A lattice-theoretical morphological view on template extraction in images

Journal of Visual Communication and Image Representation

Volumn 7, Issue 3, 1996, Pages 273-295

  Ronse, Christian ^a  

^a UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; IMAGING TECHNIQUES; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TRANSFORMATIONS; VECTOR QUANTIZATION;

ANTIEXTENSIVITY; IDEMPOTENCE; LATTICE THEORY; OVERCONDENSATION; TEMPLATE EXTRACTION;

FEATURE EXTRACTION;

EID: 0030246032     PISSN: 10473203     EISSN: None     Source Type: Journal    
DOI: 10.1006/jvci.1996.0024     Document Type: Article

References (21)

1. G. J. F. Banon and J. Barrera, Minimal representation for translation-invariant set mappings by mathematical morphology, SIAM J. Appl. Math. 51(6), Dec. 1991, 1782-1798.
2. G. J. F. Banon and J. Barrera, Decomposition of mappings between complete lattices by mathematical morphology, Part I: general lattices, Signal Process. 30, 1993, 299-327.
3. G. J. F. Banon and J. Barrera, Set operator decomposition and conditionally translation-invariant elementary operators, in Mathematical Morphology and its Applications to Image Processing (J. Serra and P. Soille, Eds.), Kluwer Academic, Dordrecht/Norwell, MA, 1994.
4. G. Birkhoff, Lattice Theory (3rd ed.), American Mathematical Society Colloquium Publications, Vol. 25, Amer. Math. Soc., Providence, RI, 1984.
5. C. R. Giardina and E. R. Dougherty, Morphological Methods in Image and Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1988.
6. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Addison-Wesley, Reading, MA, 1992.
7. G. Grätzer, Lattice Theory, Freeman, San Francisco, 1971.
8. R. M. Haralick, S. R. Sternberg, and X. Zhuang, Image analysis using mathematical morphology, IEEE Trans. Pattern Anal. Machine Intell. PAMI-9 (4), 1987, 532-550.
9. H. J. A. M. Heijmans and C. Ronse, The algebraic basis of mathematical morphology. I. Dilations and erosions, Comput. Vision Graphics Image Process. 50, 1990, 245-295.
10. H. J. A. M. Heijmans and J. Serra, Convergence, continuity and iteration in mathematical morphology, J. Visual Commun. Image Represent. 3, 1992, 84-102.
11. G. Matheron, Random Sets and Integral Geometry, Wiley, New York, 1975.
12. J. B. T. M. Roerdink, Mathematical morphology with noncommutative symmetry groups, in Mathematical Morphology in Image Processing, (E. R. Dougherty, Ed.), Series in Optical Engineering, Vol. 34, pp. 205-254, Dekker, New York, 1993.
13. C. Ronse, Why mathematical morphology needs complete lattices, Signal Process. 21(2), 1990, 129-154.
14. C. Ronse, Toggles of openings, and a new family of idempotent operators on partially ordered sets, Appl. Algebra Engineer. Commun. Comput. 3, 1992, 99-128.
15. C. Ronse, Openings: main properties, and how to construct them, in Mathematical Morphology: Theory & Hardware, (R. M. Haralick, Ed.), Oxford Series on Optical and Imaging Sciences, Vol. 10, Oxford Univ. Press, Oxford, to appear.
16. C. Ronse and H. J. A. M. Heijmans, The algebraic basis of mathematical morphology II: Openings and closings, Comput. Vision Graphics Image Process.: Image Understanding, 54(1), 1991, 74-97.
17. C. Ronse and B. Macq, Morphological shape and region description, Signal Process., 25, 1991, 91-105.
18. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982.
19. J. Serra (Ed.), Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances, Academic Press, London, 1988.
20. J. Serra, The links: definitions and properties, SPIE Visual Commun. Image Process. Conference, 1990.
21. S. R. Sternberg, Grayscale morphology, Comput. Vision Graphics Image Process. 35(3), 1986, 333-355.