Image Registration of Sectioned Brains

  • Oliver SchmittEmail author
  • Jan Modersitzki
  • Stefan Heldmann
  • Stefan Wirtz
  • Bernd Fischer


The physical (microtomy), optical (microscopy), and radiologic (tomography) sectioning of biological objects and their digitization lead to stacks of images. Due to the sectioning process and disturbances, movement of objects during imaging for example, adjacent images of the image stack are not optimally aligned to each other. Such mismatches have to be corrected automatically by suitable registration methods.

Here, a whole brain of a Sprague Dawley rat was serially sectioned and stained followed by digitizing the 20 μm thin histologic sections. We describe how to prepare the images for subsequent automatic intensity based registration. Different registration schemes are presented and their results compared to each other from an anatomical and mathematical perspective. In the first part we concentrate on rigid and affine linear methods and deal only with linear mismatches of the images. Digitized images of stained histologic sections often exhibit inhomogenities of the gray level distribution coming from staining and/or sectioning variations. Therefore, a method is developed that is robust with respect to inhomogenities and artifacts. Furthermore we combined this approach by minimizing a suitable distance measure for shear and rotation mismatches of foreground objects after applying the principal axes transform. As a consequence of our investigations, we must emphasize that the combination of a robust principal axes based registration in combination with optimizing translation, rotation and shearing errors gives rise to the best reconstruction results from the mathematical and anatomical view point.

Because the sectioning process introduces nonlinear deformations to the relative thin histologic sections as well, an elastic registration has to be applied to correct these deformations.

In the second part of the study a detailed description of the advances of an elastic registration after affine linear registration of the rat brain is given. We found quantitative evidence that affine linear registration is a suitable starting point for the alignment of histologic sections but elastic registration must be performed to improve significantly the registration result. A strategy is presented that enables to register elastically the affine linear preregistered~ rat brain sections and the first one hundred images of serial histologic sections through both occipital lobes of a human brain (6112 images). Additionally, we will describe how a parallel implementation of the elastic registration was realized. Finally, the computed force fields have been applied here for the first time to the morphometrized data of cells determined automatically by an image analytic framework.


neuroimaging human and rat brain serial sections affine registration elastic registration matching alignment warping 3D-reconstruction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abbe, E. 1873. Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Arch. Mikr. Anat, 9:413.Google Scholar
  2. Abeles, M. 1991, Corticonics. Neural circuits of the cerebral cortex Cambridge University Press: Cambridge.Google Scholar
  3. Aferzon, J., Chau, R., and Cowan, D. 1991. A microcomputer-based system for three-dimensional reconstructions from tomographic or histologic sections. Anal. Quant. Cytol. Histol, 13:80–88.Google Scholar
  4. Alexander, M., Scarth, G., and Somorjai, R. 1997. An improved robust hierarchical registration algorithm. Magn. Reson. Imaging, 15:505–514.CrossRefGoogle Scholar
  5. Alpert, N., Bradshaw, J., Kennedy, D., and Correia, J. 1990. The principal axes transformation—a method for image registration. J. Nuc. Med, 31:1717–1722.Google Scholar
  6. Amit, Y., Grenander, U., and Piccioni, M. 1991. Structural image restoration through deformable templates. J. Am. Stat. Ass, 86:376–387.CrossRefGoogle Scholar
  7. Arbib, M. 1995, The Handbook of Brain Theory and Neural Networks MIT Press: Cambridge.Google Scholar
  8. Arsigny, V., Pennec, X., and Ayache, N. 2005. Polyrigid and polyaffine transformations: A novel geometrical tool to deal with non-rigid deformations—Application to the registration of histological slices. Med. Image. Anal, 9:507–523.CrossRefGoogle Scholar
  9. Ashburner, J., Andersson, J., and Friston, K. 2000. Image registration using a symmetric prior–in three dimensions. Hum. Brain. Mapp, 9:212–225.CrossRefGoogle Scholar
