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.