[en] A statistical model for shapes in $\mathbb{R}^2$ or $\mathbb{R}^3$ is proposed. Shape modelling is a difficult problem mainly due to the non-linear nature of its space. Our approach considers curves as shape contours, and models their deformations with respect to a deformable template shape. Contours are uniformly sampled into a discrete sequence of points. Hence, the deformation of a shape is formulated as an action of transformation matrices on each of these points. A parametrized stochastic model based on Markov process is proposed to model shape variability in the deformation space. The model's parameters are estimated from a labeled training dataset. Moreover, a similarity metric based on the Mahalanobis distance is proposed. Subsequently, the model has been successfully tested for shape recognition, synthesis, and retrieval.
Disciplines :
Sciences informatiques
Auteur, co-auteur :
DEMISSE, Girum ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
AOUADA, Djamila ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
OTTERSTEN, Björn ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Template-Based Statistical Shape Modelling on Deformation Space
Date de publication/diffusion :
2015
Nom de la manifestation :
22nd IEEE International Conference on Image Processing
Organisateur de la manifestation :
IEEE Signal Processing Society in conjunction with Institute of Elecetrical and Electronics Engineers
Lieu de la manifestation :
Quebec city, Canada
Date de la manifestation :
from 27-09-2015 to 30-09-2015
Manifestation à portée :
International
Titre de l'ouvrage principal :
22nd IEEE International Conference on Image Processing
Michael Kass, Andrew Witkin, and Demetri Terzopoulos, "Snakes: Active contour models, " International journal of computer vision, vol. 1, no. 4, pp. 321-331, 1988.
Alan L Yuille, Peter W Hallinan, and David S Cohen, "Feature extraction from faces using deformable templates, " International journal of computer vision, vol. 8, no. 2, pp. 99-111, 1992.
Benjamin B Kimia, Allen R Tannenbaum, and StevenW Zucker, "Shapes, shocks, and deformations i: The components of two-dimensional shape and the reactiondiffusion space, " International journal of computer vision, vol. 15, no. 3, pp. 189-224, 1995.
David G Kendall, "Shape manifolds, procrustean metrics, and complex projective spaces, " Bulletin of the London Mathematical Society, vol. 16, no. 2, pp. 81-121, 1984.
Fred L Bookstein, Morphometric tools for landmark data: geometry and biology, Cambridge University Press, 1997.
Mingqiang Yang, Kidiyo Kpalma, Joseph Ronsin, et al., "A survey of shape feature extraction techniques, " Pattern recognition, pp. 43-90, 2008.
Serge Belongie, Jitendra Malik, and Jan Puzicha, "Shape matching and object recognition using shape contexts, " Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 24, no. 4, pp. 509-522, 2002.
Eitan Sharon and David Mumford, "2d-shape analysis using conformal mapping, " International Journal of Computer Vision, vol. 70, no. 1, pp. 55-75, 2006.
Michael E Leventon, W Eric L Grimson, and Olivier Faugeras, "Statistical shape influence in geodesic active contours, " in Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on. IEEE, 2000, vol. 1, pp. 316-323.
Yali Amit, Ulf Grenander, and Mauro Piccioni, "Structural image restoration through deformable templates, " Journal of the American Statistical Association, vol. 86, no. 414, pp. 376-387, 1991.
Oren Freifeld and Michael J Black, "Lie bodies: A manifold representation of 3d human shape, " in Computer Vision-ECCV 2012, pp. 1-14. Springer, 2012.
Christopher G Small, The Statistical Theory of Shape, Springer Series in Statistics, New York: Springer-Verlag, 1996.
Julian Besag, "Statistical analysis of non-lattice data, " The statistician, pp. 179-195, 1975.
John M Lee, Riemannian manifolds: An introduction to curvature, vol. 176, Springer, 1997.
Maher Moakher, "Means and averaging in the group of rotations, " SIAM journal on matrix analysis and applications, vol. 24, no. 1, pp. 1-16, 2002.
Rajendra Bhatia, Positive definite matrices, Princeton University Press, 2009.
Hermann Karcher, "Riemannian center of mass and mollifier smoothing, " Communications on pure and applied mathematics, vol. 30, no. 5, pp. 509-541, 1977.
Milos Zefran, Vijay Kumar, and Christopher B Croke, "On the generation of smooth three-dimensional rigid body motions, " Robotics and Automation, IEEE Transactions on, vol. 14, no. 4, pp. 576-589, 1998.
P-A Absil, Robert Mahony, and Rodolphe Sepulchre, Optimization algorithms on matrix manifolds, Princeton University Press, 2009.
Jeffrey Ho, Guang Cheng, Hesamoddin Salehian, and Baba Vemuri, "Recursive karcher expectation estimators and geometric law of large numbers, " in Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, 2013, pp. 325-332.
Haibin Ling and David W Jacobs, "Shape classification using the inner-distance, " Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 29, no. 2, pp. 286-299, 2007.
Longin Jan Latecki, Rolf Lakamper, and T Eckhardt, "Shape descriptors for non-rigid shapes with a single closed contour, " in Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on. IEEE, 2000, vol. 1, pp. 424-429.
Ninad Thakoor, Jean Gao, and Sungying Jung, "Hidden markov model-based weighted likelihood discriminant for 2-d shape classification, " Image Processing, IEEE Transactions on, vol. 16, no. 11, pp. 2707-2719, 2007.
Xiang Bai, Xingwei Yang, Longin Jan Latecki, Wenyu Liu, and Zhuowen Tu, "Learning context-sensitive shape similarity by graph transduction, " Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 32, no. 5, pp. 861-874, 2010.