  10. Auer, M., Regitnig, P., and Holzapfel, G. 2005. An automatic nonrigid registration for stained histologic sections. IEEE Trans. Imag. Proc, 14:475–486.CrossRefGoogle Scholar
  11. Baheerathan, S., Albregtsen, F., and Danielsen, H. 1998. Registration of serial sections of mouse liver cell nuclei. J. Microsc, 192:37–53.CrossRefGoogle Scholar
  12. Bajcsy, R. 1982. Matching of deformed images. Proc. 6th Int. Conf. Patt. Recogn, 6:351–353.Google Scholar
  13. Bajcsy, R. 1983. A computerized system for the elastic matching of deformed radiographic images to idealized atlas images. J. Comp. Ass. Tomo, 7:618–625.CrossRefGoogle Scholar
  14. Bajcsy, R. and Kovačíč, S. 1989. Multiresolution elastic matching. Comp. Vis. Image. Proc, 46:1–21.CrossRefGoogle Scholar
  15. Banerjee, P. and Toga, A. 1994. Image alignment by integrated rotational and translational transformation matrix. Phys. Med. Biol, 39:1969–1988.CrossRefGoogle Scholar
  16. Bardinet, E., Colchester, A., Roche, A., Zhu, Y., He, Y., Ourselin, S., Nailon, B., Hojjat, S., Ironside, J., Al-Sarraj, S., Ayache, N., and Wardlaw, J. 2001. Registration of reconstructed post mortem optical data with MR scans of the same patient. LNCS, 2208:957–965.Google Scholar
  17. Barnard, S. and Thompson, W. 1980. Disparity analysis of images. IEEE Trans. PAMI, 2:333–340.Google Scholar
  18. Barnea, D. and Silverman, H. 1972. A class of algorithms for fast digital image registration. IEEE Trans. Comp, 21:179–186.zbMATHCrossRefGoogle Scholar
  19. Baumann, M. and Scharf, H. 1994. Moderne Bildverarbeitungsverfahren als Unterstützung der räumlichen Rekonstruktion histologischer Strukturen. Ann. Anat, 176:185–188.Google Scholar
  20. Benveniste, H. and Blackband, S. 2002. MR microscopy and high resolution small animal MRI: Applications in neuroscience research. Prog. Neurobiol, 67:393–420.CrossRefGoogle Scholar
  21. Böhme, M., Hagenau, R., Modersitzki, J., and Siebert, B. 2002. Non-linear image registration on PC-clusters using parallel FFT techniques. Technical Report SIIM-TR-A-02-08, Institute of Mathematics, Medical University of Lübeck.Google Scholar
  22. Bookstein, F. 1984. A statistical method for biological shape comparisons. J. Theor. Biol, 107:475–520.CrossRefGoogle Scholar
  23. Bookstein, F. 1989. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Patt. Anal. Mach. Intell, 11:567–585.CrossRefzbMATHGoogle Scholar
  24. Borgefors, G. 1988. Hierarchical chamfer matching: A parametric edge matching algorithm. IEEE Trans. PAMI, 10:849–865.Google Scholar
  25. Born, G. 1883. Die Plattenmodellirungsmethode. Arch. Mikr. Anat, 22:584–599.CrossRefGoogle Scholar
  26. Braitenberg, V. 1978. Cell assemblies in the cerebral cortex. Lec. Notes. Biomath, 21:171–188.Google Scholar
  27. Bro-Nielsen, M. and Gramkow, C. 1996. Fast fluid registration of medical images. LNCS, 1131:267–276.Google Scholar
  28. Broit, C. 1981. Optimal registration of deformed images. Ph.D. thesis, Computer and Information science, University of Pensylvania.Google Scholar
  29. Bron, C., Launay, D., Jourlin, M., Gautschi, H., Bächi, T., and Schüpbach, J. 1990. Three dimensional electron microscopy of entire cell. J. Mircosc, 157:115–126.Google Scholar
  30. Brown, L. 1992. A survey of image registration techniques. ACM Comp. Surv, 24:325–376.CrossRefGoogle Scholar
  31. Budo, A. 1990, Theoretische Mechanik VEB Deutscher Verlag der Wissenschaften.Google Scholar
  32. Christensen, G. 1994. Deformable shape models for anatomy. Ph.D. thesis, Sever Institute of Technology, Washington University.Google Scholar
  33. Christensen, G. and Johnson, H. 2001. Consistent image registration. IEEE Trans. Med. Imaging, 20:568–582.CrossRefGoogle Scholar
  34. Christensen, G., Joshi, S., and Miller, M. 1997. Volumetric transformation of brain anatomy. IEEE Trans. Med. Imaging, 16:864–877.CrossRefGoogle Scholar
  35. Chui, H., Win, L., Schultz, E., Duncan, J., and Rangarajan, A. 2001. A unified feature registration method for brain mapping. LNCS, 2082:300–314.Google Scholar
  36. Ciarlet, P. 2000. Mathematical Elasticity Elsevier Science.Google Scholar
  37. Cohen, F., Yang, Z., Huang, Z., and Nissanov, J. 1998. Automatic matching of homologous histological sections. IEEE Trans. Biomed. Eng, 45:642–649.CrossRefGoogle Scholar
  38. Collins, D., Holmes, C., Peters, H., and Evans, A. 1995. Automatic 3D model-based neuroanatomical segmentation. Hum. Brain. Mapp, 3:190–208.CrossRefGoogle Scholar
