@PhdThesis{tal1997:functional_phd,
author = {Tal, Doron},
title = {Functional spatial architecture of orientation maps
in the primate visual cortex},
school = {Boston University},
year = 1997,
address = {Boston, MA},
abstract = {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.},
datestr = {199704},
}