliography: leaves 225-227 / v, 227, 37 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics. 1985

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The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, 1917. / "Private edition, distributed by the University of Chicago Libraries." Includes bibliographical references. Also available on the Internet.

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Thesis (Ph. D.)--University of Chicago, 1933. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."

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