  39. Dauguet, J., Mangin, J.-F., Delzescaux, T., and Frouin, V. 2004. Robust inter-slice intensity normalization using histogram scale-space analysis. LNCS, 3216:242–249.Google Scholar
  40. Davatzikos, C. 1997. Spatial transformation and registration of brain images using elastically deformable models. Comput. Vis. Image. Underst, 66:207–222.CrossRefGoogle Scholar
  41. Davatzikos, C. and Prince, J. 1994. Brain image registration based on curve mapping. Proc. IEEE Workshop. Biom. Image. Anal, 245–254.Google Scholar
  42. de Castro, E. and Morandi, C. 1987. Registration of translated and rotated images using finite Fourier transforms. IEEE Trans. PAMI, 9:700–703.Google Scholar
  43. de Munck, J., Verster, F., Dubois, E., Habraken, J., Boltjes, B., Claus, J., and van Herk, M. 1998. Registration of MR and SPECT without using external fiducial markers. Phys. Med. Biol, 43:1255–1269.CrossRefGoogle Scholar
  44. Desgeorges, M., Derosier, C., Cordoliani, Y., Traina, M., de Soultrait, F., Bernard, C., Khadiri, M., and Debono, B. 1997. Imaging networks, surgical simulation, computer-assisted neurosurgery. J. Neuroradiol, 24:108–115.Google Scholar
  45. Dierker, M. 1976, An Algorithm for the Alignment of Serial Sections John Wiley & Sons: New York, P.B. Brown: Computer technology on neuroscience edition.Google Scholar
  46. Dougherty, E. 1993, Mathematical Morphology in Image Processing Marcel Dekker: New York, Basel, Hong Kong.Google Scholar
  47. du Bois d’Aische, A., Craene, M. D., Geets, X., Gregoire, V., Macq, B., and Warfield, S. 2005. Efficient multi-modal dense field non-rigid registration: Alignment of histological and section images. Med. Image. Anal, 9:538–546.CrossRefGoogle Scholar
  48. Ferrant, M., Nabavi, A., Macq, B., Jolesz, F., Kikinis, R., and Warfield, S. 2001. Registration of 3-D intraoperative MR images of the brain using a finite-element biomechanical model. IEEE Trans. Med. Imaging, 20:1384–1397.CrossRefGoogle Scholar
  49. Fischer, A. and Modersitzki, J. 1999. Fast inversion of matrices arising in image processing. Num. Algo, 22:1–11.MathSciNetCrossRefzbMATHGoogle Scholar
  50. Fischer, A. and Modersitzki, J. 2001. A super fast registration algorithm. BVM, 22:168–173.Google Scholar
  51. Fischer, A. and Modersitzki, J. 2002. Fast diffusion registration. Contemp. Math, 313:117–129.MathSciNetGoogle Scholar
  52. Fischer, M. and Elschlager, R. 1973. The representation and matching of pictorial structure. IEEE Trans. Comput, 1:67–92.Google Scholar
  53. Fortner. 1999. User’s Guide and Reference Manual Fortner Software: Boulder.Google Scholar
  54. Fu, Y. and Ogden, R. 2001. Nonlinear Elasticity: Theory and Applications Cambridge University Press: Cambridge.Google Scholar
  55. Gefen, S., Tretiak, O., and Nissanov, J. 2003. Elastic 3-D alignment of rat brain histological images. IEEE Trans. Med. Imag, 22:1480–1489.CrossRefGoogle Scholar
  56. Gerstein, G., Bedenbaugh, P., and Aertsen, A. 1989. Neuronal assemblies. IEEE Trans. Biomed. Engin, 36:4–14.CrossRefGoogle Scholar
  57. Glaser, J. and Glaser, M. 1965. A semi-automatic computer-microscope for the analysis of neuronal morphology. IEEE Trans. Biomed. Eng, 12:22–31.Google Scholar
  58. Gold, S., Rangarajan, A., Lu, C., Pappu, S., and Mjolsness, E. 1998. New algorithms for 2-D and 3-D point matching: pose estimation and correspondence. Pat. Recogn, 31:1019–1031.CrossRefGoogle Scholar
  59. Golub, G. and van Loan, C. 1989. Matrix Computations Second edition. The John Hopkins University Press: Baltimore.Google Scholar
  60. Green, A. and Adkins, J. 1970. Large Elastic Deformations Clarendon Press: Oxford.Google Scholar
  61. Green, A. and Zerna, W. 1968. Theoretical Elasticity Clarendon Press: Oxford.Google Scholar
  62. Gremillet, P., Bron, C. Jourlin, M., Bachi, T., and Schüpbach, J. 1991. Dedicated image analysis techniques for three-dimensional reconstruction from serial sections in electron microscopy. Mach. Vis. Appl, 4:263–270.CrossRefGoogle Scholar
  63. Guimond, A., Roche, A., Ayache, N., and Meunier, J. 2001. Three-dimensional multimodal brain warping using the demons algorithm and adaptive intensity corrections. IEEE Trans. Med. Imaging, 20:58–69.CrossRefGoogle Scholar
  64. Hajnal, J., Saeed, N., Soar, E., Oatridge, A., Young, I., and Bydder, G. 1995. A registration and interpolation procedure for subvoxel matching of serially acquired MR images. J. Comput. Assist. Tomogr, 19:289–296.CrossRefGoogle Scholar
  65. Hamilton, P., McInerney, T., and Terzopoulos, D. 2001. Deformable organisms for automatic medical image analysis. LNCS, 2208:66–76.Google Scholar
