Abstract
Previous studies have
shown that early stages in visual processing involve a local
linear frequency transform
of the image followed by a nonlinear response to the
transform coefficients.
This nonlinear response involves normalization of each transform
coefficient by the responses
of neighbouring cells [Heeger92,93].
Through these two steps,
image space is mapped onto response space. Being able to
return to image space
from response space would be very useful in diverse fields,
such as psychophysics
or image coding. However, while the linear transform is invertible,
the interactions among
the coefficients in the divisive normalization make it noninvertible.
In this talk I will present
a differential approach to solve this inversion problem as
opposed to a conventional
brute-force search. In the differential approach the
inversion problem is
formulated as an 'initial-value-problem', so the existence and
uniqueness of the solution
is theoretically guaranteed.
Beyond these theoretical
advantages, the convergence results show that while the
differential method successfully
solves the problem, a comparable iterative search highly
depends on the initial
guess and is easily trapped into local minima. Finally, I will show
some applications of
this new approach in the context of image coding and vision modeling.
(Power Point Slides) (15MB) (Back to Papers Page)