Shapes, shocks and wiggles

Image and Vision Computing

Volumn 17, Issue 5, 1999, Pages 365-373

  Siddiqi, Kaleem ^a   Kimia, Benjamin B ^b   Tannenbaum, Allen ^c   Zucker, Steven W ^a  

^a YALE UNIVERSITY   (United States)

^b Brown University   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

CURVE EVOLUTION EQUATION; SHAPE DESCRIPTION; SHAPE PERCEPTION;

COMPUTER VISION;

EID: 0033116549     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0262-8856(98)00130-9     Document Type: Article

References (50)

1. Koenderink J.J. The structure of images. Biological Cybernetics. 50:1984;363-370.
2. Koenderink J.J., van Doorn A.J. Dynamic shape. Biological Cybernetics. 53:1986;383-396.
3. A.P. Witkin, Scale-space filtering. In: Proceedings of the 8th International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, August 1983, pp. 1019-1022.
4. L. Alvarez, F. Guichard, P.L. Lions, J.M. Morel, Axioms and fundamental equations of image processing. Archive of Rational Mechanics and Analysis (1993) 123.
5. G. Sapiro, A. Tannenbaum, Affine invariant scale-space. International Journal of Computer Vision, 10 (1993) 25-44.
6. T. Lindeberg, Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, Dordrecht, 1994.
7. B.M.t. Haar Romeny (Ed.), Geometry-driven Diffusion in Computer Vision. Kluwer Academic Publishers, Dordrecht, 1994.
8. Florack L.M.J., Haar Romeny B.M.t., Koenderink J.J., Viergever M.A. Linear scale-space. Journal of Mathematical Imaging and Vision. 4(4):1994;325-351.
9. Florack L.M.J., Salden A.H., Haar Romeny B.M.t., Koenderink J.J., Viergever M.A. Nonlinear scale-space. Image and Vision Computing. 13:1995;279-294.
10. Florack L.M.J., Haar Romeny B.M.t., Koenderink J.J., Viergever M.A. The Gaussian scale-space paradigm and the multiscale local jet. International Journal of Computer Vision. 18:1996;61-75.
11. Burt P.J., Adelson E.H. The Laplacian pyramid as a compact image code. IEEE Transactions on Communications. 31(4):1983;532-540.
12. T.O. Binford, Visual perception by computer. In: IEEE Conference on Systems and Control, Miami, FL, December 1971.
13. Marr D., Nishihara K.H. Representation and recognition of the spatial organization of three dimensional structure. Proceedings of the Royal Society of London, B. 200:1978;269-294.
14. S.W. Zucker, Structural scales in computational vision. In: K. Bowyer, N. Ahuja (Eds.), Advances in Image Understanding, A Festschrift for Azriel Rosenfeld. IEEE Computer Society Press, 1996, pp. 130-141.
15. B.B. Kimia, A. Tannenbaum, S.W. Zucker, The shape triangle: Parts, protrusions, and bends. In: C. Arcelli, L.P. Cordella, G.S. di Baja (Eds.), Proceedings of the Second International Workshop on Visual Form. Aspects of Visual Form Processing, World Scientific, Capri, Italy, 1994, pp. 307-323.
16. Burbeck C.A., Pizer S.M., Morse B.S., Ariely D., Zauberman G.S., Rolland J. Linking object boundaries at scale: A common mechanism for size and shape judgements. Vision Research. 36(3):1996;361-372.
17. B.B. Kimia, A. Tannenbaum, S.W. Zucker, Toward a computational theory of shape: An overview, in: Proceedings of the First European Conference on Computer Vision, Antibes, France. Lecture Notes in Computer Science, Springer-Verlag 427, 1990, pp. 402-407.
18. Kimia B.B., Tannenbaum A., Zucker S.W. Shape, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space. International Journal of Computer Vision. 15:1995;189-224.
19. P.D. Lax, Shock waves and entropy, in: Contributions to Nonlinear Functional Analysis, Academic Press, New York, 1971, pp. 603-634.
20. R. Brockett, P. Maragos, Evolution equations for continuous-scale morphology, in: Proceedings of the IEEE Conference on Acoustics, Speech and Signal Processing, San Francisco, CA, March 1992.
21. Osher S.J., Sethian J.A. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics. 79:1988;12-49.
22. J.A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, 1996.
23. P. Danielsson, Euclidean distance mapping. Computer Graphics and Image Processing, 14 (1980) 227-248.
24. K. Siddiqi, B.B. Kimia, A shock grammar for recognition, in: Conference on Computer Vision and Pattern Recognition, San Francisco, CA, IEEE Computer Society Press, June 1996, pp. 507-513.