  66. Hayakawa, N., Thevenaz, P., Nirkko, A., Uemura, M.U., Ishiwata, K., Shimada, Y., Ogi, N., Nagaoka, T., Toyama, H., Oda, K., Tanaka, A., Endo, K., and Senda, M. 2000. A PET-MRI registration technique for PET studies of the rat brain. Nucl. Med. Biol, 27:121–125.CrossRefGoogle Scholar
  67. Hebb, D. 1949, The Organization of Behavior Wiley: New York.Google Scholar
  68. Hellier, P., Barillot, C., Memin, E., and Perez, P. 2001. Hierarchical estimation of a dense deformation field for 3-D robust registration. IEEE Trans. Med. Imaging, 20:388–402.CrossRefGoogle Scholar
  69. Hibbard, L., Arnicar-Sulze, T., Dovey-Hartman, B., and Page, R. 1992. Computed alignment of dissimilar images for three-dimensional reconstructions. J. Neurosci. Methods, 41:133–152.CrossRefGoogle Scholar
  70. Hibbard, L., and Hawkins, R. 1988. Objective image alignment for three-dimensional reconstruction of digital autoradiograms. J Neurosci. Meth, 26:55–74.CrossRefGoogle Scholar
  71. Hibbard, L., McGlone, J., Davis, D., and Hawkins, R. 1987. Three-dimensional representation and analysis of brain energy metabolism. Science, 236:1641–1646.CrossRefGoogle Scholar
  72. Hill, D., Batchelor, P., Holden, M., and Hawkes, D. 2001. Medical image registration. Phys. Med. Biol, 46: R1–R45.Google Scholar
  73. Hoehn, M., Küstermann, E., Blunck, J., Wiedermann, D., Trapp, T., Wecker, S., Föking, M., Arnold, H., Hescheler, J., Fleischmann, B., Schwindt, W., and Bührle, C. 2002. Monitoring of implanted stem cell migration in vivo: a highly resolved in vivo magnetic resonance imaging investigation of experimental strocke in rat. Proc. Nat. Acad. Sci, 99:16267–16272.CrossRefGoogle Scholar
  74. Holden, M., Hill, D.H., Denton, E., Jarosz, J., Cox, T., Rohlfing, T., Goodey, J., and Hawkes, D. 2000. Voxel similarity measures for 3-D serial MR brain image registration. IEEE Trans. Med. Imaging, 19:94–102.CrossRefGoogle Scholar
  75. Horn, B. and Schunck, B. 1981. Determining optical flow. Art. Intell, 17:185–204.CrossRefGoogle Scholar
  76. Hsu, C., Wu, M., and Lee, C. 2001. Robust image registration for functional magnetic resonance imaging of the brain. Med. Biol. Eng. Comput, 39:517–524.CrossRefGoogle Scholar
  77. Hu, M. 1962. Visual pattern recognition by moment invariants. IEEE Trans. Inform. Theory, 8:179–187.Google Scholar
  78. Iosifescu, D., Fitzpatrick, J., Wang, M., Galloway, R.J., Maciunas, R., Allen, G., Shenton, M., Warfield, S., Kikinis, R., Dengler, J., Jolesz, F., and McCarley, R. 1997. An automated registration algorithm for measuring MRI subcortical brain structures. Neuroimage, 6:13–25.CrossRefGoogle Scholar
  79. Jacobs, M., Windham, J., Soltanian-Zadeh, H., Peck, D., and Knight, R. 1999. Registration and warping of magnetic resonance images to histological sections. Med. Phys, 26:1568–1578.CrossRefGoogle Scholar
  80. Jannin, P., Fleig, O., Seigneuret, E., Grova, C., Morandi, X., and Scarabin, J. 2000. A data fusion environment for multimodal and multi-informational neuronavigation. Comput. Aided. Surg, 5:1–10.CrossRefGoogle Scholar
  81. Johnson, E. and Capowski, J. 1983. A system for the three-dimensional reconstruction of biological structures. Comp. Biomed. Res, 16:79–87.CrossRefGoogle Scholar
  82. Johnson, H. and Christensen, G. 2001. Landmark and intensity-based, consistent thin-plate spline image registration. LNCS, 2082:329–343.Google Scholar
  83. Joshi, S. and Miller, M. 2000. Landmark matching via large deformation diffeomorphisms. IEEE Trans. Image. Proc, 9:1357–1370.MathSciNetCrossRefzbMATHGoogle Scholar
  84. Juan, M., Alcaniz, B., Hernandez, V., Montesinos, A., Barcia, J., Monserrat, C., and Grau, V. 2000. A new efficient method for 3D registration using human brain atlases. Stud. Health. Technol. Inform, 70:153–155.Google Scholar
  85. Kent, J. and Tyler, D. 1988. Maximum likelihood estimation for the wrapped Cauchy distribution. J. Appl. Stat, 15:247–254.Google Scholar
  86. Kiebel, S., Ashburner, J., Poline, J., and Friston, K. 1997. MRI and PET coregistration–a cross validation of statistical parametric mapping and automated image registration. Neuroimage, 5:271–279.CrossRefGoogle Scholar
  87. Kosevich, A. 1995, Theory of Elasticity 3rd Ed. Butterworth Heinemann, Oxford.Google Scholar
  88. Kostelec, P., Weaver, J., and Healy, D. J. 1998. Multiresolution elastic image registration. Med. Phys, 25:1593–1604.CrossRefGoogle Scholar
  89. Kremser, C., Plangger, C., Boesecke, R., Pallua, A., Aichner, F., and Felber, S. 1997. Image registration of MR and CT images using a frameless fiducial marker system. Mag. Res. Imag, 15:579–585.CrossRefGoogle Scholar
