A VARIATIONAL APPROACH FOR DISCONTINUITY-PRESERVING IMAGE REGISTRATION

摘要

There exist many models for deformable image registration, mainly differing in how regularization is introduced. On one hand, models minimizing first- or second-order derivatives such as diffusion, elastic, or curvature-based image registration are known to generate globally smooth deformation fields. On the other hand, regularization techniques based on total variation (TV) preserving discontinuities of the deforma- tion field are useful to a class of problems where smoothness is less a concern. It is still a challenge to design a model suitable for both smooth problems and non-smooth problems. This paper first proposes a variational model based on a modified TV regularization, which can be interpreted as a half way model between diffusion (smooth) and '[V (non-smooth) registration. The idea stems from image restoration where smoothing and preserving discontinuities are both important. Second to solve the resulting Euler- Lagrange sys-tem of two coupled, nonlinear partial differential equations (PDEs), we present a nonlinear multigrid (NMG) strategy and an adaptive parameter selection procedure. Numerical tests using both synthetic and realistic images not only confirm that the proposed model is more robust in regis-tration quality for a wide range of applications than previous models, but also that the proposed NMG method can deliver an acceptable solution many orders of magnitude faster than the gradient descent approach, popularly used in image processing.