Differential morphology and image processing

IEEE Transactions on Image Processing

Volumn 5, Issue 6, 1996, Pages 922-937

  Maragos, Petros ^a,b  

^a IEEE

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BANDPASS FILTERS; COMPUTER VISION; DIFFERENCE EQUATIONS; DIFFERENTIATION (CALCULUS); FOURIER TRANSFORMS; IMAGE ANALYSIS; MATHEMATICAL MODELS; MATHEMATICAL MORPHOLOGY; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

BEUCHER MORPHOLOGICAL DERIVATIVE; DIFFERENTIAL MORPHOLOGY; DYNAMICAL SYSTEMS; MORPHOLOGICAL DILATION; MORPHOLOGICAL EROSION;

IMAGE PROCESSING;

EID: 0030169399     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.503909     Document Type: Article

References (50)

1. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel, "Axiomatization et nouveaux operateurs de la morphologie mathematique,"C. R. Acad. Sci. Paris, t.315, serie I. pp. 265-268, 1992.
2. L. Alvarez and J. M. Morel, "Formalization and computational aspects of image analysis,"Acta Numer., pp. 1-59, 1994.
3. R. Bellman and W. Karush, "On the maximum transform," J. Math. Anal. Appl., vol. 6, pp. 67-74, 1963.
4. S. Beucher and C. Lantuejoul, "Use of watersheds in contour detection," in Proc. Int. Workshop Image Processing: Real-time Edge & Motion Detect./Estimat., Rennes, France, 1979.
5. H. Blum, "Biological shape and visual science (part I)," J. Theoret. Biol., vol. 38, pp. 205-287, 1973.
6. G. Borgefors, "Distance transformations in digital images,"Comput. Vision, Graphics, Image Processing, vol. 34, pp. 344-371, 1986.
7. M. Born and E. Wolf, Principles of Optics, 1987 ed. Oxford, UK: Pergamon, 1959.
8. R. W. Brockett and P. Maragos, "Evolution equations for continuous-scale morphology," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, San Francisco, CA, Mar. 1992.
9. _, "Evolution equations for continuous-scale morphological filtering,"IEEE Trans. Signal Processing, vol. 42, pp. 3377-3386, Dec. 1994.
10. M. A. Butt and P. Maragos, "Comparison of multiscale morphology approaches: PDEs implemented via curve evolution versus Chamfer distance transforms," in Proc. Int. Symp. on Mathematical Morphology and Its Application to Image and Signal Processing, Atlanta, GA, May 1996.
11. R. Courant and D. Hubert, Methods of Mathematical Physics. New York: Wiley, 1992.
12. L. Dorst and R. van den Boomgaard, "Morphological signal processing and the slope transform,"Signal Processing, vol. 38, pp. 79-98, July 1994.
13. D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
14. P. K. Ghosh, "An algebra of polygons through the notion of negative shapes,"CVGIP: Image Understanding, vol. 54, no. 1, pp. 119-144, 1991.
15. H. J. A. M. Heijmans, Morphological Image Operators. Boston, MA: Academic, 1994.
16. H. J. A. M. Heijmans and P. Maragos, Lattice Calculus of the Morphological Slope Tramform, CWI Rep. BS-R9531, Dec. 1995.
17. B. K. P. Horn, Robot Vision. Cambridge, MA: MIT Press, 1986.
18. Special session on "Nonlinear dynamics for image processing," in Proc. Int. Conf. Image Processing, Austin, TX, Nov. 1994.
19. R. Kimmel, N. Kiryati, and A. Bruckstein, "Sub-pixel distance maps and weighted distance transforms,"J. Math. Imag. Vision, to be published.
20. J. J. Koenderink, "The structure of images,"Biol. Cybern., vol. 50, pp. 363-370, 1984.
21. B. Lay, "Recursive algorithms in mathematical morphology,"Acta Stereol., vol. 6, no. III, pp. 691-696, 1987.
22. G. Levi and U. Montanari, "A grey-weighted skeleton,"Inform. Contr., vol. 17, pp. 62-91, 1970.
23. P. Maragos, "Morphological systems: slope transforms and max-min difference and differential equations,"Signal Processing, vol. 38, pp. 57-77, July 1994.