  90. Kuglin, C. and Hines, D. 1975. The phase correlation image alignment method. Proc. IEEE Int. Conf. Cyb. Soc, 163–165.Google Scholar
  91. Kuljis, R. and Rakic, P. 1990. Hypercolumns in primate visual cortex can develop in the absence of cues from photoreceptors. Proc. Natl. Acad. Sci. USA, 87:5303–5306.CrossRefGoogle Scholar
  92. Kullback, S. and Leibler, R. 1951. On information and sufficiency. Ann. Math. Statist, 122:79–86.MathSciNetGoogle Scholar
  93. Lamadø, W., Glombitza, G., Demiris, A., Cardenas, C., Thorn, M., Meinzer, H., Grenacher, L., Bauer, H., Lehnert, T., and Herfarth, C. 2000. The impact of 3-dimensional reconstructions on operation planing in liver surgery. Arch. Surg, 135:1256–1261.CrossRefGoogle Scholar
  94. Lester, H. and Arridge, S. 1999. A survey of hierarchical non-linear medical image registration. Pat. Rec, 32:129–149.CrossRefGoogle Scholar
  95. Likar, B. and Pernus, F. 1999. Automatic extraction of corresponding points for the registration of medical images. Med. Phys, 26:1678–1686.CrossRefGoogle Scholar
  96. Lurie, A. 1990, Nonlinear Theory of Elasticity North-Holland: Amsterdam.zbMATHGoogle Scholar
  97. Macagno, E., Levinthal, C., and Sobel, I. 1979. Three-dimensional computer reconstruction of neurons and neuronal assemblies. Annu. Rev. Biophys. Bioeng, 8:323–351.CrossRefGoogle Scholar
  98. Macagno, E., Levinthal, C., Tountas, C., Bornholdt, R., and Abba, R. 1976, Recording and Analysis of 3-D Information from Serial Section Micrographs: The Cartos System Hemisphere Publishing Corporation: Washington, P.B. Brown: Computer technology in neuroscience edition.Google Scholar
  99. MacDonald, D., Kabani, N., Avis, D., and Evans, A. 2000. Automated 3d extraction of inner and outer surfaces of cerebral cortex from MRI. NeuroImage, 12:340–356.CrossRefGoogle Scholar
  100. Maintz, J. and Viergever, M. 1981. A survey of medical image registration. Med. Image. Anal, 2:1–36.CrossRefGoogle Scholar
  101. Malandain, G. and Bardinet, E. 2003. Intensity compensation within series of images. LNCS, 2879:41–49.Google Scholar
  102. Malandain, G., Bardinet, E., Nelissen, K., and Vanduffel, W. 2004. Fusion of autoradiographs with an MR volume using 2-D and 3-D linear transformations. NeuroImage, 23:111–127.CrossRefGoogle Scholar
  103. Maurer, C. and Fitzpatrick, J. 1993. Interactive Image-Guided Neurosurgery R.J. Maciunas (Ed.). A review of medical image registration, American Association of Neurological Surgeons, Park Ridge, IL, pp. 17–44.Google Scholar
  104. Maurer, C., Fitzpatrick, J., Wang, M., Galloway, R., Maciunas, R., and GS, G.A. 1997. Registration of head volume images using implantable fiducial markers. IEEE Trans. Med. Imag, 16:447–462.CrossRefGoogle Scholar
  105. Maurer, C., Hill, D., Martin, A., Liu, H., McCue, M., Rueckert, D., Lloret, D., Hall, W., Maxwell, R., Hawkes, D., and Truwit, C. 1998a. Investigation of intraoperative brain deformation using a 1.5-T interventional MR system: preliminary results. J. Anat, 193:347–361.CrossRefGoogle Scholar
  106. Maurer, C., Hill, D., Martin, A., Liu, H., McCue, M., Rueckert, D., Lloret, D., Hall, W., Maxwell, R., Hawkes, D., and Truwit, C. 1998b. Investigation of intraoperative brain deformation using a 1.5-T interventional MR system: preliminary results. IEEE Trans. Med. Imaging, 17:817–825.CrossRefGoogle Scholar
  107. Maurer, C., Maciunas, R., and Fitzpatrick, J. 1998c. Registration of head CT images to physical space using a weighted combination of points and surfaces. IEEE Trans. Med. Imaging, 17:753–761.CrossRefGoogle Scholar
  108. McInerney, J. and Roberts, D. 1998. An object-based volumetric deformable atlas for the improved localization of neuroanatomy in MR images. LNCS, 1496:861–869.Google Scholar
  109. Mega, M., Berdichevsky, D., Levin, Z., Morris, E., Fischman, A., Chen, S., Thompson, P., Woods, R., Karaca, T., Tiwari, A., Vinters, H., Small, G., and Toga, A. 1997. Mapping histology to metabolism: Coregistration of stained whole-brain sections to premortem PET in Alzheimer’s disease. Neuroimage, 5:147–153.CrossRefGoogle Scholar
  110. Miller, K. and Chinzei, K. 1997. Constitutive modelling of brain tissue: experiment and theory. J. Biomech, 30:1115–1121.CrossRefGoogle Scholar
  111. Modersitzki, J. 2004, Numerical Methods for Image Registration Oxford University Press.Google Scholar
