The spatial organization of cortical responses to different stimulus
orientations measured by recent optical imaging methods in the
mammalian striate cortex has revealed a dramatic pattern of
pinwheel-like (vortex) structures. The present thesis provides a
computational analysis of some aspects of the structure, function and
development of such cortical orientation maps. The general conditions
under which orientation vortices are expected to occur is analyzed
from a topological viewpoint. Then, the nature of possible
experimental artifacts associated with current optical imaging methods
is investigated quantitatively. A linear relationship is shown to
exist between the width of the experimental point spread function of
the optical imaging method and the resulting measurement error in
vortex location. A recent theorem derived in the context of random
optical wave fields (the `sign-principle') is shown to predict
alternation of vortex signs in near-neighbor vortices along zero
crossing curves of the complex-valued orientation map function. This
theorem leads to a novel visualization of cortical orientation maps
that is applied to experimental optical recording data from monkey
visual cortex provided by the laboratory of G. Blasdel, showing a
perfect alternating arrangement of singularities, as predicted by the
sign principle. Statistical analysis demonstrates a repulsion among
vortices that is interpreted as a consequence of the sign principle.
Finally, a model (the `vortex transform') of visual surface and shape
representation is proposed. The underlying cortical orientation map
and vortex structure segments a visual scene into surfaces. Each
surface is represented locally at a small region near the surface's
centroid. The resulting representation appears in the form of the
surface's boundary-angle function (the sequence of tangent angles
along the shape's boundary). This predicted shape representation is
rotation-, size- and shift-invariant. The model bears a direct
relationship to both a medial-axis shape representation and also to
the fourier-descriptor representation of shape, both of which have
been investigated physiologically and in psychophysical studies.