Unsupervised learning of an Atlas from unlabeled point-sets

One of the key challenges in deformable shape modeling is the problem of estimating a meaningful average or mean shape from a set of unlabeled shapes. We present a new joint clustering and matching algorithm that is capable of computing such a mean shape from multiple shape samples which are represented by unlabeled point-sets. An iterative bootstrap process is used wherein multiple shape sample point-sets are nonrigidly deformed to the emerging mean shape, with subsequent estimation of the mean shape based on these nonrigid alignments. The process is entirely symmetric with no bias toward any of the original shape sample point-sets. We believe that this method can be especially useful for creating atlases of various shapes present in medical images. We have applied the method to create mean shapes from nine hand-segmented 2D corpus callosum data sets and 10 hippocampal 3D point-sets.

[1]  Anil K. Jain,et al.  Learning 2D shape models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[2]  Jean Meunier,et al.  Average Brain Models: A Convergence Study , 2000, Comput. Vis. Image Underst..

[3]  A. Toga,et al.  Detection and mapping of abnormal brain structure with a probabilistic atlas of cortical surfaces. , 1997, Journal of computer assisted tomography.

[4]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Michael I. Miller,et al.  Landmark matching via large deformation diffeomorphisms , 2000, IEEE Trans. Image Process..

[6]  Joachim M. Buhmann,et al.  Pairwise Data Clustering by Deterministic Annealing , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Robert T. Schultz,et al.  A unified non-rigid feature registration method for brain mapping , 2003, Medical Image Anal..

[8]  Timothy F. Cootes,et al.  A Minimum Description Length Approach to Statistical Shape Modelling , 2001 .

[9]  R. Hathaway.  Another interpretation of the EM algorithm for mixture distributions , 1986 .

[10]  W. Eric L. Grimson,et al.  Statistical Shape Analysis Using Fixed Topology Skeletons: Corpus Callosum Study , 1999, IPMI.

[11]  Gary E. Christensen,et al.  Consistent Linear-Elastic Transformations for Image Matching , 1999, IPMI.

[12]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[13]  R. Menzel,et al.  Bee brains, B-splines and computational democracy: generating an average shape atlas , 2001, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA 2001).

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

[15]  Lawrence H. Staib,et al.  Boundary Finding with Prior Shape and Smoothness Models , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  H. Chui,et al.  A feature registration framework using mixture models , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[17]  Philip N. Klein,et al.  Constructing 2D curve atlases , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[18]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .

[19]  Alejandro F. Frangi,et al.  Automatic Construction of 3D Statistical Deformation Models Using Non-rigid Registration , 2001, MICCAI.

[20]  Timothy F. Cootes,et al.  A minimum description length approach to statistical shape modeling , 2002, IEEE Transactions on Medical Imaging.

[21]  Hemant D. Tagare,et al.  Shape-based nonrigid correspondence with application to heart motion analysis , 1999, IEEE Transactions on Medical Imaging.

[22]  Laurent Younes,et al.  Geodesic Interpolating Splines , 2001, EMMCVPR.

[23]  H. Chui,et al.  Learning an atlas from unlabeled point-sets , 2001, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA 2001).

[24]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[25]  Christopher J. Taylor,et al.  A Framework for Automatic Landmark Identification Using a New Method of Nonrigid Correspondence , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[27]  Rose,et al.  Statistical mechanics and phase transitions in clustering. , 1990, Physical review letters.

[28]  Alan L. Yuille,et al.  Statistical Physics, Mixtures of Distributions, and the EM Algorithm , 1994, Neural Computation.

[29]  Rikard Berthilsson,et al.  A Statistical Theory of Shape , 1998, SSPR/SPR.

[30]  Anil K. Jain,et al.  Automatic Construction of 2D Shape Models , 2001, IEEE Trans. Pattern Anal. Mach. Intell..