  112. Modersitzki, J., Obelöer, W., Schmitt, O., and Lustig, G. 1999. Elastic matching of very large digital images on high performance clusters. LNCS, 1593:141–149.Google Scholar
  113. Mountcastle, V. 1997. The columnar organization of the neocortex. Brain, 120:701–722.CrossRefGoogle Scholar
  114. Murphy, M., O’Brien, T., Morris, K., and Cook, M. 2001. Multimodality image-guided epilepsy surgery. J. Clin. Neurosci, 8:534–538.CrossRefGoogle Scholar
  115. Mutic, S., Hellier, P., Barillot, C., Dempsey, J., Bosch, W., Low, D., Drzymala, R., Chao, K., Goddu, S., Cutler, P., and Purdy, J. 2001. Multimodality image registration quality assurance for conformal three-dimensional treatment planning. Int. J. Radiat. Oncol. Biol. Phys, 51:255–260.CrossRefGoogle Scholar
  116. Nowinski, W., Scarth, G., Somorjai, R., Fang, A., Nguyen, B., Raphel, J., Jagannathan, L., Raghavan, R., Bryan, R., and Miller, G. 1997. Multiple brain atlas database and atlas-based neuroimaging system. Comput. Aided. Surg, 2:42–66.CrossRefGoogle Scholar
  117. Nowinski, W. and Thirunavuukarasuu, A. 2001. Atlas-assisted localization analysis of functional images. Med. Image. Anal, 5:207–220.CrossRefGoogle Scholar
  118. Okajima, K. 1986. A mathematical model of the primary cortex and hypercolumn. Biol. Cyber, 54:107–114.CrossRefzbMATHGoogle Scholar
  119. Ongaro, I., Sperber, G., Machin, G., and Murdoch, C. 1991. Fiducial points for three-dimensional computer-assisted reconstruction of serial light microscopic sections of umbilical cord. Anat. Rec, 229:285–289.CrossRefGoogle Scholar
  120. Otte, M. 2001. Elastic registration of fMRI data using Bezier-spline transformations. IEEE Trans. Med. Imaging, 20:193–206.CrossRefGoogle Scholar
  121. Ourselin, S., Bardinet, E., Dormont, D., Malandain, G., Roche, A., Ayache, N., Tandé, D. Parain, K., and Yelnik, J. 2001a. Fusion of histological sections and MR images: towards the construction of an atlas of the human basal ganglia. LNCS, 2208:743–751.Google Scholar
  122. Ourselin, S., Roche, A., Subsol, G., Pennec, X., and Ayache, N. 2001b. Reconstructing a 3D structure from serial histologic sections. Image. Vis. Comp, 19:25–31.CrossRefGoogle Scholar
  123. Palm, G. 1982, Studies of Brain Function: Neural Assemblies Springer: Berlin.Google Scholar
  124. Pawley, J. 1995, Handbook of Biological Confocal Microscopy Plenum: New York.Google Scholar
  125. Penney, G., Weese, J., Little, J., Desmedt, P., Hill, D., and Hawkes, D. 1998. A comparison of similarity measures for use in 2-D-3-D medical image registration. IEEE Trans. Med. Imaging, 17:586–595.CrossRefGoogle Scholar
  126. Perkins, W. and Green, R. 1982. Three-dimensional reconstruction of biological sections. J. Biomed. Eng 4:37–43.CrossRefGoogle Scholar
  127. Rangarajan, A., Chui, H., and Duncan, J. 1999. Rigid point feature registration using mutual information. Med. Image. Anal, 3:425–440.CrossRefGoogle Scholar
  128. Rangarajan, A., Chui, H., Mjolsness, E., Pappu, S., Davachi, L., Goldman-Rakic, P., and Duncan, J. 1997. A robust point matching algorithm for autoradiographic alignment. Med. Image. Anal, 4:379–398.CrossRefGoogle Scholar
  129. Rohlfing, T. and Maurer, C. 2001. Intensity-based non-rigid registration using adaptive multilevel free-form deformation with an incompressibility constraint. LNCS, 2208:111–119.Google Scholar
  130. Rohlfing, T., West, J., Beier, J., Liebig, T., Taschner, C., and Thomale, U. 2000. Registration of functional and anatomical MRI: accuracy assessment and application in navigated neurosurgery. Comput. Aided. Surg, 5:414–425.CrossRefGoogle Scholar
  131. Rohr, K., Stiehl, H., Sprengel, R., Buzug, T., Weese, J., and Kuhn, M. 2001. Landmark-based elastic registration using approximating thin-plate splines. IEEE Trans. Med. Imaging, 20:526–534.CrossRefGoogle Scholar
  132. Rouet, J., Jacq, J., and Roux, C. 2000. Genetic algorithms for a robust 3-D MR-CT registration. IEEE Trans. Inf. Technol. Biomed, 4:126–136.CrossRefGoogle Scholar
  133. Rueckert, D., Sonoda, L., Hayes, C., Hill, D., Leach, M., and Hawkes, D. 1999. Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans. Med. Imaging, 18:712–721.CrossRefGoogle Scholar
  134. Rusinek, H., Tsui, W.-H., Levy, A., Noz, M., and de Leon, M. 1993. Principal axes and surface fitting methods for three-dimensional image registration. J. Nuc. Med, 34:2019–2024.Google Scholar
  135. Russo, R. 1996, Mathematical Problems in Elasticity World Scientific Publ: Singapore.zbMATHGoogle Scholar
