This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations
August 2006 (vol. 28 no. 8)
pp. 1303-1318
ASCII Text
x 
 
Xiaolei Huang, Nikos Paragios, Dimitris N. Metaxas, "Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1303-1318, August, 2006.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2006.171,
author = {Xiaolei Huang and Nikos Paragios and Dimitris N. Metaxas},
title = {Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {28},
number = {8},
issn = {0162-8828},
year = {2006},
pages = {1303-1318},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2006.171},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations
IS - 8
SN - 0162-8828
SP1303
EP1318
EPD - 1303-1318
A1 - Xiaolei Huang,
A1 - Nikos Paragios,
A1 - Dimitris N. Metaxas,
PY - 2006
KW - Shape registration
KW - mutual information
KW - free form deformations
KW - correspondences
KW - implicit shape representation
KW - distance transforms
KW - partial differential equations.
VL - 28
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
We present a novel, variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher-dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then, a B-spline-based Incremental Free Form Deformations (IFFD) model is used to minimize a Sum-of-Squared-Differences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: 1) it naturally deals with shapes of arbitrary dimension (2D, 3D, or higher) and arbitrary topology (multiple parts, closed/open) and 2) it preserves shape topology during local deformation and produces local registration fields that are smooth, continuous, and establish one-to-one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion, and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well-known shape registration algorithms.