24. _, "Slope transforms: Theory and application to nonlinear signal processing,"IEEE Trans. Signal Processing, vol. 43. pp. 864-877, Apr. 1995.
25. P. Maragos and R. W. Schafer, "Morphological systems for multidimensional signal processing,"Proc. IEEE, vol. 78, pp. 690-710, Apr. 1990.
26. J. Mattioli, "Differential relations of morphological operators," in Proc. 1st Int. Workshop Math. Morph. Applic. Signal Processing, Barcelona, Spain, May 1993.
27. F. Meyer, "Integrals and gradients of images,"Proc. SPIE vol. 1769: Image Algebra Morph. Image Processing III, pp. 200-211, 1992.
28. _, "Topographic distance and watershed lines."Signal Processing, vol. 38, pp. 113-125, July 1994.
29. L. Najman and M. Schmitt, "Watershed of a continuous function,"Signal Processing, vol. 38, pp. 99-112, July 1994.
30. S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys., vol. 79, pp. 12-49, 1988.
31. Y. Pnueli and A. M. Bruckstcin, "Gridless halftoning: A reincarnation of the old method," Technion, Israel, CIS Rep. #9323, Oct. 1993.
32. _, "Digitaler - a digital engraving system,"Visual Comput., vol. 10, pp. 277-292, 1994.
33. F. Preteux, "On a distance function approach for gray-level mathematical morphology," in Mathematical Morphology in Image Processing, E. R. Dougherty, Ed. New York: Marcel Dekker, 1993.
34. R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1972.
35. A. Rosenfeld and J. L. Pfaltz, "Sequential operations in digital picture processing," J. Assoc. Comput. Mach vol. 13, pp. 471-494, Oct. 1966.
36. _, "Distance functions on digital pictures,"Pattern Recog., vol. 1, pp. 33-61, 1968.
37. E. Rouy and A. Tourin. "A viscocity solutions approach to shape from shading,"SIAM J. Numer. Anal., vol. 29, no. 3, pp. 867-884, June 1992.
38. D. Rutovitz, "Data structures for operations on digital images," in Pictorial Pattern Recog., G. C. Cheng et al., Eds. Washington, DC: Thompson, 1968, pp. 105-133.
39. B. E. A. Salch and M. C. Teich, Fundamentals of Photonics. New York: Wiley, 1991.
40. P. Salembier and J. Serra, "Morphological multiscale image segmentation," in Proc. SPIE vol. 1818: Visual Commun. Image Proc. '92, 1992, pp. 620-631.
41. G. Sapiro, R. Kimmel, D. Shaked, B. Kimia, and A. Bruckstein, "Implementing continuous-scale morphology via curve evolution,"Pattern Recogn., vol. 26, no. 9, pp. 1363-1372, 1993.
42. M. Schröder, "The eikonal equation,"Math. Intelligencer, vol. 1, pp. 36-37, 1983.
43. J. Serra, Image Analysis and Mathematical Morphology. New York: Academic, 1982.
44. J. Serra, Ed., Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances. New York: Academic, 1988.
45. F. Y.-C. Shih and O. R. Mitchell, "Decomposition of gray-scale morphological structuring elements,"Pattern Recog., vol. 24, pp. 195-203, 1991.
46. R. van der Boomgaard, "Mathematical morphology: Extensions toward computer vision," Ph.D. dissertation, Univ. of Amsterdam, 1992.
47. R. van der Boomgaard and A. Smeulders, "The morphological structure of images: The differential equations of morphological scale-space," IEEE Trans. Pattern Anal Machine Intell., vol. 16, pp. 1101-1113, Nov. 1994.
48. P. W. Verbeek and B. J. H. Verwer, "Shading from shape, the eikonal equation solved by grey-weighted distance transform,"Pattern Recogn. Lett., vol. 11, pp. 618-690, 1990.
49. B. J. H. Verwer, "Distance transforms: metrics, algorithms, and applications," Ph.D. dissertation, Tech. Univ. of Delft, The Netherlands, 1991.
50. L. Vincent, "Morphological algorithms," in Mathematical Morphology in Image Processing, E. R. Dougherty, Ed. New York: Marcel Dekker, 1993.