Recursive binary dilation and erosion using digital line structuring elements in arbitrary orientations

IEEE Transactions on Image Processing

Volumn 9, Issue 5, 2000, Pages 749-759

  Nadadur, Desikachari ^b   Haralick, Robert M ^a,c  

^a IEEE   (United States)

^b SIEMENS CORPORATE RESEARCH   (United States)

^c University of Washington   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY MORPHOLOGY; DIGITAL LINE STRUCTURING ELEMENTS; IMAGE DILATION; IMAGE EROSION;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TRANSFORMATIONS; SET THEORY;

IMAGE CODING;

EID: 0033740487     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.841511     Document Type: Article

References (49)

1. P. Soille, E. J. Breen, and R. Jones, "Recursive implementation of erosions and dilations along discrete lines at arbitrary angles," IEEE Trans. Pattern Anal. Machine Intell., vol. 18, pp. 562-567, May 1996.
2. J. Serra, Image Analysis and Mathematical Morphology. New York: Academic, 1982.
3. J. Serra, Ed., Image Analysis and Mathematical Morphology, Part II: Theoretical Advances, New York: Academic, 1988.
4. R. M. Haralick, S. R. Sternberg, and X. Zhuang, "Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 532-550, Apr. 1987.
5. P. Maragos, "Pattern spectrum and multiscale shape representation," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 701-716, July 1989.
6. S.R. Sternberg, "Morphology for graytone functions," Comput. Vis., Graph., Image Process., vol. 35, pp. 333-355, 1986.
7. P. Maragos and R. W. Schafer, "Morphological filters I: Their set theoretic analysis and relations to linear shift invariant filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 1153-1169, 1987.
8. _, "Morphological filters II: Their relation to median, order-statistics and stack filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 1170-1184, 1987.
9. T. R. Crimmins and W. M. Brown, "Image algebra and automatic shape recognition," IEEE Trans. Aerosp., Electron. Syst., vol. 21, pp. 60-69.
10. R. C. Vogt, Automatic Generation of Morphological Set Recognition Algorithms. New York: Springer-Verlag, 1989.
11. G. X. Ritter, J. N. Wilson, and J. L. Davidson, Image algebra: An overview, in Computer Vision, Graphics and Image Processing, to appear.
12. M. Van Droogenbroeck, "On the implementation of morphological operations," in Mathematical Morphology and Its Applications to Image Processing, J. Serra and P. Soille, Eds. Dordrecht, The Netherlands: Kluwer, 1994, pp. 241-248.
13. J. Serra and L. Vincent, "An overview of morphological filtering," Circuits, Syst., Signal Process., vol. 11, no. 1, pp. 47-108, 1992.
14. I. Young and R. Pevereni et al., "A new implementation for the binary and Minkowski operators," Comput. Graph. Image Process., vol. 17, pp. 189-210, 1981.
15. R. M. Lougheed, "Architectures and algorithms for digital image processing II," in Proc. Soc. Photo-Optic Instrumentation Engineering, vol. 534, 1985, pp. 22-33.
16. S. R. Sternberg, "Cellular computers and biomedical image processing," in Multicomputers and Image Processing - Algorithms and Programs, L. Uhr, Ed. New York: Academic, 1982, vol. 35, pp. 291-305.
17. J. L. Potter, "Image processing on the massively parallel processor," Comput., vol. 16, pp. 62-67, 1983.
18. J. N. Wilson, G. R. Fischer, and G. X. Ritter, "Implementation and use of an image processing algebra for programming massively parallel machines," Frontiers Mass. Parallel Comput., Oct. 1988.
19. G. X. Ritter and P. D. Gader, "Image algebra techniques for parallel image processing," J. Parallel Distrib. Comput., vol. 4, pp. 7-44, 1987.
20. P. D. Gader, "Image algebra techniques for parallel computation of discrete Fourier transforms and general linear transforms," Ph.D. dissertation, Univ. Florida, Gainesville, FL, 1986.
21. J. L. Davidson, "Lattice structures in the image algebra and applications to image algebra," Ph.D. dissertation, Univ. Florida, Gainesville, FL, 1986.
