Abstract
We introduce a new point-based elastic registration scheme for medical images which is based on elastic body splines (EBS). Since elastic body splines result from a physical model in form of analytical solutions of the Navier equation these splines describe elastic deformations of physical objects. This property is advantageous in medical registration applications, in which the geometric differences between the images are often caused by physical deformations of human tissue due to surgical interventions or pathological processes. In this contribution we introduce a new class of elastic body splines which is based on Gaussian forces (GEBS).
By varying the standard deviation of the Gaussian forces our new approach is well suited to cope with local as well as global differences in the images. This is in contrast to the previous EBS approach where polynomial and rational forces have been used. We demonstrate the performance of our new approach by presenting two different kinds of experiments. First, we demonstrate that this approach well approximates deformations given by an analytic solution of the Navier equation. Second, we apply our approach to pre- and postsurgical tomographic images of the human brain. It turns out that the new EBS approach well models the physical deformation behavior of tissues and in the case of local deformations performs significantly better than the previous EBS.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Bajcsy and S. Kovačič, “Multiresolution elastic matching,” Computer Vision, Graphics, and Image Processing, Vol. 46, No. 1, pp. 1–21, 1989.
J. Betten, Kontinuumsmechanik, Springer-Verlag: Berlin, 1993.
F.L. Bookstein, “Principal warps: Thin—plate splines and the decomposition of deformations,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 6, pp. 567–585, 1989.
D.S. Chandrasekharaiah and L. Debnath. Continuum Mechanics, Academic Press: San Diego, 1994.
G.E. Christensen, S.C. Joshi, and M.I. Miller, “Volumetric transformation of brain anatomy,” IEEE Trans. on Medical Imaging, Vol. 16, No. 6, pp. 864–877, 1997.
C. Davatzikos, J.L. Prince, and R.N. Bryan, “Image registration based on boundary mapping,” IEEE Transactions on Medical Imaging, Vol. 15, No. 1, pp. 112–115, 1996.
M. H. Davis, “Deformable matching of 3D medical images,” PhD thesis, Southern Methodist University, Dallas, 1996.
M.H. Davis, A. Khotanzad, D.P. Flamig, and S.E. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Transactions on Medical Imaging, Vol. 16, No. 3, pp. 317–328, 1997.
J. Declerck, G. Subsol, J.-P. Thirion, and N. Ayache, “Automatic retrieval of anatomical structures in 3d medical images,” in Lecture Notes in Computer Science 905, N. Ayache, editor, Proc. First Internat. Conf. Computer Vision, Virtual Reality and Robotics in Medicine (CVRMed’95), Nice/France, Springer Verlag: Berlin Heidelberg, 1995, p. 153–162.
A.W. Toga (Ed.). Brain Warping, Academic Press: San Diego, 1999.
H. Eschenauer and W. Schnell, Elastizitätstheorie, BI Wissenschaftsverlag, Mannheim, 1993.
A.C. Evans, W. Dai, L. Collins, P. Neelin, and T. Marrett, “Warping of a computerized 3-d atlas to match brain image volumes for quantitative neuroanatomical and funtional analysis,” in Proceedings of the International Society of Optical Engineering: Medical Imaging V, Vol. 1445, San Jose, California, SPIE, 27 February–1 March 1991, pp. 236–246.
B. Fischer and J. Modersitzki, “Curvature based image registration,” Journal of Mathematical Imaging and Vision, Vol. 18, No. 1, pp. 81–85, 2003.
M. Fornefett, K. Rohr, and H.S. Stiehl, “Elastic Registration of Medical Images Using Radial Basis Functions with Compact Support,” in Proc. Internat. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’99), June 23–25, IEEE Computer Society: Fort Collins, CO, USA, 1999, pp. 402–407.
P. Frank and R. Mises, Die Differential—und Integralgleichungen der Mechanik und Physik, Vieweg & Sohn, Braunschweig, 1961.
T. Gaens, F. Maes, D. Vandermeulen, and P. Suetens, “Non-rigid multimodal image registration using mutual information,” in Lecture Notes in Computer Science 1496, W. M. Wells, A. Colchester, and S. Delp (Ed.), Proc. First Internat. Conf. on Medical Image Computing and Computer-Assisted Intervention (MICCAI’98), Massachusetts Institute of Technology (MIT): Cambridge/MA, USA, Springer Verlag Berlin Heidelberg, 1998, pp. 1099–1106.
G. Hämmerlin and K.-H. Hoffmann, Numerische Mathematik, Springer-Verlag: Berlin, 1989.
J. Kohlrausch, Theoretische und experimentelle Untersuchung der “Elastic-Body-Splines” zur elastischen Registrierung medizinischer Bilddaten, 1999. Master Thesis, Fachbereich Informatik der Universität Hamburg, Germany.
J. Kohlrausch, K. Rohr, and H.S. Stiehl, “A New Class of Elastic Body Splines for Nonrigid Registration of Medical Images,” in H. Handels, A. Horsch, T. Lehmann, and H.-P. Meinzer, (eds.), Workshop: Bildverarbeitung für die Medizin 2001, Medizinische Universität zu übeck, übeck/Germany, 4.-6. März 2001, Springer-Verlag Berlin Heidelberg 2001, pp. 164–168,
L.D. Landau and E.M. Lifschitz, Lehrbuch der theoretischen Physik, Band 7, Elastizitätstheorie, Akademie-Verlag: Berlin, 1989.
