On infinitesimal increase of volumes of morphological transforms

Mathematika

Volumn 53, Issue 1, 2006, Pages 103-127

  Kiderlen, Markus ^a   Rataj, Jan ^b  

^a AARHUS UNIVERSITY   (Denmark)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846856176     PISSN: 00255793     EISSN: None     Source Type: Journal    
DOI: 10.1112/s002557930000005x     Document Type: Article

References (25)

1. H. Federer, Curvature measures. Trans. Amer. Math. Soc. 93 (1959), 418-491.
2. H. Federer, Geometric Measure Theory. Springer (Heidelberg, 1969).
3. P. Gutkowski, E. B. V. Jensen and M. Kiderlen, Directional analysis of digitized 3D images by configuration counts. J. Microsc. 216 (2004), 175-185.
4. P. Hall and I. Molchanov, Corrections for systematic boundary effects in pixel-based area counts. Pattern Recog. 32 (1999), 1519-1528.
5. D. Hug, Contact distributions of Boolean models. Suppl. Rend. Circ. Mat. Palermo II 65 (2000), 137-181.
6. D. Hug and G. Last, On support measures in Minkowski spaces and contact distributions in stochastic geometry. Ann. Probab. 28 (2000), 796-850.
7. D. Hug, G. Last and W. Weil, A survey on contact distributions. Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems. Lecture Notes in Physics (K. Mecke and D. Stoyan, eds.), 600 Springer (Berlin, 2002), 317-357.
8. D. Hug, G. Last and W. Weil, Generalized contact distributions of inhomogeneous Boolean models. Adv. Appl. Probab. (SGSA) 34 (2002), 21-47.
9. D. Hug, G. Last and W. Weil, A local Steiner-type formula for general closed sets and applications. Math. Z. 246 (2004), 237-272.
10. M. Kiderlen and E. B. V. Jensen, Estimation of the directional measure of planar random sets by digitization. Adv. in Appl. Probab. 35 (2003), 583-602.
11. G. Matheron, La formule de Steiner pour les érosions. J. Appl. Prob. 15 (1978), 126-135.
12. I. Molchanov, Statistics of the Boolean model for practitioners and mathematicians. Wiley Series in Probab. and Statist., Wiley (New York, 1997).
13. I. Molchanov, Grey-scale images and random sets. In Mathematical Morphology and its Applications to Image and Signal Processing (H. Heijmans and J. Roerdink, eds.), Kluwer Acad. Publ. (Amsterdam, 1998), 247-257.
14. J. Rataj, Determination of spherical area measures by means of dilation volumes. Math. Nachr. 235 (2002), 143-162.
15. J. Rataj, On boundaries of unions of sets with positive reach. Beiträge Alg. Geom. 46 (2005), 397-404.
16. J. Rataj and M. Zähle, Curvatures and currents for unions of sets with positive reach, II. Ann. Global Anal. Geom. 20 (2001), 1-21.
17. R. Schneider, Additive Transformationen konvexer Körper. Geom. Dedicata 3 (1974), 221-228.
18. R. Schneider, Convex Bodies: the Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications 44, Cambridge Univ. Press (Cambridge, 1993).
19. R. Schneider, On the mean normal measures of a particle process. Adv. Appl. Probab. 33 (2001), 25-38.
20. R. Schneider and W. Weil, Stochastische Geometrie. Teubner (Stuttgart, 2000).
21. D. Stoyan, W. S. Kendall and J. Mecke, Stochastic Geometry and its Applications (2nd edition). John Wiley (New York, 1995).
22. J. Serra, Image Analysis and Mathematical Morphology. Academic Press (New York, 1982).
23. C. Schütt and E. Werner, The convex floating body. Math. Scand. 66 (1990), 275-290.
24. M. Zähle, Integral and current representation of Federer's curvature measures. Arch. Math. 46 (1986), 557-567.
25. M. Zähle, Curvatures and currents for unions of sets with positive reach. Geom. Dedicata 23 (1987), 155-171.