Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Authors:
Ben Glocker;Nikos Komodakis;Nikos Paragios;Nassir Navab
Affiliations:
Computer Aided Medical Procedures (CAMP), TU München, Germany and Laboratoire MAS, Ecole Centrale Paris, Chatenay-Malabry, France;Computer Science Department, University of Crete, Greece;Laboratoire MAS, Ecole Centrale Paris, Chatenay-Malabry, France and Equipe GALEN, INRIA Saclay - Ile-de-France, Orsay, France;Computer Aided Medical Procedures (CAMP), TU München, Germany
Venue:
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Year:
2009

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Abstract

Labeling of discrete Markov Random Fields (MRFs) has become an attractive approach for solving the problem of non-rigid image registration. Here, regularization plays an important role in order to obtain smooth deformations for the inherent ill-posed problem. Smoothness is achieved by penalizing the derivatives of the displacement field. However, efficient optimization strategies (based on iterative graph-cuts) are only available for second-order MRFs which contain cliques of size up to two. Higher-order cliques require graph modifications and insertion of auxiliary nodes, while pairwise interactions actually allow only regularization based on the first-order derivatives. In this paper, we propose an approximated curvature penalty using second-order derivatives defined on the MRF pairwise potentials. In our experiments, we demonstrate that our approximated term has similar properties as higher-order approaches (invariance to linear transformations), while the computational efficiency of pairwise models is preserved.