Over the years, we have designed a variety of image registration algorithms:
 Intramodal, rigidbody or affine: this basic algorithm is best suited for precise (e.g., subpixel) motion compensation.
 Intermodal, rigidbody or affine: this method uses "mutual information" and is designed to align images of the same patient obtained from different modalities (e.g., MRI, CT, PET).
 2Dto3D, rigid body: this method estimates the 3D pose of an object by matching a set of 2D projections (radiographs) to a reference 3D volume.
 Intramodal, elastic: the source image is geometrically transformed to best match the reference. The freeform deformation is represented in a Bspline basis.
 Intramodal, mosaicking: given a collection of partially overlapping tiles, we propose an efficient strategy to select which pairs to register in order to create a mosaic.
All approaches are parametric in the sense that the geometrical transformation is represented by a small number of parameters (e.g., translation vector and Euler angles for a rigidbody transformation, or a set of control points [or Bspline coefficients] for a freeform deformation). In all cases, we use a multiresolution optimization strategy that is particularly efficient with respect to both computation time and robustness. The clever use of spline functions result in precise registration; they play a role in the continuous representation of images, the Parzenbased estimation of joint histograms, and the parametrization of freeform deformations.
These methods require the development of specialpurpose optimization algorithms that are capable of superlinear convergence when sufficiently close to the optimum. This is essential if one wants to take full advantage of a coarsetofine iteration strategy in which the current solution is propagated to the next finer scale.
We have also investigated the impact of the criterion that is used to drive the registration. We have proposed vectorspline regularization to combine an imagedriven criterion with a landmarkdriven one; the novelty of this contribution is that the resulting regularization fully takes into account the vectorial nature of the deformation, including cross terms. In the context of mutual information, we have proposed that the criterion be computed out of discrete data samples that follow a Halton distribution; when computed this way, mutual information exhibits a much lesser tendency to align the transformation with the grid of pixels than with methods based on regular sampling. 

[5]  S. Jonić, P. Thévenaz, M. Unser, "MultiresolutionBased Registration of a Volume to a Set of Its Projections," Proceedings of the SPIE International Symposium on Medical Imaging: Image Processing (MI'03), San Diego CA, USA, February 1720, 2003, vol. 5032, part II, pp. 10491052.

[7]  S. Jonić, C.Ó. Sánchez Sorzano, P. Thévenaz, C. ElBez, S. De Carlo, M. Unser, "SplineBased ImagetoVolume Registration for ThreeDimensional Electron Microscopy," Ultramicroscopy, vol. 103, no. 4, pp. 303317, July 2005.

[8]  M.J. LedesmaCarbayo, J. Kybic, M. Desco, A. Santos, M. Sühling, P. Hunziker, M. Unser, "SpatioTemporal Nonrigid Registration for Ultrasound Cardiac Motion Estimation," IEEE Transactions on Medical Imaging, vol. 24, no. 9, pp. 11131126, September 2005.

[9]  S. Jonić, C.Ó. Sánchez Sorzano, P. Thévenaz, C. ElBez, S. De Carlo, M. Unser, "SplineBased ImagetoVolume Registration for ThreeDimensional Electron Microscopy," Ultramicroscopy, vol. 103, no. 4, pp. 303317, July 2005.

[12]  C.Ó.S. Sorzano, I. ArgandaCarreras, P. Thévenaz, A. Beloso, G. Morales, I. Valdés, C. PérezGarcía, C. Castillo, E. Garrido, M. Unser, "Elastic Image Registration of 2D Gels for Differential and Repeatability Studies," Proteomics, vol. 8, no. 1, pp. 6265, January 2008.

[14]  I. ArgandaCarreras, C.Ó.S. Sorzano, P. Thévenaz, A. Muñoz Barrutia, J. Kybic, R. Marabini, J.M. Carazo, C. Ortiz de Solórzano, "NonRigid Consistent Registration of 2D Image Sequences," Physics in Medicine and Biology, vol. 55, no. 20, pp. 62156242, October 2010.

