Abstract
We present a deformable registration algorithm for multi-modality images based on information theoretic similarity measures at the scale of individual image voxels. We derive analytical expressions for the mutual information, the joint entropy, and the sum of marginal entropies of two images over a small neighborhood in terms of image gradients. Using these expressions, we formulate image registration algorithms maximizing local similarity over the whole image domain in an energy minimization framework. This strategy produces highly elastic image alignment as the registration is driven by voxel similarities between the images, the algorithms are easily implementable using the closed-form expressions for the derivative of the optimization function with respect to the deformation, and avoid estimation of joint and marginal probability densities governing the image intensities essential to conventional information theoretic image registration methods.
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Breiman, L. 1993. Hinging hyperplanes for regression, classification, and function approximation. IEEE Transactions on Information Theory, 39(3):999–1013.
Collignon, A., Maes, F., Delaere, D., Vandermeulen, D., Suetens, P., and Marchal, G. 1995. Automated multimodality image registration using information theory. In Proceedings of Information Processing in Medical Imaging, pp. 263–274.
Collignon, A., Vandermeulen, D., Suetens, P., and Marchal, G. 1995. 3d multimodality medical image registration using feature space clustering. In Computer Vision, Virtual Reality and Robotics in Medicine, pp. 195–204.
Crum, W.R., Griffin, L.D., Hill, D.L.G., and Hawkes, D.J. 2003. Zen and the art of medical image registration: Correspondence, homology and quality. NeuroImage, 20:1425–1437.
Hallpike, L. and Hawkes, D.J. 2002. Medical image registration: An overview. Imaging, 14:455–463.
Karaçalı, B. 2004. Fully elastic multi-modality image registration using mutual information. In IEEE International Symposium on Biomedical Imaging, pp. 1455–1458.
Kim, J. and Fessler, J.A. 2002. Image registration using robust correlation. In Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 353–356.
Maes, F., Collignon, A., Vandermuelen, D., Marchal, G., and Suetens, P. 1997. Multimodality image registration by maximization of mutual information. IEEE Transactions on Medical Imaging, 16:187–198.
Maintz, J.B.A., vandenElsen, P.A., and Viergever, M.A. 1996a. Comparison of edge-based and ridge-based registration of ct and mr brain images. Medical Image Analysis, 1(2):151– 161.
Maintz, J.B.A., vandenElsen, P.A., and Viergever, M.A. 1996b. Evaluation of ridge seeking operators for multimodality medical image matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(4):353–365.
Mattes, D., Haynor, D.R., Vesselle, H., Lewellen, T.K., and Eubank, W. 2003. Pet-ct image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging, 22(1):120–128.
Paillou, P. and Gelautz, M. 1999. Relief reconstruction from sar stereo pairs: The “optimal gradient” matching method. IEEE Transactions on Geoscience and Remote Sensing, 37(4):2099–2107.
Penney, G.P., Weese, J., Little, J.A., Desmedt, P., Hill, D.L.G., and Hawkes, D.J. 1998. A comparison of similarity measures for use in 2-d–3-d medical image registration. IEEE Transactions on Medical Imaging, 17(4):586–595.
Pluim, J.P.W. and Fitzpatrick, J.M. 2003. Image registration. IEEE Transactions on Medical Imaging, 22(11):1341–1343.
Pluim, J.P.W., Maintz, J.B.A., and Viergever, M.A. 2000. Image registration by maximization of combined mutual information and gradient information. IEEE Transactions on Medical Imaging, 19(8):809–814.
Pluim, J.P.W., Maintz, J.B.A., and Viergever, M.A. 2001. f-information measures in medical image registration. In Proceedings of the SPIE, vol. 4322, pp.79–587.
Pluim, J.P.W., Maintz, J.B.A., and Viergever, M.A. 2003. Mutual-information-based registration of medical images: A survey. IEEE Transactions on Medical Imaging, 22(8):986–1004.
Roche, A., Malandain, G., Pennec, X., and Ayache, N. 1998. Multimodal registration by maximization of the correlation ratio. Technical report, INRIA.
Rogejl, P., Kovacic, S., and Gee, J.C. 2003. Point similarity measures for non-rigid registration of multi-modal data. Computer Vision and Image Understanding, 92:112–140.
Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., and Hawkes, D.J. 1999. Nonrigid registration using free-form deformations: Application to breast mr images. IEEE Transactions on Medical Imaging, 18(8):712–721.
Scharstein, D. 1994. Matching images by comparing their gradient fields. In Proceedings of the International Conference on Pattern Recognition, pp. 572–575.
Studholme, C., Hill, D., and Hawkes, D. 1995. Multiresollution voxel similarity measures for mr-pet registration. In Proceedings of Information Processing in Medical Imaging, pp. 287–298.
Toga, A.W. and Thompson, P.M. 2001. The role of image registration in brain mapping. Image and Vision Computing, 19:3–24.
Viola, P. and Wells, W.M. 1995. Alignment by maximization of mutual information. In Proceedings of the 5th International Conference on Computer Vision, pp. 12–23.
Wei, Q.Q., Brauer W., and Hirzinger, G. 1998. Intensity—and gradient-based stereo matching using hierarchical gaussian basis functions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(11):1143–1160.
Wells, W.M., Viola, P., and Kikinis, R. 1995. Multi-modal volume registration by maximization of mutual information. In Proceedings of the 2nd Annual International Symposium on Medical Robotics and Computer Assisted Surgery, pp. 55–62.
West, J., Fitzpatric, J.M. et al. 1997. Comparison and evaluation of retrospective intermodality brain image registration techniques. Journal of Computer Assisted Tomography, 21(4):554– 568.
Woods, R., Mazziotta, J., and Cherry, S. 1993. Mri-pet registration with automated algorithm. Journal of Computer Assisted Tomography, 17:536–546.
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This work has been supported in part by NIH grants R01-NS42645 and R01-AG14971.
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Karaçali, B. Information Theoretic Deformable Registration Using Local Image Information. Int J Comput Vision 72, 219–237 (2007). https://doi.org/10.1007/s11263-006-8704-0
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DOI: https://doi.org/10.1007/s11263-006-8704-0