Baladin: robust registration of images

General principle

This method is very similar to the ICP (Iterative Closest Point) algorithm [1], which consists in extracting feature points in the two images (say the reference and the floating images) to be registered and in iterating the following steps until convergence:

1. to pair each feature point of the floating image with the closest feature point in the reference image,
2. to compute the transformation that will best superimpose the paired points, and
3. to apply this transformation to the feature points of the floating image.

Indeed, after applying the transformation, the pairings may have changed, thus a better transformation may be found by iterating these three steps.

To the opposite to the ICP algorithm, we do not extract feature points in the block matching algorithm but consider sub-images (i.e. blocks) in the floating image that will be paired to the most similar sub-image in the reference image. The computed transformation is the one that will best superimpose the centers of the paired sub-images.

Some details

The most similar block is the one that optimizes a certain similarity measure with respect to translations in a given search neighborhood.

For small blocks (i.e., 4x4 in 2D or 4x4x4 in 3D), we may assume a linear relationship between the intensities of two blocks, this makes the correlation coefficient the optimal similarity measure to determine the most similar block[2].

Only the most significant blocks (i.e.the ones with the largest standard deviation) are considered for pairing. Once all the pairings are calculated, the parametric transformation (i.e. rigid, affine, ...) is computed using robust estimators (least trimmed squares in our case) so that outliers can be detected and removed from the transformation estimation.

To allow for the capture of both small and huge displacements, we have implemented the block matching algorithm within a multi-scale strategy. Each image is represented by a pyramid of a number of levels: from one level to the next, the image is subsampled by a factor 2 along every dimension. The registration is done at each level, while the initial transformation comes from the previous level.

Much more details about the algorithm can be found in Sebastien Ourselin's Phd thesis [9].

Some Applications

This method was originally designed to reconstruct a volume from a stack of sections (histological sections, autoradiographs, etc) [3]. Since two successive sections are similar, but not identical, the robustness is crucial for this application. Although the aboce described application deals with 2-D images, the same methodology stands for 3-D images, yielding a pretty good accuracy as shown in [4].

In a collaboration with the INSERM unit U289, we have used this software to build an atlas of the human basal ganglia [5,6,7].

Within the european project MAPAWAMO, we used it to fuse autoradiographs with a 3D MR image [8].

Baladin will also be integrated into the software Imago, from Dosisoft, to fuse images coming from different modalities (e.g. MR with CT-scan, etc.).

Some References

1. P.J. Besl and N.D. McKay. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14:239--256, February 1992.
   
   
2. A. Roche, G. Malandain, and N. Ayache. Unifying Maximum Likelihood Approaches in Medical Image Registration. International Journal of Imaging Systems and Technology: Special Issue on 3D Imaging, 11(1):71--80, 2000.
   
   
3. S. Ourselin, A. Roche, G. Subsol, X. Pennec, and N. Ayache. Reconstructing a 3D Structure from Serial Histological Sections. Image and Vision Computing, 19(1-2):25--31, January 2001.
   
   
4. S. Ourselin, A. Roche, S. Prima, and N. Ayache. Block Matching: A General Framework to Improve Robustness of Rigid Registration of Medical Images. In A.M. DiGioia and S. Delp, editors, Third International Conference on Medical Robotics, Imaging And Computer Assisted Surgery (MICCAI 2000), volume 1935 of Lectures Notes in Computer Science, Pittsburgh, Pennsylvanie USA, pages 557--566, octobre 11-14 2000. Springer.
   
   
5. E. Bardinet, A.C.F Colchester, A. Roche, Y. Zhu, Y. He, S. Ourselin, B. Nailon, S.A. Hojjat, J. Ironside, S. Al-Sarraj, N. Ayache, and J. Wardlaw. Registration of Reconstructed Post Mortem Optical Data with MR Scans of the Same Patient. In W.J. Niessen and M.A. Viergever, editors, 4th Int. Conf. on Medical Image Computing and Computer-Assisted Intervention (MICCAI'01), volume 2208 of LNCS, Utrecht, The Netherlands, pages 957--965, October 2001.
   
   
6. Eric Bardinet, Sébastien Ourselin, Grégoire Malandain, Dominique Tandé, Karine Parain, Nicholas Ayache, and Jérôme Yelnik. Three dimensional functional cartography of the human basal ganglia by registration of optical and histological serial sections. In IEEE International Symposium on Biomedical Imaging, Washington, USA, pages 329--332, 2002.
   
   
7. Eric Bardinet, Sébastien Ourselin, Didier Dormont, Grégoire Malandain, Dominique Tandé, Karine Parain, Nicholas Ayache, and Jérôme Yelnik. Co-registration of histological, optical and MR data of the human brain. In Takeyoshi Dohi and Ron Kikinis, editors, Medical Image Computing and Computer-Assisted Intervention (MICCAI'02), volume 2488 of LNCS, Tokyo, pages 548--555, September 2002. Springer.
   
   
8. G. Malandain and E. Bardinet. Fusion of autoradiographies with an MR volume using 2-D and 3-D linear transformations. In Chris Taylor and Alison Noble, editors, Proceedings of Information Processing in Medical Imaging (IPMI'03), volume 2732 of LNCS, pages 487--498, 2003. Springer.
   
   
9. Sébastien Ourselin. Recalage d'images médicales par appariement de régions - Application à la construction d'atlas histologiques 3D. Thèse de sciences, Université de Nice Sophia-Antipolis, January 2002.
   
   

Contact

Gregoire Malandain