Affine-permutation invariance of 2-D shapes

IEEE Transactions on Image Processing

Volumn 14, Issue 11, 2005, Pages 1687-1700

  Ha, Victor H S ^a   Moura, José M F ^b  

^a SAMSUNG INFORMATION SYSTEMS AMERICA   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Affine permutation invariance; Blind algorithm for intrinsic shape recovery; Fold number; Intrinsic shape; Orbits; Orientation indicator index (OII); Point based reorientation algorithm (PRA); Shape invariance; Shape space

Indexed keywords

ALGORITHMS; EDGE DETECTION; EQUIVALENCE CLASSES; FEATURE EXTRACTION; INVARIANCE; MATHEMATICAL TRANSFORMATIONS;

AFFINE-PERMUTATION INVARIANCE; FOLD NUMBER; INTRINSIC SHAPE; ORIENTATION INDICATOR INDEX; POINT-BASED REORIENTATION ALGORITHM; SHAPE INVARIANCE; SHAPE SPACE;

OBJECT RECOGNITION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER PROGRAM; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; PATTERN RECOGNITION, AUTOMATED; SOFTWARE;

EID: 27844457607     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.857271     Document Type: Article

References (40)

1. D. Casasent and G. Ravichandran, "Advanced distortion-invariant minimum average correlation energy (MACE) filters," Appl. Opt., vol. 31, no. 8, pp. 1109-1116, Mar. 1992.
2. B. V. K. V. Kumar, "Tutorial survey of composite filter designs for optical correlators," Appl. Opt., vol. 31, no. 23, pp. 4773-4801, Aug. 1992.
3. S. A. Benno and J. M. F. Moura, "Scaling functions robust to translations," IEEE Trans. Signal Process., vol. 46, no. 12, pp. 3269-3281, Dec. 1998.
4. C. He and J. M. F. Moura, "Robust detection with the gap metric," IEEE Trans. Signal Process., vol. 45, no. 6, pp. 1591-1604, Jun. 1997.
5. V. H. S. Ha and J. M. F. Moura, "Affine invariant wavelet transform," in Proc. Int. Conf. Acoustics, Speech, and Signal Processing, vol. 3, Salt Lake City, UT, May 2001, pp. 1937-1940.
6. V H. S. Ha, "Blind recovery of intrinsic shape," Ph.D. dissertation, Dept. Elect. Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, Aug. 2002.
7. V. H. S. Ha and J. M. F. Moura, "Intrinsic shape," in Proc. 36th Asilomar Conf. Signals, Systems, and Computers, vol. 1, Monterey, CA, Nov. 2002, pp. 139-143.
8. D. Sepiashvili, J. M. F. Moura, and V. H. S. Ha, "Affine-permutation symmetry: Invariance and shape space," Proc. 12th IEEE Signal Processing Workshop on Statistical Signal Processing, pp. 293-296, 2003.
9. V. H. S. Ha and J. M. F. Moura, "Efficient 2D shape orientation," in Proc. IEEE Int. Conf. Image Processing, vol. 1, Sep. 2003, pp. 225-228.
10. V. H. S. Ha and J. M. F. Moura, "Three-dimensional intrinsic shapes," presented at the IEEE Int. Conf. Image Processing, Oct. 2004.
11. K. Åström, "Affine and projective normalization of planar curves and regions," in Proc. Eur. Conf. Computer Vision, vol. II, 1994, pp. 439-448.
12. K. Åström, "Affine invariants of planar sets," in Proc. SCIA8, Tromso, Norway, 1993, pp. 769-776.
13. D. G. Kendall, "The diffusion of shape," Adv. Appl. Prob., vol. 9, pp. 428-430, 1977.
14. D. G. Kendall, D. Barden, T. K. Carne, and H. Le, Shape and Shape Theory. New York: Wiley, 1999.
15. I. L. Dryden and K. V. Mardia, Statistical Shape Analysis. New York: Wiley, 1998.
16. U. Grenander, Lectures in Pattern Theory. New York: Springer-Verlag, 1976.