  136. Sabbah, P., Zagrodsky, V., Foehrenbach, H., Dutertre, G., Nioche, C., DeDreuille, O., Bellegou, N., Mangin, J., Leveque, C., Faillot, T., Gaillard, J., Desgeorges, M., and Cordoliani, Y. 2002. Multimodal anatomic, functional, and metabolic brain imaging for tumor resection. Clin. Imaging, 26:6–12.CrossRefGoogle Scholar
  137. Santori, E. and Toga, A. 1993. Superpositioning of 3-dimensional neuroanatomic data sets. J. Neurosci. Methods, 50:187–196.CrossRefGoogle Scholar
  138. Schieweck, F. 1993. A parallel multigrid algorithm for solving the Navier-Stockes equations. Imp. Comp. Sci. Eng, 5:345–378.MathSciNetCrossRefzbMATHGoogle Scholar
  139. Schlaug, G., Schleicher, A., and Zilles, K. 1995. Quantitative analysis of the columnar arrangement of neurons in the human cingulate cortex. J. Comp. Neurol, 351:441–452.CrossRefGoogle Scholar
  140. Schmitt, O. and Eggers, R. 1997a. High contrast and homogeneous staining of paraffin sections of whole human brains for three dimensional ultrahigh resolution image analysis. Biotech. Histochem, 73:44–51.CrossRefGoogle Scholar
  141. Schmitt, O. and Eggers, R. 1997b. Systematic investigations of the contrast results of histochemical stainings of neurons and glial cells in the human brain by means of image analysis. Micron, 28:197–215.CrossRefGoogle Scholar
  142. Schmitt, O. and Eggers, R. 1999. Flat-bed scanning as a tool for quantitative neuroimaging. J. Microsc, 196:337–346.CrossRefGoogle Scholar
  143. Schmitt, O., Eggers, R., and Modersitzki, J. 2005. Videomicroscopy, image processing, and analysis of whole histologic sections of the human brain. Micr. Res. Tech, 66:203–218.CrossRefGoogle Scholar
  144. Schmitt, O., Modersitzki, J., and Obelöer, W. 1999. The human neuroscanning project. Neuroimage, 9:S22.Google Scholar
  145. Schmolke, C. 1996. Tissue compartments in laminae II-V of rabbit visual cortex–three-dimensional arrangement, size and developmental changes. Anat. Embryol, 193:15–33.CrossRefGoogle Scholar
  146. Schmolke, C. and Fleischhauer, K. 1984. Morphological characteristics of neocortical laminae when studied in tangential semithin sections through the visual cortex of the rabbit. Anat. Embryol, 169:125–133.CrossRefGoogle Scholar
  147. Schormann, T. 1996. A new approach to fast elastic alignment with applications to human brains. LNCS, 1131:337–342.Google Scholar
  148. Schormann, T., Darbinghaus, A., and Zilles, K. 1997. Extension of the principle axes theory for the determination of affine transformations. Informatik aktuell, 19:384–391.Google Scholar
  149. Schormann, T. and Zilles, K. 1997. Limitations of the principal axes theory. IEEE Trans. Med. Imag, 16:942–947.CrossRefGoogle Scholar
  150. Schormann, T. and Zilles, K. 1998. Three-dimensional linear and nonlinear transformations: an integration of light microscopical and MRI data. Hum. Brain. Mapp, 6:339–347.CrossRefGoogle Scholar
  151. Silva, A. and Koretsky, A. 2002. Laminar specificity of functional MRI onset times during somatosensory stimulation in rat. Proc. Nat. Acad. Sci, 99:15182–15187.CrossRefGoogle Scholar
  152. Sjöstrand, R. 1958. Ultrastructure of retinal rod synapses of the guinea pig eye as revealed by 3-D reconstructions from serial sections. J. Ultrastruct. Res, 2:122–170.CrossRefGoogle Scholar
  153. Sokolnikoff, I. 1956, Mathematical Theory of Elasticity McGraw-Hill: New York.zbMATHGoogle Scholar
  154. Street, C. and Mize, R. 1983. A simple microcomputer-based three-dimensional serial reconstruction system (MICROS). J. Neurosci. Meth, 7:359–375.CrossRefGoogle Scholar
  155. Studholme, C., Hill, D., and Hawkes, D. 1999. An overlap invariant entropy measure of 3D medical image alignment. Pat. Recog, 32:71–86.CrossRefGoogle Scholar
  156. Symon, K. 1971, Mechanics 3rd edition, Addison-Wesley: Reading, MA.Google Scholar
  157. Tanaka, S. 1991. Theory of ocular dominance column formation. Biol. Cyber, 64:263–272.CrossRefGoogle Scholar
  158. Thirion, J.-P. 1998. Image matching as a diffusion process: An analogy with Maxwell’s demons. Med. Image. Anal, 2:243–260.CrossRefGoogle Scholar
  159. Thompson, J., Peterson, M., and Freeman, R. 2003. Single-Neuron activity and tissue oxygenation in the cerebral cortex. Science, 299:1070–1072.CrossRefGoogle Scholar
  160. Thompson, M. and Ferziger, J. 1989. An adaptive multigrid technique for the incompressible Navier-Stockes equations. J. Comp. Phys, 82:94–121.CrossRefzbMATHGoogle Scholar
  161. Thurfjell, L., Bohm, C., and Bengtsson, E. 1995. CBA–an atlas-based software tool used to facilitate the interpretation of neuroimaging data. Comput. Methods. Programs. Biomed, 47:51–71.CrossRefGoogle Scholar
