@PhdThesis{rojer1990:space_phd,
author = {Rojer, Alan},
title = {Space-variant computer vision with a
complex-logarithmic sensor geometry},
school = {New York University},
year = 1990,
address = {New York, NY},
abstract = {The complex logarithm as a conformal mapping has
drawn interest as a sensor architecture for computer
vision due to its psuedo-invariance with respect to
rotation and scaling, its high ratio of field width
to resolution for a given number of pixels, and its
utilization in biological vision as the topographic
mapping from the retina to primary visual cortex.
This thesis extends the computer vision applications
of the complex-logarithmic geometry. Sensor design
is based on the complex log mapping $w=\log(z+a)$,
with real $a>0$, which smoothly removes the
singularity in the log at the origin. Previous
applications of the complex-logarithmic geometry to
computer vision, graphics and sensory neuroscience
are surveyed. A quantitative analysis of the space
complexity of a complex-logarithmic sensor as a
function of map geometry, field width and angular
resolution is presented. The computer-graphic
problems of warping uniform scenes according to the
complex logarithm and inversion of log-mapping
scenes to recover the original uniform scene are
considered, as is the problem of blending the
resulting inverse log maps to reconstruct the
original (uniform) scene. A series of simple
algorithms for segmentation of log scenes by contour
completion and region filling are presented. A
heuristic algorithm for figure/ground segmentation
using the log geometry is also shown. The problem of
fixation-point selection (visual attention) is
considered. Random selection of fixation points,
inhibition around previous fixations, spatial and
temporal derivatives in the sensor periphery, and
regions found by segmentation are all examined as
heuristic attentional algorithms. For the special
case where targets can be parametrically defined, a
theory of model-based attention based on the Hough
transform is introduced. A priori knowledge about
the consistency between potential objects in the
scene and measured features in the scene is used to
select fixation points. The exponential storage
requirements of the usual Hough transform are
avoided.},
datestr = {199005},
}