[1] R. Veltkamp and M. Hagedoorn, “State-of-the-Art in Shape Matching,” Technical Report UU-CS-1999-27, Utrecht Univ., 1999.
[2] T. Cootes, C. Taylor, D. Cooper, and J. Graham, “Active Shape Models— Their Training and Application,” Computer Vision and Image Understanding, vol. 61, pp. 38-59, 1995.
[3] N. Paragios, M. Rousson, and V. Ramesh, “Non-Rigid Registration Using Distance Functions,” Computer Vision and Image Understanding, vol. 89, pp. 142-165, 2003.
[4] Z. Zhang, “Iterative Point Matching for Registration of Free-Form Curves and Surfaces,” Int'l J. Computer Vision, vol. 13, no. 2, pp. 119-152, 1994.
[5] P.J. Besl and N.D. McKay, “A Method for Registration of 3-D Shapes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992.
[6] S. Belongie, J. Malik, and J. Puzicha, “Matching Shapes,” Proc. IEEE Int'l Conf. Computer Vision, pp. 456-461, 2001.
[7] R.H. Davies, C.J. Twining, T.F. Cootes, J.C. Waterton, and C.J. Taylor, “3D Statistical Shape Models Using Direct Optimization of Description Length,” Proc. European Conf. Computer Vision, pp. 3-20, 2002.
[8] T. Sebastian, P. Klein, and B. Kimia, “Alignment-Based Recognition of Shape Outlines,” Lecture Notes in Computer Science, vol. 2059, pp. 606-618, 2001.
[9] H. Chui and A. Rangarajan, “A New Algorithm for Non-Rigid Point Matching,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. II: 44-51, 2000.
[10] D. Metaxas, Physics-Based Deformable Models. Kluwer Academic, 1996.
[11] L.H. Staib and J.S. Duncan, “Boundary Finding with Parametrically Deformable Models,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 11, pp. 1061-1075, Nov. 1992.
[12] T. Sebastian, P. Klein, and B. Kimia, “Recognition of Shapes by Editting Shock Graphs,” Proc. IEEE Int'l Conf. Computer Vision, pp. 755-762, 2001.
[13] M. Leventon, E. Grimson, and O. Faugeras, “Statistical Shape Influence in Geodesic Active Contours,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. I: 316-322, 2001.
[14] C. Chefd'Hotel, G. Hermosillo, and O. Faugeras, “A Variational Approach to Multi-Modal Image Matching,” Proc. IEEE Workshop Variational and Level Set Methods, pp. 21-28, 2001.
[15] M. Fornefett, K. Rohr, and H. Stiehl, “Elastic Registration of Medical Images Using Radial Basis Functions with Compact Support,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 1402-1409, 1999.
[16] T. Sederberg and S. Parry, “Free-Form Deformation of Solid Geometric Models,” Proc. ACM SIGGRAPH, pp. 151-160, 1986.
[17] D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images,” IEEE Trans. Medical Imaging, vol. 8, pp. 712-721, 1999.
[18] Y. Gdalyahu and D. Weinshall, “Flexible Syntactic Matching of Curves and Its Application to Automatic Hierarchical Classification of Silhouettes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 12, pp. 1312-1328, Dec. 1999.
[19] A.E. Johnson and M. Hebert, “Recognizing Objects by Matching Oriented Points,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 684-689, 1997.
[20] S. Osher and J. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on the Hamilton-Jacobi Formulation,” J. Computational Physics, vol. 79, pp. 12-49, 1988.
[21] A. Collignon, F. Maes, D. Vandermeulen, P. Suetens, and G. Marchal, “Automated Multimodality Image Registration Using Information Theory,” Information Processing in Medical Images, pp. 263-274, 1995.
[22] P. Viola and W. Wells, “Aligment by Maximization of Mutual Information,” Proc. IEEE Int'l Conf. Computer Vision, pp. 16-23, 1995.
[23] C. Studholme, D.L.G. Hill, and D.J. Hawkes, “An Overlap Invariant Entropy Measure of 3D Medical Image Alignment,” Pattern Recognition, vol. 32, no. 1, pp. 71-86, 1999.
[24] W. Zhu and T. Chan, “Stability for Shape Comparison Model,” Technical Report 0308, Univ. of California, Los Angeles-CAM, 2003.
[25] B. Zitova and J. Flusser, “Image Registration Methods: A Survey,” Image and Vision Computing, vol. 21, no. 11, pp. 977-1000, 2003.
[26] X. Huang, N. Paragios, and D. Metaxas, “Establishing Local Correspondences towards Compact Representations of Anatomical Structures,” Proc. Int'l Conf. Medical Imaging Copmuting and Computer-Assisted Intervention, pp. 926-934, 2003.
[27] J.P.W. Pluim, J.B. A. Maintz, and M.A. Viergever, “Mutual Information Based Registration of Medical Images: A Survey,” IEEE Trans. Medical Imaging, vol. 22, no. 8, pp. 986-1004, 2003.
[28] J. Feldmar and N. Ayache, “Rigid, Affine and Locally Affine Registration of Free-Form Surfaces,” Int'l J. Computer Vision, vol. 18, pp. 99-119, 1996.
[29] P. Faloutsos, M. vande Panne, and D. Terzopoulos, “Dynamic Free-Form Deformations for Animation Synthesis,” IEEE Trans. Visualization and Computer Graphics, vol. 3, pp. 201-214, 1997.
[30] S. Lee, K.-Y. Chwa, J. Hahn, and S. Shin, “Image Morphing Using Deformation Techniques,” J. Visualization and Computer Animation, vol. 7, pp. 3-23, 1996.
[31] S. Lee, K.-Y. Chwa, and S. Shin, “Image Metamorphosis with Scattered Feature Constraints,” IEEE Trans. Visualization and Computer Graphics, vol. 2, pp. 337-354, 1996.
[32] D. Forsey and R. Bartels, “Hierachical B-Spline Refinement,” ACM Trans. Computer Graphics, vol. 22, pp. 205-212, 1988.
[33] T. Hartkens, D. Hill, A. Castellano-Smith, D. Hawkes, C. Maurer, A. Martin, W. Hall, H. Liu, and C. Truwit, “Using Points and Surfaces to Improve Voxel-Based Nonrigid Registration,” Proc. Int'l Conf. Medical Imaging Computing and Computer-Assisted Intervention, pp. II: 565-572, 2002.
[34] P. Laskov and C. Kambhamettu, “Curvature-Based Algorithms for Nonrigid Motion and Correspondence Estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1349-1354, Oct. 2003.
[35] X. Huang, S. Zhang, Y. Wang, D. Metaxas, and D. Samaras, “A Hierarchical Framework for High Resolution Facial Expression Tracking,” Proc. Third IEEE Workshop Articulated and Nonrigid Motion, in conjunction with CVPR '04, July 2004.
[36] P.S. Huang, Q. Hu, F. Jin, and F.P. Chiang, “Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring,” Optical Eng., vol. 38, no. 6, pp. 1065-1071, 1999.
[37] L. Zhang, B. Curless, and S.M. Seitz, “Spacetime Stereo: Shape Recovery for Dynamic Scenes,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 367-374, 2003.
[38] S. Ilic and P. Fua, “Using Dirichlet Free Form Deformation to Fit Deformable Models to Noisy 3-D Data,” Proc. European Conf. Computer Vision, pp. 704-717, 2002.

Index Terms:
Shape registration, mutual information, free form deformations, correspondences, implicit shape representation, distance transforms, partial differential equations.
Citation:
Xiaolei Huang, Nikos Paragios, Dimitris N. Metaxas, "Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1303-1318, Aug. 2006, doi:10.1109/TPAMI.2006.171
Usage of this product signifies your acceptance of the Terms of Use.