25. K. Siddiqi, B.B. Kimia, A shock grammar for recognition. Technical Report LEMS 143, LEMS, Brown University, September 1995.
26. Shu C.-W., Osher S.J. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics. 77:1988;439-471.
27. Osher S.J., Shu C.-W. High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations. SIAM Journal of Numerical Analysis. 28:1991;907-922.
28. Siddiqi K., Kimia B.B., Shu C. Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution. Graphical Models and Image Processing. 59(5):1997;278-301.
29. H. Tek, F. Leymarie, B.B. Kimia, Interpenetrating waves and multiple generation shocks via the CEDT. In: C. Arcelli, L.P. Cordella, G.S. di Baja (Eds.), Proceedings of the Third International Workshop on Visual Form: Advances in Visual Form Analysis, World Scientific, Capri, Italy, 1997, pp. 582-593.
30. Hoffman D.D., Richards W.A. Parts of recognition. Cognition. 18:1985;65-96.
31. Siddiqi K., Tresness K.J., Kimia B.B. Parts of visual form: Psychophysical aspects. Perception. 25:1996;399-424.
32. Blum H. Biological shape and visual science. Journal of Theoretical Biology. 38:1973;205-287.
33. B.S. Morse, S.M. Pizer, C.A. Burbeck, General shape and specific detail: Context-dependent use of scale in determining visual form, in: C. Arcelli, L.P. Cordelia, G.S. di Baja (Eds.), Proceedings of the Second International Workshop on Visual Form: Aspects of Visual Form Processing, World Scientific, 1994, pp. 374-383.
34. Burbeck C.A., Pizer S.M. Object representation by cores: Identifying and representing primitive spatial regions. Vision Research. 35(13):1995;1917-1930.
35. C. Burbeck, S. Hadden, Scaled position integration areas: Accounting for Weber's law for separation. Journal of the Optical Society of America A, 10(1) (1993) 5-15.
36. C. Arcelli, L.P. Cordella, S. Leviadi, From local maxima to connected skeletons. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3(2) (1981) 134-143.
37. Arcelli C., de Baja G.S. Euclidean skeleton via centre-of-maximal-disc extraction. Image and Vision Computing. 11(3):1993;163-173.
38. Brady M., Asada H. Smoothed local symmetries and their implementation. International Journal of Robotics Research. 3(3):1984;36-61.
39. Leyton M. Symmetry-curvature duality. Computer Vision, Graphics, and Image Processing. 38:1987;327-341.
40. S.M. Pizer, W.R. Oliver, S.H. Bloomberg, Hierarchial shape description via the multiresolution symmetric axis transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(4) (1987) 505-511.
41. F. Leymarie, M.D. Levine, Simulating the grassfire transform using an active contour model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (1992) 56-75.
42. R.L. Ogniewicz, Discrete Voronoi Skeletons, Hartung-Gorre, 1993.
43. H. Rom, G. Medioni, Hierarchial decomposition and axial shape description. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(10) (1993) 973-981.
44. Kovacs I., Julesz B. Perceptual sensitivity maps within globally defined visual shapes. Nature. 370:1994;644-646.
45. M. Kelly, M.D. Levine, Annular symmetry operators: A method for locating and describing objects. In: Fifth International Conference on Computer Vision, June 1995, pp. 1016-1021, Boston, MA.
46. Siddiqi K., Lauzière Y.B., Tannenbaum A., Zucker S.W. Area and length-minimizing flows for shape segmentation. IEEE Transactions on Image Processing. 7(3):1998;433-443.
47. K. Siddiqi, A. Shokoufandeh, S.J. Dickinson, S.W. Zucker, Shock graphs and shape matching. In: Proceedings of the International Conference on Computer Vision, Bombay, India, 1998, pp. 222-229.
48. Zhu S., Yuille A.L. Forms: a flexible object recognition and modelling system. International Journal of Computer Vision. 20(3):1996;187-212.
49. A. Francois, G. Medioni, Generic shape learning and recognition, in: J. Pance, A. Zisserman, M. Herbert (Eds.), International Workshop on Object Representation in Computer Vision, Cambridge, England, 1996, Lecture Notes in Computer Science 1144, Springer-Verlag.
50. M. Pelillo, K. Siddiqi, S.W. Zucker, Matching hierarchical structures using association graphs, in: H. Burkhardt, B. Neumann (Eds.), Proceedings of the Fifth European Conference on Computer Vision, June 1998, vol II, pp. 3-16. Lecture Notes in Computer Science 1406, Springer-Verlag, Freiburg, Germany.