Automatic shape model building based on principal geodesic analysis bootstrapping

We present a novel method for automatic shape model building from a collection of training shapes. The result is a shape model consisting of the mean model and the major modes of variation with a dense correspondence map between individual shapes. The framework consists of iterations where a medial shape representation is deformed into the training shapes followed by computation of the shape mean and modes of shape variation. In the first iteration, a generic shape model is used as starting point - in the following iterations in the bootstrap method, the resulting mean and modes from the previous iteration are used. Thereby, we gradually capture the shape variation in the training collection better and better. Convergence of the method is explicitly enforced. The method is evaluated on collections of artificial training shapes where the expected shape mean and modes of variation are known by design. Furthermore, collections of real prostates and cartilage sheets are used in the evaluation. The evaluation shows that the method is able to capture the training shapes close to the attainable accuracy already in the first iteration. Furthermore, the correspondence properties measured by generality, specificity, and compactness are improved during the shape model building iterations.

[1]  Paul A. Yushkevich,et al.  Segmentation, registration, and measurement of shape variation via image object shape , 1999, IEEE Transactions on Medical Imaging.

[2]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[3]  L. R. Dice.  Measures of the Amount of Ecologic Association Between Species , 1945 .

[4]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[5]  Martin Styner,et al.  Medial Models Incorporating Object Variability for 3D Shape Analysis , 2001, IPMI.

[6]  Christopher J. Taylor,et al.  A Method of Automated Landmark Generation for Automated 3D PDM Construction , 2000, BMVC.

[7]  P. Thomas Fletcher,et al.  Prostate Shape Modeling Based on Principal Geodesic Analysis Bootstrapping , 2004, MICCAI.

[8]  Christian R. Shelton,et al.  Morphable Surface Models , 2000, International Journal of Computer Vision.

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

[10]  Andrew Thall,et al.  Fast C 2 Interpolating Subdivision Surfaces using Iterative Inversion of Stationary Subdivision Rules , 2003 .

[11]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[12]  Olivier D. Faugeras,et al.  Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics , 2005, Found. Comput. Math..

[13]  Hildur Ólafsdóttir,et al.  Adding Curvature to Minimum Description Length Shape Models , 2003, BMVC.

[14]  Hans Henrik Thodberg,et al.  Minimum Description Length Shape and Appearance Models , 2003, IPMI.

[15]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Christopher J. Taylor,et al.  Automatic construction of eigenshape models by direct optimization , 1998, Medical Image Anal..

[17]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[18]  P. Thomas Fletcher,et al.  Gaussian Distributions on Lie Groups and Their Application to Statistical Shape Analysis , 2003, IPMI.

[19]  Daniel Cremers,et al.  Nonlinear Shape Statistics in Mumford-Shah Based Segmentation , 2002, ECCV.

[20]  Martin Styner,et al.  Evaluation of 3D Correspondence Methods for Model Building , 2003, IPMI.

[21]  P. Danielsson.  Euclidean distance mapping , 1980 .

[22]  J. Kellgren,et al.  Radiological Assessment of Osteo-Arthrosis , 1957, Annals of the rheumatic diseases.

[23]  Hans-Peter Meinzer,et al.  Optimal landmark distributions for statistical shape model construction , 2006, SPIE Medical Imaging.

[24]  HARRY BLUM,et al.  Shape description using weighted symmetric axis features , 1978, Pattern Recognit..

[25]  Hans-Peter Meinzer,et al.  3D Active Shape Models Using Gradient Descent Optimization of Description Length , 2005, IPMI.

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

[27]  Edward L. Chaney,et al.  Medical anatomy segmentation kit: combining 2D and 3D segmentation methods to enhance functionality , 1994, Optics & Photonics.

[28]  Jh. Kellgren.  Radiological assessment of osteoarthrosis , 1957 .

[29]  Tim Cootes.  Timeline of Developments in Algorithms for Finding Correspondences across Sets of Shapes and Images , 2005 .

[30]  P. Thomas Fletcher,et al.  Statistics of shape via principal geodesic analysis on Lie groups , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[31]  Timothy F. Cootes,et al.  A Unified Information-Theoretic Approach to Groupwise Non-rigid Registration and Model Building , 2005, IPMI.

[32]  Geoffrey E. Hinton,et al.  Learning Generative Texture Models with extended Fields-of-Experts , 2009, BMVC.

[33]  Paul A. Yushkevich,et al.  Deformable M-Reps for 3D Medical Image Segmentation , 2003, International Journal of Computer Vision.

[34]  P. Thomas Fletcher,et al.  Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors , 2004, ECCV Workshops CVAMIA and MMBIA.

[35]  Alejandro F Frangi,et al.  Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration , 2003, IEEE Transactions on Medical Imaging.

[36]  Paul A. Yushkevich,et al.  Multiscale deformable model segmentation and statistical shape analysis using medial descriptions , 2002, IEEE Transactions on Medical Imaging.