A new technique for the modelling of perceptual
systems called formal modelling is developed. This
technique begins with qualitative observations about the
perceptual system, the so-called perceptual symmetries, to
obtain through mathematical analysis certain model
structures which may then be calibrated by experiment.
The analysis proceeds in two different ways depending upon
the choice of linear or nonlinear models. For the linear
case, the analysis proceeds through the methods of unitary
representation theory. It begins with a unitary group
representation on the image space and produces what we
have called the fundamental structure theorem. For the
nonlinear case, the analysis makes essential use of
infinite-dimensional manifold theory. It begins with a
Lie group action on an image manifold and produces the
fundamental structure formula.
These techniques will be used to study the brightness
perception mechanism of the human visual system. Several
visual groups are defined and their corresponding
structures for visual system models are obtained. A new
transform called the Mandala transform will be deduced
from a certain visual group and its implications for image processing will be discussed. Several new phenomena of
brightness perception will be presented. New facts about
the Mach band illusion along with new adaptation phenomena
will be presented. Also a new visual illusion will be
presented. A visual model based on the above techniques
will be presented. It will also be shown how use of
statistical estimation theory can be made in the study of
contrast adaptation. Furthermore, a mathematical
interpretation of unconscious inference and a simple
explanation of the Tolhurst effect without mutual channel
inhibition will be given. Finally, image processing
algorithms suggested by the model will be used to process
a real-world image for enhancement and for "form" and
texture extraction
