A Nonlinear Variational Problem for Image Matching (Amit)

======================================================================
SIAM Journal on Scientific Computing
Volume 15-1, January 1994, pp. 207-224
(C) 1994 by Society for Industrial and Applied Mathematics
All rights reserved.

Title:            A Nonlinear Variational Problem for Image Matching

Author:           Yali Amit

AMS Subject
Classifications:  68V10, 65M70, 49N60     

Key words:        image matching, movement compensation, nonlinear 
                  variational problem, spectral methods, wavelets

----

ABSTRACT

Minimizing a nonlinear functional is presented as a way of obtaining
a planar mapping that matches two similar images. A smoothing term is
added to the nonlinear functional to penalize discontinuous and
irregular solutions. One option for the smoothing term is a quadratic
form generated by a linear differential 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 finite dimensional
approximations, it is easier to accommodate local deformations using
the wavelet basis.


======================================================================

SIAM
3600 University City Science Center
Philadelphia, PA  19104-2688, USA

Phone:  215-382-9800, 800-447-7426 (USA only)
Fax:  215-386-7999
E-mail:  journals@siam.org