 
Summary: A NONLINEAR VARIATIONAL PROBLEM
FOR IMAGE MATCHING
Yali Amit
Division of Applied Mathematics
Brown University
Providence R.I., 02912, USA
Appeared in SIAM J. SCI. COMPUT., Vol. 15, No. 1, January 1994.
Permanent address: Department of Statistics, University of Chicago, Chicago IL, 60637.
Partially supported by ONR N0001488K0289 and ARO DAAL0390G0033
ABSTRACT
Minimizing a nonlinear functional is presented as a way of obtaining a planar mapping
which matches two similar images. A smoothing term is added to the nonlinear functional
in order to penalize discontinuous and irregular solutions. One option for the smoothing
term is a quadratic form generated by a linear di erential operator. The functional is then
minimized using the Fourier representation of the planar mapping. With this representation
the quadratic form is diagonalized. Another option is a quadratic form generated via a
basis of compactly supported wavelets. In both cases a natural approximation scheme is
described. Both quadratic forms are shown to impose the same smoothing. However in
terms of the nite dimensional approximations it turns out that it is easier to accommodate
local deformations using the wavelet basis.