S. Lavallìe, Registration for computer-integrated surgery: Methodology, state of the art, in R. H. Taylor, S. Lavallìe, G.C. Burdea, and R. Mósges (Eds.), Computer-Integrated Surgery, The MIT Press: Cambridge/Massachusetts, 1996, pp. 77–97.
J.A. Little, D.L.G. Hill, and D.J. Hawkes, “Deformations incorporating rigid structures,” Computer Vision and Image Understanding, Vol. 66, No. 2, pp. 223–232, 1997.
J.B.A. Maintz and M.A. Viergever, “A survey of medical image registration,” Medical Image Analysis, Vol. 2, No. 1, pp. 1–36, 1998.
K. Mardia and J. Little, “Image warping using derivative information,” in Mathematical Methods in Medical Imaging III, F. Bookstein, J. Duncan, N. Lange, and D. Wilson (Eds.), Proc. SPIE 2299, San Diego, 1994, pp. 16–31.
C.R. Meyer, J.L. Boes, B. Kim, P. H. Bland, K.R. Zasadny, P.V. Kison, K. Koral, K.A. Frey, and R.L. Wahl, “Demonstration of accuracy and clinical versatility of mutual information for automatic multimodality image fusion using affine and thin-plate spline warped geometric deformations,” Medical Image Analysis, Vol. 1, No. 3, pp. 195–206, 1996/7.
K. Rohr, M. Fornefett, and H.S. Stiehl, “Spline-based elastic image registration: Integration of landmark errors and orientation attributes,” Computer Vision and Image Understanding, Vol. 90, No. 2, pp. 153–168, May 2003.
L. Voo, S. Kumaresan, F.A. Pintar, N. Yoganandan, and A. Sances, “Finite-element models of the human head,” Medical & Biological Engineering & Computing, Vol. 34, No. 5, pp. 375–381, 1996.
Author information
Authors and Affiliations
Additional information
Now with University of Heidelberg, IPMB, DKFZ Heidelberg, Dept. Intelligent Bioinformatics Systems, Im Neuenheimer Feld 580, D-69120 Heidelberg.
Jan Kohlrausch received his Diplom (master) in Computer Science from the University of Hamburg, Germany in June 2000. His research interests included medical image processing with main interest in elastic registration.
He currently is a senior CSIRT member at the DFN-CERT Services GmbH which operates the Computer Emergency Response Team (CERT) for the German Research Network (DFN). His research interests in computer security include the deployment of honeypot technologies and the analysis and classification of network flows.
Karl Rohr is an Associate Professor of Computer Science in the School of Information Technology at the International University in Germany, Bruchsal, and head of the Computer Vision & Graphics Group. He studied Electrical Engineering at the University of Karlsruhe and received his Ph.D. degree (1994) as well as his Habilitation degree (1999) in Computer Science from the University of Hamburg, Germany. From 1992–2000 he was with the Department of Computer Science, University of Hamburg, where he was project leader of the IMAGINE project during 1994–2000 (funded by Philips Research Laboratories, Hamburg). In summer 1999 he spent a research stay at the Surgical Planning Laboratory, Harvard Medical School, in Boston/MA, USA.
In 1990 Dr. Rohr was awarded a DAGM prize for his paper on model-based recognition of corners, and in 1995 he was a co-recipient of the Springer Best Paper Award KI-95 (for work on model-based recognition and natural language description of human movements). In 2000 he received a Honorable Mention for the 26th Annual Pattern Recognition Society Award for his article on 3D landmark detection in the journal Pattern Recognition.
His research interests are in Image Processing, Computer Vision, and particularly Biomedical Image Analysis. He has written one book on Landmark-Based Image Analysis (Kluwer Academic Publishers, 2001) covering both landmark extraction and elastic image registration, and he has published more than 100 refereed scientific articles. He serves the editorial board of the international journal Pattern Recognition and he is program committee member of various international conferences and workshops.
H. Siegfried Stiehl was born in 1951 and received the Ing.grad. degree in Electrical Engineering from the Fachhochschule Furtwangen, Germany, in 1973. Moreover he earned the Diploma degree in Computer Science (Dipl.-Inf.) in 1976 and the Dr.-Ing. degree in 1980 both from the Department of Computer Science at the Technical University Berlin, Germany, where he also was employed as Hochschulassistent from 1982–1988. After his habilitation at TU Berlin, he was appointed as Associate Professor in the Department of Informatics at the University of Hamburg, Germany, in 1988 and since then he has been with the Cognitive Systems Group. Since 2001 he has served as dean of the Department of Informatics. His research interests have focussed on computational neuroscience of the visual system, computer vision, cognitive science, biomedical image computing, and nanoscience.
Rights and permissions
About this article
Cite this article
Kohlrausch, J., Rohr, K. & Stiehl, H.S. A New Class of Elastic Body Splines for Nonrigid Registration of Medical Images. J Math Imaging Vis 23, 253–280 (2005). https://doi.org/10.1007/s10851-005-0483-7
Issue Date:
DOI: https://doi.org/10.1007/s10851-005-0483-7