A Scale-Space Approach to Landmark Constrained Image Registration

Adding external knowledge improves the results for ill-posed problems. In this paper we present a new multi-level optimization framework for image registration when adding landmark constraints on the transformation. Previous approaches are based on a fixed discretization and lack of allowing for continuous landmark positions that are not on grid points. Our novel approach overcomes these problems such that we can apply multi-level methods which have been proven being crucial to avoid local minima in the course of optimization. Furthermore, for our numerical method we are able to use constraint elimination such that we trace back the landmark constrained problem to a unconstrained optimization leading to an efficient algorithm.

[1]  R. Maciunas,et al.  Interactive image-guided neurosurgery , 1992, IEEE Transactions on Biomedical Engineering.

[2]  J. Modersitzki,et al.  Combining landmark and intensity driven registrations , 2003 .

[3]  O. Scherzer,et al.  ANALYSIS OF OPTICAL FLOW MODELS IN THE FRAMEWORK OF THE CALCULUS OF VARIATIONS , 2002 .

[4]  Leo Grady,et al.  A Lattice-Preserving Multigrid Method for Solving the Inhomogeneous Poisson Equations Used in Image Analysis , 2008, ECCV.

[5]  Karl Rohr,et al.  Landmark-Based Image Analysis , 2001, Computational Imaging and Vision.

[6]  A. Ardeshir Goshtasby,et al.  2-D and 3-D Image Registration , 2004 .

[7]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[8]  E. Haber,et al.  Intensity Gradient Based Registration and Fusion of Multi-modal Images , 2007, Methods of Information in Medicine.

[9]  K. Mardia,et al.  A review of image-warping methods , 1998 .

[10]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[11]  Ma Bin-rong,et al.  A review of medical image registration , 1999 .

[12]  J. Hadamard.  Sur les problemes aux derive espartielles et leur signification physique , 1902 .

[13]  Knut-Andreas Lie,et al.  Scale Space and Variational Methods in Computer Vision, Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings , 2009, SSVM.

[14]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Gene H. Golub,et al.  Matrix computations , 1983 .

[16]  D. Hill,et al.  Medical image registration , 2001, Physics in medicine and biology.

[17]  Jan Modersitzki,et al.  Fast Curvature-Based Registration of MR Mammography Images , 2002, Bildverarbeitung für die Medizin.

[18]  Guy Marchal,et al.  3D multi-modality image registration , 1992 .

[19]  Joachim Weickert,et al.  A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion , 2001, International Journal of Computer Vision.

[20]  Thomas Martin Deserno,et al.  Bildverarbeitung für die Medizin: Grundlagen, Modelle, Methoden, Anwendungen , 1997, Bildverarbeitung für die Medizin.

[21]  Harald Köstler,et al.  A multigrid framework for variational approaches in medical image processing and computer vision , 2008 .

[22]  Paul M. Thompson,et al.  Brain Image Registration Using Cortically Constrained Harmonic Mappings , 2007, IPMI.

[23]  J. Modersitzki,et al.  A unified approach to fast image registration and a new curvature based registration technique , 2004 .

[24]  Will Light.  Variational Methods for Interpolation , Particularly by Radial BasisFunctionsWill , 1995 .

[25]  Martin Rumpf,et al.  A Variational Approach to Nonrigid Morphological Image Registration , 2004, SIAM J. Appl. Math..

[26]  Karl J. Friston,et al.  Human Brain Function , 1997 .

[27]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[28]  G. Watson,et al.  Numerical Analysis 1995 , 1996 .

[29]  Mads Nielsen,et al.  Motion Compensated Video Super Resolution , 2007, SSVM.

[30]  Guy Marchal,et al.  Automated multi-modality image registration based on information theory , 1995 .

[31]  Karl J. Friston,et al.  Spatial Normalization using Basis Functions , 2003 .

[32]  Paul A. Viola,et al.  Alignment by Maximization of Mutual Information , 1997, International Journal of Computer Vision.

[33]  Eldad Haber,et al.  A Multilevel Method for Image Registration , 2005, SIAM J. Sci. Comput..

[34]  U. Clarenz,et al.  Towards fast non-rigid registration , 2003 .

[35]  Max A. Viergever,et al.  Mutual-information-based registration of medical images: a survey , 2003, IEEE Transactions on Medical Imaging.

[36]  M. Fitzpatrick.  A Review of Medical Image Registration , 1993 .

[37]  Jan Modersitzki,et al.  Numerical Methods for Image Registration , 2004 .