On matching brain volumes

Abstract To characterize the complex morphological variations that occur naturally in human neuroanatomy so that their confounding effect can be minimized in the identification of brain structures in medical images, a computational framework has evolved in which individual anatomies are modeled as warped versions of a canonical representation of the anatomy, known as an atlas . To realize this framework, the method of elastic matching was invented for determining the spatial mapping between a three-dimensional image pair in which one image volume is modeled as an elastic continuum that is deformed to match the appearance of the second volume. In this paper, we review the seminal ideas underlying the elastic matching technique, consider the practical implications of an integral formulation of the approach, and explore a more general Bayesian interpretation of the method in order to address issues that are less naturally resolved within a continuum mechanical setting, such as the examination of a solution’s reliability or the incorporation of empirical information that may be available about the spatial mappings into the analysis.

[1]  M I Miller,et al.  Mathematical textbook of deformable neuroanatomies. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Michael I. Miller,et al.  Hierarchical brain mapping via a generalized Dirichlet solution for mapping brain manifolds , 1995, Optics & Photonics.

[3]  Julian Besag,et al.  Towards Bayesian image analysis , 1993 .

[4]  D. Kendall.  MORPHOMETRIC TOOLS FOR LANDMARK DATA: GEOMETRY AND BIOLOGY , 1994 .

[5]  Morten Bro-Nielsen,et al.  Fast Fluid Registration of Medical Images , 1996, VBC.

[6]  Michael I. Miller,et al.  Deformable templates using large deformation kinematics , 1996, IEEE Trans. Image Process..

[7]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[8]  Ruzena Bajcsy,et al.  Multiresolution elastic matching , 1989, Comput. Vis. Graph. Image Process..

[9]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[10]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[11]  Kanti V. Mardia,et al.  Bayesian image analysis , 1997 .

[12]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[13]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[14]  Ulf Grenander,et al.  Hands: A Pattern Theoretic Study of Biological Shapes , 1990 .

[15]  James C. Gee,et al.  Atlas warping for brain morphometry , 1998, Medical Imaging.

[16]  Lisa M. Brown,et al.  A survey of image registration techniques , 1992, CSUR.

[17]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Jerry L Prince,et al.  A computerized approach for morphological analysis of the corpus callosum. , 1996, Journal of computer assisted tomography.

[19]  G. Strang.  Introduction to applied mathematics / Gilbert Strang , 1986 .

[20]  Nicholas Ayache,et al.  Automatic Retrieval of Anatomical Structures in 3D Medical Images , 1995, CVRMed.

[21]  Christian Barillot,et al.  Bayesian approach to the brain image matching problem , 1995, Medical Imaging.

[22]  Christos Davatzikos,et al.  Spatial Transformation and Registration of Brain Images Using Elastically Deformable Models , 1997, Comput. Vis. Image Underst..

[23]  Dimitris N. Metaxas,et al.  Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  James C. Gee,et al.  Probabilistic Matching of Brain Images , 1995 .

[25]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[26]  M. D’Esposito,et al.  The parahippocampus subserves topographical learning in man , 1996, NeuroImage.

[27]  J. Gee,et al.  An Empirical Model of Brain Shape , 1998 .

[28]  James C. Gee,et al.  Finite element approach to warping of brain images , 1994, Medical Imaging.

[29]  M.N.M. vanLieshout.  Discussion contribution to U. Grenander and M.I. Miller: Representations of knowledge in complex systems , 1994 .

[30]  A. Toga,et al.  High-Resolution Random Mesh Algorithms for Creating a Probabilistic 3D Surface Atlas of the Human Brain , 1996, NeuroImage.

[31]  C. Broit.  Optimal registration of deformed images , 1981 .

[32]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[33]  Michael I. Miller,et al.  Individualizing Anatomical Atlases of the Head , 1996, VBC.

[34]  James C. Gee,et al.  Effect of spatial normalization on analysis of functional data , 1997, Medical Imaging.

[35]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .