Shape-tree semilattice

Journal of Mathematical Imaging and Vision

Volumn 22, Issue 2, 2005, Pages 309-331

  Keshet, Renato ^a  

^a HEWLETT PACKARD LABORATORIES   (United States)

Author keywords

Complete inf semilattices; Disconnected sets; Mathematical morphology; Self dual; Separated sets; Tree of shapes

Indexed keywords

IMAGE ANALYSIS; IMAGE PROCESSING; MATHEMATICAL OPERATORS; SET THEORY; TOPOLOGY; TREES (MATHEMATICS); IMAGE QUALITY; IMAGE RECONSTRUCTION; IMAGE SEGMENTATION; IMAGE UNDERSTANDING; MATHEMATICAL MORPHOLOGY; THEOREM PROVING;

COMPLETE INF-SEMILATTICES; DISCONNECTED SETS; SELF-DUAL; SEPARATED SETS; TREE OF SHAPES;

MATHEMATICAL MORPHOLOGY; IMAGE ANALYSIS;

GRAYSCALE FUNCTIONS; SEPARATED SETS; SHAPE TREE SEMILATTICES; TREE OF SHAPES;

EID: 17444377561     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-4896-0     Document Type: Article

References (24)

1. C. Ballester, V. Caselles, and P. Monasse, "The tree of shapes of an image," ESAIM: Control, Optimisation and Calculus of Variations, Vol. 9, pp. 1-18, 2003.
2. V. Caselles and P. Monasse, "Grain filters," Journal of Mathematical Imaging and Vision, Vol. 17, No. 3, pp. 249-270, 2002.
3. J. Crespo, J. Serra, and R.W. Schafer, "Image segmentation using connected filters," in Mathematical Morphology and its Applications to Signal Processing, J. Serra and Ph. Salembier (Eds.), Universitat Politécnica de Catalunya, 1993, pp. 52-57.
4. S.A. Gaal, Point Set Topology, Academic Press: NY, 1964.
5. H.J.A.M. Heijmans, "Theoretical aspects of gray-level morphology," IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, pp. 568-582, 1991.
6. H.J.A.M. Heijmans, "Self-dual morphological operators and filters," Journal of Mathematical Imaging and Vision, Vol. 6, No. 1, pp. 15-36, 1996.
7. H.J.A.M. Heijmans, "Connected morphological operators for binary images," Computer Vision and Image Understanding, Vol. 73, No. 1, pp. 99-120, 1999.
8. H.J.A.M. Heijmans and R. Keshet, "Inf-semilattice approach to self-dual morphology," Journal of Mathematical Imaging Vision, Vol. 17, No. 1, pp. 55-80, 2002.
9. J.G. Hocking and G.S. Young, Topology, Addison-Wesley: Reading, MA, 1961.
10. R. Keshet (Kresch), "Mathematical morphology on complete semilattices and its applications to image processing," Fundamenta Informatic, Vol. 41, Nos. 1/2, pp. 33-56, 2000.
11. R. Kresch and D. Malah, "Two-sided skeletons," in Mathematical Morphology and its Applications to Signal Processing, J. Serra and Ph. Salembier, (Eds.), Universitat Politécnica de Catalunya, 1993, pp. 133-138.
12. A.J.H. Mehnert and P.T. Jackway, "Folding induced self-dual filters," Mathematical Morphology and its Applications to Image and Signal Processing, J. Goutsias, L. Vincent and D.S. Bloomberg, (Eds.), Kluwer Academic Publishers: Boston, 2000, pp. 99-108.
13. F. Meyer, "From connected operators to levelings," in Mathematical Morphology and its Applications to Signal Processing, H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.), Kluwer: Dordrecht, 1998, pp. 191-198.
14. F. Meyer, "Levelings," in Mathematical Morphology and its Applications to Signal Processing, H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.), Kluwer: Dordrecht, 1998, pp. 199-206.
15. P. Monasse and F. Guichard, "Fast computation of a contrast-invariant image representation," IEEE Trans. on Image Processing, Vol. 5, No. 9, pp. 860-872, 2000.
16. P. Monasse and F. Guichard, "Scale-space from a level lines tree," Journal of Visual Communication and Image Representation, Vol. 11, pp. 224-236, 2000.
17. C. Ronse, "Set-theoretical algebraic approaches to connectivity in continuous or digital spaces," Journal of Mathematical Imaging and Vision, Vol. 8, No. 1, pp. 41-58, 1998.
18. P. Salembier and L. Garrido, "Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval," IEEE Transactions on Image Processing, Vol. 9, No. 4, pp. 561-576, 2000.
19. P. Salembier, J. Llach, and L. Garrido, "Visual segment tree creation for MPEG-7 description schemes," Pattern Recognition, Vol. 35, No. 3, pp. 563-579, 2002.
20. Ph. Salembier and J. Serra, "Flat zones filtering, connected operators, and filters by reconstruction," IEEE Trans. on Image Processing, Vol. 8, No. 4, pp. 1153-1160, 1995.
21. J. Serra, Image Analysis and Mathematical Morphology, Vol. 1, Academic Press: London, 1982.
22. J. Serra, "Connections for sets and functions," Fundamenta Informatic, Vol. 41, Nos. 1/2, pp. 147-186, 2000.
23. P. Soille, Morphological Image Analysis: Principles and Applications, 2nd edn. Springer: NY, 2003.
24. P. Soille and M. Pesaresi, "Advances in mathematical morphology applied to geoscience and remote sensing," IEEE Trans. on Geoscience and Remote Sensing, Vol. 40, No. 9, pp. 2042-2055, 2002.