17. U. Grenander, Abstract Inference. New York: Springer-Verlag, 1981.
18. U. Grenander, Tutorial in Pattern Theory. Providence, RI: Brown Univ., 1983.
19. U. Grenander and D. M. Keenan, "On the shape of plane images," SIAM J. Appl. Math., vol. 53, no. 4, pp. 1072-1094, Aug. 1993.
20. U. Grenander and M. Miller, "Representations of knowledge in complex systems," J. Roy. Stat. Soc. B, vol. 56, no. 4, pp. 549-603, 1994.
21. O. Schreier and E. Sperner, Introduction to Modern Algebra and Matrix Theory. New York: Chelsea, 1951.
22. J. R. Magnus and H. Neudecker, Matrix Differential Calculus. New York: Wiley, 1988, ch. 2. Kronecker products, the vec operator and the Moore-Penrose inverse.
23. J. Mundy and A. Zisserman, Geometric Invariance in Computer Vision. Cambridge, MA: MIT Press, 1992.
24. A. Graham, Kronecker Products and Matrix Calculus with Applications. Chichester, U.K.: Ellis Horwood, 1981.
25. S. MacLane and G. Birkoff, Algebra. London, U.K.: MacMillan, 1967.
26. M. A. Armstrong, Groups and Symmetry. New York: Springer-Verlag, 1980.
27. J. G. Leu, "Shape normalization through compacting," Pattern Recognit. Lett., vol. 10, pp. 243-250, Oct. 1989.
28. A. K. Jain, Fundamentals of Digital Image Processing. New York: Prentice-Hall, 1989.
29. A. Taza and C. Y. Suen, "Discrimination of planar shapes using shape matrices," IEEE Trans. Syst., Man, Cybern., vol. 19, no. 5, pp. 1281-1289, Oct. 1989.
30. G. Marola, "On the detection of the axes of symmetry of the symmetric and almost symmetric planar image," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 1, pp. 104-108, Jan. 1989.
31. S. C. Pei and C. N. Lin, "Normalization of rotationally symmetric shapes for pattern recognition," Pattern Recognit., vol. 25, no. 9, pp. 913-920, 1992.
32. S. C. Pei and L. G. Liou, "Automatic symmetry determination and normalization for rotationally symmetric 2D shapes and 3D solid objects," Pattern Recognit., vol. 27, no. 9, pp. 1193-1208, 1994.
33. W. H. Tsai and S. L. Chou, "Detection of generalized principal axes in rotational symmetric shapes," Pattern Recognit., vol. 24, pp. 95-104, 1991.
34. S. L. Chou, J. C. Lin, and W. H. Tsai, "Fold principal axis - A new tool for defining the orientations of rotationally symmetric shapes," Pattern Recognit. Lett., vol. 12, pp. 109-115, 1991.
35. J. C. Lin, S. L. Chou, and W. H. Tsai, "Detection of rotationally symmetric shape orientation by fold-invariant shape-specific points," Pattern Recognit., vol. 25, pp. 473-482, 1992.
36. J. J. Leou and W. H. Tsai, "Automatic rotational symmetric determination for shape analysis," Pattern Recognit., vol. 20, no. 6, pp. 571-582, 1987.
37. J. C. Lin, W. H. Tsai, and J. A. Chen, "Detecting number of folds by a simple mathematical property," Pattern Recognit., vol. 15, pp. 1081-1088, 1994.
38. J. C. Lin, "Universal principal axes: An easy-to-construct tool useful in defining shape orientations for almost every kind of shape," Pattern Recognit., vol. 26, no. 4, pp. 485-493, 1993.
39. D. Shen and H. Ip, "General affine invariant image normalization," IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 5, pp. 431-440, May 1997.
40. D. Shen and H. H. S. Ip, "Symmetry detection by generalized complex (GC) moments: A close-form solution," IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 5, pp. 466-476, May 1999.