22. X. Zhuang and R. M. Haralick, "Morphological structuring element decomposition," Comput. Vis., Graph., Image Process., vol. 35, pp. 370-382, 1986.
23. F. Y. Shih and O. R. Mitchell, "Threshold decomposition of grayscale morphology into binary morphology," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 31-42, 1989.
24. _, "Decomposition of grayscale morphological structuring elements," in IEEE Workshop Comput. Vis., Miami Beach, FL, Dec. 1987, pp. 304-306.
25. G. X. Ritter and D. Li, "Template decomposition in image algebra," preprint.
26. P. Soille, E. Breen, and R. Jones, "A fast algorithm for min/max filters along lines arbitrary orientation," in Proc. 1995 IEEE Workshop Non-linear Signal Image Processing, June 1995, pp. 987-990.
27. M. Van Herk, "A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernals," Pattern Recognit. Lett., vol. 13, pp. 517-521, 1992.
28. X. Wang and G. Bertrand, "Some sequential algorithms for a generalized distance transformation based on Minskowski operations," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 1114-1121, Nov. 1992.
29. S. Chen and R. M. Haralick, "Recursive erosion, dilation, opening, and closing transforms," IEEE Trans. Image Processing, vol. 4, pp. 335-345, Mar. 1995.
30. I. Pitas, "Fast algorithms for running ordering and max/min calculations," IEEE Trans. Circuits Syst., vol. 36, pp. 795-804, June 1989.
31. A. Rosenfeld and J. L. Pfaltz, "Distance functions in digital pictures," Pattern Recognit., vol. 1, pp. 33-61, 1968.
32. G. Bertrand and X. Wang, "An algorithm for a generalized distance transformation based on Minskowski operations," in Proc. 9th ICPR, Nov. 1988, pp. 1163-1167.
33. D. Nadadur, A recursive algorithm for binary dilation using line structuring elements, ISL Tech. Rep. ISL-TR-94-08, 1994.
34. D. Nadadur and R. M. Haralick, "Recursive morphology using line structuring elements," in Proc. ISMM'96, Atlanta, GA, May 11-13, 1996.
35. S. Crabtree, L.-P. Yuan, and R. Ehrlich, "A fast and accurate erosion-dilation method suitable for microcomputers," Comput. Vis., Graph., Image Process., vol. 53, pp. 283-290, May 1991.
36. B. Laÿ, "Recursive algorithms in mathematical morphology," ACM Trans. Graph., vol. 6, pp. 691-696, 1987.
37. J. Pecht, "Speeding up successive Minskowski operations," Pattern Recognit. Lett., vol. 3, no. 2, pp. 113-117, 1985.
38. I. Ragnemalm, "Fast erosion and dilation by contour processing and thresholding of distance maps," Pattern Recognit. Lett., vol. 13, pp. 161-166, 1985.
39. R. van den Boomgaard and R. van Balen, "Methods for fast morphological image transforms using bitmapped images," Comput. Vis., Graph., Image Process., vol. 54, pp. 252-258, May 1992.
40. L. Vincent, "Morphological transformations of binary images with arbitrary structuring elements," Signal Process., vol. 22, pp. 3-33, Jan. 1991.
41. W. Wu, "Automated boundary detection for ultrasound images of the left ventricle," M.S. thesis, Univ. Washington, Seattle, WA, 1993.
42. J. Bresenham, "Algorithm for computer control of digital plotter," IBM Syst. J., vol. 4, pp. 25-30, 1965.
43. A. Rosenfeld, "Digital straight line segments," IEEE Trans. Comput., vol. C-23, pp. 1264-1269, 1974.
44. R. M. Haralick and L. G. Shapiro, Comput. Robot Vis.. Reading, MA: Addison-Wesley, 1992.
45. A. Gillies, "Machine learning procedures for generating image domain feature detectors," Ph.D. dissertation, Univ. Michigan, Ann Arbor, MI, 1985.
46. J. S. Wiejak, H. Buxton, and B. F. Buxton, "Convolution with separable masks for early image processing," Comput. Vis., Graph., Image Process., vol. 32, pp. 279-290, 1985.
47. G. Strang, Linear Algebra and Its Applications. New York: Academic, 1976.
48. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Press, 1983.
49. B. Chaudhuri, "An efficient algorithm for running window pel gray level ranking in 2D images," Pattern Recognit. Lett., vol. 11, no. 2, pp. 77-80, 1990.