Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing

Journal of Mathematical Imaging and Vision

Volumn 9, Issue 1, 1998, Pages 49-67

  Pennec, Xavier ^a,b,c   Ayache, Nicholas ^a,d,e  

^a INRIA   (France)

^b ECOLE POLYTECHNIQUE   (France)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d Epidaure Research Group   (France)

^e UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Expected features; Geometric features; Invariant distance; Invariant measure; Mean features; Transformation groups; Uniform distribution

Indexed keywords

ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; OBJECT RECOGNITION; PROBABILITY; SET THEORY; STATISTICAL METHODS; VECTORS; COMPUTER VISION; DATA ACQUISITION; MATHEMATICAL MODELS; PROBLEM SOLVING;

EXPECTED FEATURES; GEOMETRIC FEATURES; INVARIANT DISTANCE; INVARIANT MEASURE; MEAN FEATURES; TRANSFORMATION GROUPS; UNIFORM DISTRIBUTION;

COMPUTATIONAL GEOMETRY; FEATURE EXTRACTION;

EID: 0032123712     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008270110193     Document Type: Article

References (32)

1. S.L. Altmann, Rotations, Quaternions, and Double Groups, Clarendon Press: Oxford, 1986.
2. N. Ayache, Artificial Vision for Mobile Robots - Stereo-Vision and Multisensor Perception, MIT Press, 1991.
3. N. Ayache and O.D. Faugeras, "Hyper: A new approach for the recognition and positioning of two-dimensional objects," IEEE Trans, on Pattern Analysis and Machine Intelligence, Vol. 8, No. 1, pp. 44-54, 1986.
4. P.J. Besl and N. McKay, "A method for registration of 3D shapes," PAMI, Vol. 14, No. 2, pp. 239-256, 1992.
5. H.F. Durrant-Whyte, Integration, Coordination and Control of Multi-Sensor Robot Systems, Kluwer Academic Publishers, 1988.
6. J. Feldmar and N. Ayache, "Rigid, affine and locally affine registration of free-form surfaces," IJCV, Vol. 18, No. 2, pp. 99-119, 1996.
7. M. Fidrich and J.P. Thirion, "Multiscale representation and analysis of features from medical images," in Computer Vision, Virtual Reality and Robotics in Medicine (Proc. first CVRMed'95), N. Ayache (Ed.), number 905 in LNCS, INRIA, Springer, 1995, pp. 358-364.
8. M. Fréchet, "Les éléments aléatoires de nature quelconque dans un espace distancié," Ann. Inst. H. Poincaré, Vol. 10, pp. 215-310, 1948.
9. W.E.L. Grimson, Object Recognition by Computer - The Role of Geometric Constraints, MIT Press, 1990.
10. W.E.L. Grimson and D.P. Huttenlocher, "On the sensitivity of geometric hashing," in Proc. Third ICCV, 1990, pp. 334-338.
11. W.E.L. Grimson, D.P. Huttenlocher, and D.W Jacobs, "A study of affine matching with bounded sensor error," Int. Journ. of Comput. Vision, Vol. 13, No. 1, pp. 7-32, 1994.
12. G. Hochschild, The Structure of Lie Groups, Holden-Day, 1965.
13. D.P. Huttenlocher and S. Ullman, "Object recognition using alignment," in Proc. of ICCV, 1987, pp. 72-78.
14. H. Karcher, "Riemannian center of mass and mollifier smoothing," Comm. Pure Appl. Math, Vol. 30, pp. 509-541, 1977.
15. W.S. Kendall, "Probability, convexity, and harmonic maps with small image i: uniqueness and fine existence," in Proc. London Math. Soc., 1990, Vol. 61, No. 2, pp. 371-406.
16. M.G. Kendall and P.A.P. Moran, Geometrical Probability, Number 10 in Griffin's Statistical Monographs and Courses, Charles Griffin & Co. Ltd., 1963.
17. F. Klein, Erlangen program, Inaugural address at the University of Erlangen, 1872.
18. Y. Lamdan and H.J. Wolfson, "Geometric hashing: A general and efficient model-based recognition scheme," in Proc. of Second ICCV, 1988, pp. 238-289.
19. Y. Lamdan and H.J. Wolfson, "On the error analysis of geometric hashing," in IEEE Int. Conf. on Comput. Vis. and Patt. Recog., 1991, pp. 22-27.
20. X. Pennec, "Correctness and robustness of 3D rigid matching with bounded sensor error," Research Report 2111, INRIA, November 1993.
21. 2) algorithm for 3D substructure matching of proteins," in Shape and Pattern Matching in Computational Biology, A. Califano, I. Rigoutsos, and H.J. Wolson (Eds.), Proc. First Int. Workshop, Seattle, Wash, June 20, 1994, Plenum Publishing, 1996.
22. X. Pennec, "L'incertitude dans les problèmes de reconnaissance et de recalage - Applications en imagerie médicale et biologie moléculaire," Ph.D. Thesis, Ecole Polytechnique, Palaiseau (France), December 1996. http://www.inria.fr/epidaure/personnel/pennec/These.html
23. X. Pennec and J.P. Thirion, "Validation of 3D registration methods based on points and frames," in Proceedings of the 5th Int. Conf on Comp. Vision (ICCV'95), Cambridge, MA, June 1995, pp. 557-562, Part of the INRIA Research Report no 2470.
24. X. Pennec and J.P. Thirion, "A framework for uncertainty and validation of 3D registration methods based on points and frames," Int. Journal of Computer Vision, 1997, Vol. 25, No. 3, pp. 203-229.
25. H. Poincaré, Calcul des Probabilités, 2nd edition, Paris, 1912.
26. I. Rigoutsos and R. Hummel, "Distributed Bayesian object recognition," in Proceedings of Int. Conf on Comput. Vis. and Pat. Recog, IEEE Computer Society Press, June 1993, pp. 180-186.
27. L.A. Santalo, Integral Geometry and Geometric Probability, volume 1 of Encyclopedia of Mathematics and its Applications, Addison-Wesley Publishing Company, 1976.
28. G. Subsol, J.Ph. Thirion, and N. Ayache, "A general scheme for automatically building 3D morphometric anatomical atlases: application to a skull atlas," in MRCAS'95, November 1995.
29. J.P. Thirion, "New feature points based on geometric invariants for 3D image registration," Int. Journ. Comp. Vis., Vol. 18, No. 2, pp. 121-137, 1996.
30. H.J. Wolfson, "Model-based recognition by geometric hashing," in Proc. of 1st Europ. Conf. on Comput. Vision (ECCV 90), O. Faugeras (Ed.), Springer-Verlag, Lecture Notes in Computer Science 427, April 1990, pp. 526-536.
31. Z. Zhang, "Iterative point matching for registration of free-form curves and surfaces," Int. Journ. Comp. Vis., Vol. 13, No. 2, pp. 119-152, 1994, Also Research Report No.1658, INRIA Sophia-Antipolis, 1992.
32. Z. Zhang and O. Faugeras, 3D Dynamic Scene Analysis: A Stereo Based Approach, volume 27 of Springer Series in Information Science, chapter 2: Uncertainty Manipulation and Parameter Estimation, Springer Verlag, 1992, pp. 9-27.