  162. Toga, A. and Banerjee, P. 1993. Registration revisited. J. Neurosci. Meth, 48:1–13.CrossRefGoogle Scholar
  163. Toga, A., Santori, E., Hazani, R., and Ambach, K. 1995. A 3D digital map of rat brain. Brain. Res. Bull, 38:77–85.CrossRefGoogle Scholar
  164. Toga, A. and Thompson, P. 2001. The role of image registration in brain mapping. Image. Vis. Comp, 19:3–24.CrossRefGoogle Scholar
  165. van den Elsen, P., Pol, E.-J., and Viergever, M. 1993. Medical image matching - a review with classification. IEEE Eng. Med. Biol, 12:26–39.CrossRefGoogle Scholar
  166. van Essen, D. 1997. A tension-based theory of morphologenesis and compact wiring in the central nervous system. Nature, 285:313–318.CrossRefGoogle Scholar
  167. Vatsa, V. and Wedan, B. 1990. Development of a multigrid code for 3-D Navier-Stokes equations and its application to a grid-refinement study. Comp. Fluids, 18:391–403.CrossRefzbMATHGoogle Scholar
  168. Viergever, M., Maintz, J., and Stokking, R. 1997. Integration of functional and anatomical brain images. Biophys. Chem, 68:207–219.CrossRefGoogle Scholar
  169. Viola, P. and Wells, W. 1993. Alignment by maximization of mutual information—a review with classification. 5th Int. Conf. Comp. Vis., IEEE, 5:16–23.Google Scholar
  170. Viola, P. and Wells, W.: 1997. Alignment by maximization of mutual information. Int. J. Comp. Vision, 24:137–154.CrossRefGoogle Scholar
  171. Ware, R. and LoPresti, V. 1975. Three-Dimensional reconstruction from serial sections. Int. Rev. Cytol, 40:325–440.CrossRefGoogle Scholar
  172. Watanabe, H., Andersen, F., Simonsen, C., Evans, S., Gjedde, A., and Cumming, P. 2001. MR-based statistical atlas of the Gottingen minipig brain. Neuroimage, 14:1089–1096.CrossRefGoogle Scholar
  173. Webster, R. 1994. An algebraic multigrid solver for Navier-Stokes problems. Int. J. Num. Meth. Fluids, 18:761–780.CrossRefzbMATHGoogle Scholar
  174. West, J., Fitzpatrick, J., Toms, S., Maurer, C., and Maciunas, R. 2001. Fiducial point placement and the accuracy of point-based, rigid body registration. Neurosurgery, 48:810–817.CrossRefGoogle Scholar
  175. White, E. 1989, Cortical Circuits. Synaptic Organization of the Cerebral Cortex. Structure, Function, and Theory Birkhäuser, Boston.Google Scholar
  176. Widrow, B. 1973. The rubber-mask technique. I. Pattern Measurement and analysis. Pat. Recog, 5:175–197.CrossRefGoogle Scholar
  177. Woods, R., Dapretto, M., Sicotte, N., Toga, A., and Mazziotta, J. 1999. Creation and use of a Talairach-compatible atlas for accurate, automated, nonlinear intersubject registration, and analysis of functional imaging data. Hum. Brain. Mapp, 8:73–79.CrossRefGoogle Scholar
  178. Woods, R., Grafton, S., Holmes, C., Cherry, S., and Mazziotta, J. 1998a. Automated image registration: I. General methods and intrasubject, intramodality validation. J. Comput. Assist. Tomogr, 22:139–152.CrossRefGoogle Scholar
  179. Woods, R., Grafton, S., Watson, J., Sicotte, N., and Mazziotta, J. 1998b. Automated image registration: II. Intersubject validation of linear and nonlinear models. J. Comput. Assist. Tomogr, 22:153–165.CrossRefGoogle Scholar
  180. Yeshurun, Y. and Schwartz, E. 1999. Cortical hypercolumn size determines stereo fusion limits. Biol. Cyber, 80:117–129.CrossRefzbMATHGoogle Scholar
  181. You, J. 1995. Efficient image matching: A hierarchical chamfer matching scheme via distributed system. Real-time Imag, 1:245–259.CrossRefGoogle Scholar
  182. Young, M. 1992. Objective analysis of the topological organization of the primate cortical visual system. Nature, 358:152–155.CrossRefGoogle Scholar
  183. Young, M. 1996, The Analysis of Cortical Connectivity Springer.Google Scholar
  184. Zeiss: 1992. KS400 Reference Guide Zeiss Vision: Jena.Google Scholar
  185. Zhao, W., Young, T., and Ginsberg, M. 1993. Registration and three-dimensional reconstruction of autoradiographic images by the disparity analysis method. IEEE Trans. Med. Imag, 12:782–791.CrossRefGoogle Scholar
  186. Zhu, Y. 2002. Volume image registration by cross-entropy optimization. IEEE Trans. Med. Imaging, 21:174–180.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Oliver Schmitt
    • 1
    Email author
  • Jan Modersitzki
    • 2
  • Stefan Heldmann
    • 2
  • Stefan Wirtz
    • 2
  • Bernd Fischer
    • 3
  1. 1.Institute of AnatomyUniversity of RostockRostockGermany
  2. 2.Institute of MathematicsUniversity of LübeckLübeckGermany
  3. 3.Institute of MathematicsMedical University of LübeckLübeckGermany

Personalised recommendations