Morphological sampling of closed sets

Image Analysis and Stereology

Volumn 23, Issue 2, 2004, Pages 89-109

  Ronse, Christian ^a   Tajine, Mohamed ^a  

^a Faculté de Médecine   (France)

Author keywords

Boundedly compact set; Compact set; Dilation; Discretization; Hausdorff metric; Metric space; Proximinal set; Sampling

Indexed keywords

EID: 24344455356     PISSN: 15803139     EISSN: 18545165     Source Type: Journal    
DOI: 10.5566/ias.v23.p89-109     Document Type: Review

References (30)

1. Baddeley AJ (1991). Hausdorff metric for capacities. CWI Report BS-R9127.
2. Barnsley MF (1993). Fractals Everywhere. Academic Press, 2nd edition.
3. Borwein JM, Fitzpatrick S (1989). Existence of nearest points in Banach spaces. Canadian J Math 51(4):702-720.
4. Busemann H (1955). The Geometry of Geodesics. New York: Academic Press.
5. Choquet G (1966). Topology, Academic Press.
6. Cohen-Or D, Kaufman A (1995). Fundamentals of surface voxelization. Graph Model Im Proc 57(6):453-461.
7. Deutsch F, Lambert J (1980). On continuity of metric projections. J Approx Theory 29:116-131.
8. Fell JMG (1962). A Hausdorff topology for the closed sets of a locally compact non-Hausdorff space. Proc Am Math Soc 13:472-176.
9. Hall P, Molchanov IS (1999). Corrections for systematic boundary effects in pixel-based area counts. Patt Recogn 32:1519-1528.
10. Heijmans HJAM (1991). Morphological discretization. In U. Eckhardt et al., editors, Geometrical Problems in Image Processing. Berlin: Akademie Verlag, pp. 99-106.
11. Heijmans HJAM (1992). Discretization of morphological operators. J Vis Commun Image Repr 3(2):182-193.
12. Heijmans HJAM (1994). Morphological Image Operators. Boston: Academic Press.
13. Heijmans HJAM, Toet A (1991). Morphological sampling. CVGIP-Imag Understan 54(3):384-400.
14. Hocking JG, Young GS (1988). Topology. New York: Dover Publications Inc.
15. Latecki LJ, Conrad C, Gross A (1998). Preserving topology by a digitization process. J Math Imaging Vis 8:131-159.
16. Matheron G (1975). Random Sets and Integral Geometry. New York: J. Wiley & Sons.
17. Michael E (1951). Topologies on spaces of subsets. Trans Am Math Soc 71:152-182.
18. Ronse C (1990). Why mathematical morphology needs complete lattices. Signal Process 21(2):129-154.
19. Ronse C, Tajine M (2000). Discretization in Hausdorff space. J Math Imaging Vis 12(3):219-242.
20. Ronse C, Tajine M (2001). Hausdorff discretization for cellular distances, and its relation to cover and supercover discretizations. J Vis Commun Image Repr 12(2):169-200.
21. Ronse C, Tajine M (2002). Hausdorff sampling of closed sets into a boundedly compact space. In Digital and Image Geometry: Advanced Lectures, Proceedings Winterschool Wadern, Germany, Dec. 2000, G. Bertrand, A. Imiya & R. Klette, eds., LNCS 2243, Springer-Verlag, pp. 250-271.
22. Schmitt M (1998). Digitization and connectivity. In International Symposium on Mathematical Morphology 1998. Mathematical morphology and its applications to image and signal processing IV, H. Heijmans & J. Roerdink, eds., Kluwer Academic Publishers, pp. 67-74.
23. Sendov B (1990). Hausdorff Approximations. Kluwer Academic Publishers.
24. Serra J (1982). Image Analysis and Mathematical Morphology. London: Academic Press.
25. Serra J (1988). Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances. London: Academic Press.
26. Sivakumar K, Goutsias J (1996). Binary random fields, random closed sets, and morphological sampling. IEEE Trans Image Proc 5(6):899-912.
27. Sivakumar K, Goutsias J (1997). On the discretization of morphological operators. J Vis Commun Image Repr 8(1):39-19.
28. Tajine M, Ronse C (2002). Topological properties of Hausdorff discretization, and comparison to other discretization schemes. Theor Comput Sci 283(1):243-268.
29. Vervaat W (1988). Narrow and vague convergence of set functions. Stat Probabil Lett 6:295-298.
30. Vietoris L (1922). Bereiche zweiter Ordnung. Monatsh Math Phys 32:258-280.